---
_id: '15172'
abstract:
- lang: eng
text: 'We propose a novel approach to concentration for non-independent random variables.
The main idea is to “pretend” that the random variables are independent and pay
a multiplicative price measuring how far they are from actually being independent.
This price is encapsulated in the Hellinger integral between the joint and the
product of the marginals, which is then upper bounded leveraging tensorisation
properties. Our bounds represent a natural generalisation of concentration inequalities
in the presence of dependence: we recover exactly the classical bounds (McDiarmid’s
inequality) when the random variables are independent. Furthermore, in a “large
deviations” regime, we obtain the same decay in the probability as for the independent
case, even when the random variables display non-trivial dependencies. To show
this, we consider a number of applications of interest. First, we provide a bound
for Markov chains with finite state space. Then, we consider the Simple Symmetric
Random Walk, which is a non-contracting Markov chain, and a non-Markovian setting
in which the stochastic process depends on its entire past. To conclude, we propose
an application to Markov Chain Monte Carlo methods, where our approach leads to
an improved lower bound on the minimum burn-in period required to reach a certain
accuracy. In all of these settings, we provide a regime of parameters in which
our bound fares better than what the state of the art can provide.'
article_processing_charge: No
article_type: original
author:
- first_name: Amedeo Roberto
full_name: Esposito, Amedeo Roberto
id: 9583e921-e1ad-11ec-9862-cef099626dc9
last_name: Esposito
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: Esposito AR, Mondelli M. Concentration without independence via information
measures. IEEE Transactions on Information Theory. doi:10.1109/TIT.2024.3367767
apa: Esposito, A. R., & Mondelli, M. (n.d.). Concentration without independence
via information measures. IEEE Transactions on Information Theory. IEEE.
https://doi.org/10.1109/TIT.2024.3367767
chicago: Esposito, Amedeo Roberto, and Marco Mondelli. “Concentration without Independence
via Information Measures.” IEEE Transactions on Information Theory. IEEE,
n.d. https://doi.org/10.1109/TIT.2024.3367767.
ieee: A. R. Esposito and M. Mondelli, “Concentration without independence via information
measures,” IEEE Transactions on Information Theory. IEEE.
ista: Esposito AR, Mondelli M. Concentration without independence via information
measures. IEEE Transactions on Information Theory.
mla: Esposito, Amedeo Roberto, and Marco Mondelli. “Concentration without Independence
via Information Measures.” IEEE Transactions on Information Theory, IEEE,
doi:10.1109/TIT.2024.3367767.
short: A.R. Esposito, M. Mondelli, IEEE Transactions on Information Theory (n.d.).
date_created: 2024-03-24T23:01:00Z
date_published: 2024-02-20T00:00:00Z
date_updated: 2024-03-25T07:15:51Z
day: '20'
department:
- _id: MaMo
doi: 10.1109/TIT.2024.3367767
external_id:
arxiv:
- '2303.07245'
language:
- iso: eng
month: '02'
oa_version: None
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: inpress
publisher: IEEE
quality_controlled: '1'
related_material:
record:
- id: '14922'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Concentration without independence via information measures
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '14083'
abstract:
- lang: eng
text: "In this work we consider the list-decodability and list-recoverability of
arbitrary q-ary codes, for all integer values of q ≥ 2. A code is called (p,L)_q-list-decodable
if every radius pn Hamming ball contains less than L codewords; (p,\U0001D4C1,L)_q-list-recoverability
is a generalization where we place radius pn Hamming balls on every point of a
combinatorial rectangle with side length \U0001D4C1 and again stipulate that there
be less than L codewords.\r\nOur main contribution is to precisely calculate the
maximum value of p for which there exist infinite families of positive rate (p,\U0001D4C1,L)_q-list-recoverable
codes, the quantity we call the zero-rate threshold. Denoting this value by p_*,
we in fact show that codes correcting a p_*+ε fraction of errors must have size
O_ε(1), i.e., independent of n. Such a result is typically referred to as a \"Plotkin
bound.\" To complement this, a standard random code with expurgation construction
shows that there exist positive rate codes correcting a p_*-ε fraction of errors.
We also follow a classical proof template (typically attributed to Elias and Bassalygo)
to derive from the zero-rate threshold other tradeoffs between rate and decoding
radius for list-decoding and list-recovery.\r\nTechnically, proving the Plotkin
bound boils down to demonstrating the Schur convexity of a certain function defined
on the q-simplex as well as the convexity of a univariate function derived from
it. We remark that an earlier argument claimed similar results for q-ary list-decoding;
however, we point out that this earlier proof is flawed."
acknowledgement: "Nicolas Resch: Research supported in part by ERC H2020 grant No.74079
(ALGSTRONGCRYPTO). Chen Yuan: Research supported in part by the National Key Research
and Development Projects under Grant 2022YFA1004900 and Grant 2021YFE0109900, the
National Natural Science Foundation of China under Grant 12101403 and Grant 12031011.\r\nAcknowledgements
YZ is grateful to Shashank Vatedka, Diyuan Wu and Fengxing Zhu for inspiring discussions."
alternative_title:
- LIPIcs
article_number: '99'
article_processing_charge: Yes
author:
- first_name: Nicolas
full_name: Resch, Nicolas
last_name: Resch
- first_name: Chen
full_name: Yuan, Chen
last_name: Yuan
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
citation:
ama: 'Resch N, Yuan C, Zhang Y. Zero-rate thresholds and new capacity bounds for
list-decoding and list-recovery. In: 50th International Colloquium on Automata,
Languages, and Programming. Vol 261. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik; 2023. doi:10.4230/LIPIcs.ICALP.2023.99'
apa: 'Resch, N., Yuan, C., & Zhang, Y. (2023). Zero-rate thresholds and new
capacity bounds for list-decoding and list-recovery. In 50th International
Colloquium on Automata, Languages, and Programming (Vol. 261). Paderborn,
Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2023.99'
chicago: Resch, Nicolas, Chen Yuan, and Yihan Zhang. “Zero-Rate Thresholds and New
Capacity Bounds for List-Decoding and List-Recovery.” In 50th International
Colloquium on Automata, Languages, and Programming, Vol. 261. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2023. https://doi.org/10.4230/LIPIcs.ICALP.2023.99.
ieee: N. Resch, C. Yuan, and Y. Zhang, “Zero-rate thresholds and new capacity bounds
for list-decoding and list-recovery,” in 50th International Colloquium on Automata,
Languages, and Programming, Paderborn, Germany, 2023, vol. 261.
ista: 'Resch N, Yuan C, Zhang Y. 2023. Zero-rate thresholds and new capacity bounds
for list-decoding and list-recovery. 50th International Colloquium on Automata,
Languages, and Programming. ICALP: International Colloquium on Automata, Languages,
and Programming, LIPIcs, vol. 261, 99.'
mla: Resch, Nicolas, et al. “Zero-Rate Thresholds and New Capacity Bounds for List-Decoding
and List-Recovery.” 50th International Colloquium on Automata, Languages, and
Programming, vol. 261, 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023, doi:10.4230/LIPIcs.ICALP.2023.99.
short: N. Resch, C. Yuan, Y. Zhang, in:, 50th International Colloquium on Automata,
Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023.
conference:
end_date: 2023-07-14
location: Paderborn, Germany
name: 'ICALP: International Colloquium on Automata, Languages, and Programming'
start_date: 2023-07-10
date_created: 2023-08-20T22:01:13Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-08-21T07:26:01Z
day: '01'
ddc:
- '000'
department:
- _id: MaMo
doi: 10.4230/LIPIcs.ICALP.2023.99
external_id:
arxiv:
- '2210.07754'
file:
- access_level: open_access
checksum: a449143fec3fbebb092cb8ef3b53c226
content_type: application/pdf
creator: dernst
date_created: 2023-08-21T07:23:18Z
date_updated: 2023-08-21T07:23:18Z
file_id: '14091'
file_name: 2023_LIPIcsICALP_Resch.pdf
file_size: 1141497
relation: main_file
success: 1
file_date_updated: 2023-08-21T07:23:18Z
has_accepted_license: '1'
intvolume: ' 261'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: 50th International Colloquium on Automata, Languages, and Programming
publication_identifier:
isbn:
- '9783959772785'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Zero-rate thresholds and new capacity bounds for list-decoding and list-recovery
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 261
year: '2023'
...
---
_id: '13315'
abstract:
- lang: eng
text: How do statistical dependencies in measurement noise influence high-dimensional
inference? To answer this, we study the paradigmatic spiked matrix model of principal
components analysis (PCA), where a rank-one matrix is corrupted by additive noise.
We go beyond the usual independence assumption on the noise entries, by drawing
the noise from a low-order polynomial orthogonal matrix ensemble. The resulting
noise correlations make the setting relevant for applications but analytically
challenging. We provide characterization of the Bayes optimal limits of inference
in this model. If the spike is rotation invariant, we show that standard spectral
PCA is optimal. However, for more general priors, both PCA and the existing approximate
message-passing algorithm (AMP) fall short of achieving the information-theoretic
limits, which we compute using the replica method from statistical physics. We
thus propose an AMP, inspired by the theory of adaptive Thouless–Anderson–Palmer
equations, which is empirically observed to saturate the conjectured theoretical
limit. This AMP comes with a rigorous state evolution analysis tracking its performance.
Although we focus on specific noise distributions, our methodology can be generalized
to a wide class of trace matrix ensembles at the cost of more involved expressions.
Finally, despite the seemingly strong assumption of rotation-invariant noise,
our theory empirically predicts algorithmic performance on real data, pointing
at strong universality properties.
acknowledgement: J.B. was funded by the European Union (ERC, CHORAL, project number
101039794). Views and opinions expressed are however those of the author(s) only
and do not necessarily reflect those of the European Union or the European Research
Council. Neither the European Union nor the granting authority can be held responsible
for them. M.M. was supported by the 2019 Lopez-Loreta Prize. We would like to thank
the reviewers for the insightful comments and, in particular, for suggesting the
BAMP-inspired denoisers leading to AMP-AP.
article_number: e2302028120
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Jean
full_name: Barbier, Jean
last_name: Barbier
- first_name: Francesco
full_name: Camilli, Francesco
last_name: Camilli
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Manuel
full_name: Sáenz, Manuel
last_name: Sáenz
citation:
ama: Barbier J, Camilli F, Mondelli M, Sáenz M. Fundamental limits in structured
principal component analysis and how to reach them. Proceedings of the National
Academy of Sciences of the United States of America. 2023;120(30). doi:10.1073/pnas.2302028120
apa: Barbier, J., Camilli, F., Mondelli, M., & Sáenz, M. (2023). Fundamental
limits in structured principal component analysis and how to reach them. Proceedings
of the National Academy of Sciences of the United States of America. National
Academy of Sciences. https://doi.org/10.1073/pnas.2302028120
chicago: Barbier, Jean, Francesco Camilli, Marco Mondelli, and Manuel Sáenz. “Fundamental
Limits in Structured Principal Component Analysis and How to Reach Them.” Proceedings
of the National Academy of Sciences of the United States of America. National
Academy of Sciences, 2023. https://doi.org/10.1073/pnas.2302028120.
ieee: J. Barbier, F. Camilli, M. Mondelli, and M. Sáenz, “Fundamental limits in
structured principal component analysis and how to reach them,” Proceedings
of the National Academy of Sciences of the United States of America, vol.
120, no. 30. National Academy of Sciences, 2023.
ista: Barbier J, Camilli F, Mondelli M, Sáenz M. 2023. Fundamental limits in structured
principal component analysis and how to reach them. Proceedings of the National
Academy of Sciences of the United States of America. 120(30), e2302028120.
mla: Barbier, Jean, et al. “Fundamental Limits in Structured Principal Component
Analysis and How to Reach Them.” Proceedings of the National Academy of Sciences
of the United States of America, vol. 120, no. 30, e2302028120, National Academy
of Sciences, 2023, doi:10.1073/pnas.2302028120.
short: J. Barbier, F. Camilli, M. Mondelli, M. Sáenz, Proceedings of the National
Academy of Sciences of the United States of America 120 (2023).
date_created: 2023-07-30T22:01:02Z
date_published: 2023-07-25T00:00:00Z
date_updated: 2023-10-17T11:44:55Z
day: '25'
ddc:
- '000'
department:
- _id: MaMo
doi: 10.1073/pnas.2302028120
external_id:
pmid:
- '37463204'
file:
- access_level: open_access
checksum: 1fc06228afdb3aa80cf8e7766bcf9dc5
content_type: application/pdf
creator: dernst
date_created: 2023-07-31T07:30:48Z
date_updated: 2023-07-31T07:30:48Z
file_id: '13323'
file_name: 2023_PNAS_Barbier.pdf
file_size: 995933
relation: main_file
success: 1
file_date_updated: 2023-07-31T07:30:48Z
has_accepted_license: '1'
intvolume: ' 120'
issue: '30'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the National Academy of Sciences of the United States
of America
publication_identifier:
eissn:
- 1091-6490
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/fcamilli95/Structured-PCA-
scopus_import: '1'
status: public
title: Fundamental limits in structured principal component analysis and how to reach
them
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 120
year: '2023'
...
---
_id: '14459'
abstract:
- lang: eng
text: Autoencoders are a popular model in many branches of machine learning and
lossy data compression. However, their fundamental limits, the performance of
gradient methods and the features learnt during optimization remain poorly understood,
even in the two-layer setting. In fact, earlier work has considered either linear
autoencoders or specific training regimes (leading to vanishing or diverging compression
rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders
trained in the challenging proportional regime in which the input dimension scales
linearly with the size of the representation. Our results characterize the minimizers
of the population risk, and show that such minimizers are achieved by gradient
methods; their structure is also unveiled, thus leading to a concise description
of the features obtained via training. For the special case of a sign activation
function, our analysis establishes the fundamental limits for the lossy compression
of Gaussian sources via (shallow) autoencoders. Finally, while the results are
proved for Gaussian data, numerical simulations on standard datasets display the
universality of the theoretical predictions.
acknowledgement: Aleksandr Shevchenko, Kevin Kogler and Marco Mondelli are supported
by the 2019 Lopez-Loreta Prize. Hamed Hassani acknowledges the support by the NSF
CIF award (1910056) and the NSF Institute for CORE Emerging Methods in Data Science
(EnCORE).
alternative_title:
- PMLR
article_processing_charge: No
author:
- first_name: Aleksandr
full_name: Shevchenko, Aleksandr
id: F2B06EC2-C99E-11E9-89F0-752EE6697425
last_name: Shevchenko
- first_name: Kevin
full_name: Kögler, Kevin
id: 94ec913c-dc85-11ea-9058-e5051ab2428b
last_name: Kögler
- first_name: Hamed
full_name: Hassani, Hamed
last_name: Hassani
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Shevchenko A, Kögler K, Hassani H, Mondelli M. Fundamental limits of two-layer
autoencoders, and achieving them with gradient methods. In: Proceedings of
the 40th International Conference on Machine Learning. Vol 202. ML Research
Press; 2023:31151-31209.'
apa: 'Shevchenko, A., Kögler, K., Hassani, H., & Mondelli, M. (2023). Fundamental
limits of two-layer autoencoders, and achieving them with gradient methods. In
Proceedings of the 40th International Conference on Machine Learning (Vol.
202, pp. 31151–31209). Honolulu, Hawaii, HI, United States: ML Research Press.'
chicago: Shevchenko, Aleksandr, Kevin Kögler, Hamed Hassani, and Marco Mondelli.
“Fundamental Limits of Two-Layer Autoencoders, and Achieving Them with Gradient
Methods.” In Proceedings of the 40th International Conference on Machine Learning,
202:31151–209. ML Research Press, 2023.
ieee: A. Shevchenko, K. Kögler, H. Hassani, and M. Mondelli, “Fundamental limits
of two-layer autoencoders, and achieving them with gradient methods,” in Proceedings
of the 40th International Conference on Machine Learning, Honolulu, Hawaii,
HI, United States, 2023, vol. 202, pp. 31151–31209.
ista: 'Shevchenko A, Kögler K, Hassani H, Mondelli M. 2023. Fundamental limits of
two-layer autoencoders, and achieving them with gradient methods. Proceedings
of the 40th International Conference on Machine Learning. ICML: International
Conference on Machine Learning, PMLR, vol. 202, 31151–31209.'
mla: Shevchenko, Aleksandr, et al. “Fundamental Limits of Two-Layer Autoencoders,
and Achieving Them with Gradient Methods.” Proceedings of the 40th International
Conference on Machine Learning, vol. 202, ML Research Press, 2023, pp. 31151–209.
short: A. Shevchenko, K. Kögler, H. Hassani, M. Mondelli, in:, Proceedings of the
40th International Conference on Machine Learning, ML Research Press, 2023, pp.
31151–31209.
conference:
end_date: 2023-07-29
location: Honolulu, Hawaii, HI, United States
name: 'ICML: International Conference on Machine Learning'
start_date: 2023-07-23
date_created: 2023-10-29T23:01:17Z
date_published: 2023-07-30T00:00:00Z
date_updated: 2023-10-31T08:52:28Z
day: '30'
department:
- _id: MaMo
- _id: DaAl
external_id:
arxiv:
- '2212.13468'
intvolume: ' 202'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2212.13468
month: '07'
oa: 1
oa_version: Preprint
page: 31151-31209
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 40th International Conference on Machine Learning
publication_identifier:
eissn:
- 2640-3498
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fundamental limits of two-layer autoencoders, and achieving them with gradient
methods
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 202
year: '2023'
...
---
_id: '12838'
abstract:
- lang: eng
text: We study the problem of high-dimensional multiple packing in Euclidean space.
Multiple packing is a natural generalization of sphere packing and is defined
as follows. Let N > 0 and L ∈ Z ≽2 . A multiple packing is a set C of points in
R n such that any point in R n lies in the intersection of at most L – 1 balls
of radius √ nN around points in C . Given a well-known connection with coding
theory, multiple packings can be viewed as the Euclidean analog of list-decodable
codes, which are well-studied for finite fields. In this paper, we derive the
best known lower bounds on the optimal density of list-decodable infinite constellations
for constant L under a stronger notion called average-radius multiple packing.
To this end, we apply tools from high-dimensional geometry and large deviation
theory.
acknowledgement: "YZ thanks Jiajin Li for making the observation given by Equation
(23). He also would like to thank Nir Ailon and Ely Porat for several helpful conversations
throughout this project, and Alexander Barg for insightful comments on the manuscript.\r\nYZ
has received funding from the European Union’s Horizon 2020 research and innovation
programme under grant agreement No 682203-ERC-[Inf-Speed-Tradeoff]. The work of
SV was supported by a seed grant from IIT Hyderabad and the start-up research grant
from the Science and Engineering Research Board, India (SRG/2020/000910)."
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. Multiple packing: Lower bounds via infinite constellations.
IEEE Transactions on Information Theory. 2023;69(7):4513-4527. doi:10.1109/TIT.2023.3260950'
apa: 'Zhang, Y., & Vatedka, S. (2023). Multiple packing: Lower bounds via infinite
constellations. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/TIT.2023.3260950'
chicago: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via
Infinite Constellations.” IEEE Transactions on Information Theory. IEEE,
2023. https://doi.org/10.1109/TIT.2023.3260950.'
ieee: 'Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via infinite constellations,”
IEEE Transactions on Information Theory, vol. 69, no. 7. IEEE, pp. 4513–4527,
2023.'
ista: 'Zhang Y, Vatedka S. 2023. Multiple packing: Lower bounds via infinite constellations.
IEEE Transactions on Information Theory. 69(7), 4513–4527.'
mla: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Infinite
Constellations.” IEEE Transactions on Information Theory, vol. 69, no.
7, IEEE, 2023, pp. 4513–27, doi:10.1109/TIT.2023.3260950.'
short: Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory 69 (2023) 4513–4527.
date_created: 2023-04-16T22:01:09Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-12-13T11:16:46Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TIT.2023.3260950
external_id:
arxiv:
- '2211.04407'
isi:
- '001017307000023'
intvolume: ' 69'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2211.04407
month: '07'
oa: 1
oa_version: Preprint
page: 4513-4527
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multiple packing: Lower bounds via infinite constellations'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 69
year: '2023'
...
---
_id: '13321'
abstract:
- lang: eng
text: We consider the problem of reconstructing the signal and the hidden variables
from observations coming from a multi-layer network with rotationally invariant
weight matrices. The multi-layer structure models inference from deep generative
priors, and the rotational invariance imposed on the weights generalizes the i.i.d.
Gaussian assumption by allowing for a complex correlation structure, which is
typical in applications. In this work, we present a new class of approximate message
passing (AMP) algorithms and give a state evolution recursion which precisely
characterizes their performance in the large system limit. In contrast with the
existing multi-layer VAMP (ML-VAMP) approach, our proposed AMP – dubbed multilayer
rotationally invariant generalized AMP (ML-RI-GAMP) – provides a natural generalization
beyond Gaussian designs, in the sense that it recovers the existing Gaussian AMP
as a special case. Furthermore, ML-RI-GAMP exhibits a significantly lower complexity
than ML-VAMP, as the computationally intensive singular value decomposition is
replaced by an estimation of the moments of the design matrices. Finally, our
numerical results show that this complexity gain comes at little to no cost in
the performance of the algorithm.
acknowledgement: Marco Mondelli was partially supported by the 2019 Lopez-Loreta prize.
article_processing_charge: No
author:
- first_name: Yizhou
full_name: Xu, Yizhou
last_name: Xu
- first_name: Tian Qi
full_name: Hou, Tian Qi
last_name: Hou
- first_name: Shan Suo
full_name: Liang, Shan Suo
last_name: Liang
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Xu Y, Hou TQ, Liang SS, Mondelli M. Approximate message passing for multi-layer
estimation in rotationally invariant models. In: 2023 IEEE Information Theory
Workshop. Institute of Electrical and Electronics Engineers; 2023:294-298.
doi:10.1109/ITW55543.2023.10160238'
apa: 'Xu, Y., Hou, T. Q., Liang, S. S., & Mondelli, M. (2023). Approximate message
passing for multi-layer estimation in rotationally invariant models. In 2023
IEEE Information Theory Workshop (pp. 294–298). Saint-Malo, France: Institute
of Electrical and Electronics Engineers. https://doi.org/10.1109/ITW55543.2023.10160238'
chicago: Xu, Yizhou, Tian Qi Hou, Shan Suo Liang, and Marco Mondelli. “Approximate
Message Passing for Multi-Layer Estimation in Rotationally Invariant Models.”
In 2023 IEEE Information Theory Workshop, 294–98. Institute of Electrical
and Electronics Engineers, 2023. https://doi.org/10.1109/ITW55543.2023.10160238.
ieee: Y. Xu, T. Q. Hou, S. S. Liang, and M. Mondelli, “Approximate message passing
for multi-layer estimation in rotationally invariant models,” in 2023 IEEE
Information Theory Workshop, Saint-Malo, France, 2023, pp. 294–298.
ista: 'Xu Y, Hou TQ, Liang SS, Mondelli M. 2023. Approximate message passing for
multi-layer estimation in rotationally invariant models. 2023 IEEE Information
Theory Workshop. ITW: Information Theory Workshop, 294–298.'
mla: Xu, Yizhou, et al. “Approximate Message Passing for Multi-Layer Estimation
in Rotationally Invariant Models.” 2023 IEEE Information Theory Workshop,
Institute of Electrical and Electronics Engineers, 2023, pp. 294–98, doi:10.1109/ITW55543.2023.10160238.
short: Y. Xu, T.Q. Hou, S.S. Liang, M. Mondelli, in:, 2023 IEEE Information Theory
Workshop, Institute of Electrical and Electronics Engineers, 2023, pp. 294–298.
conference:
end_date: 2023-04-28
location: Saint-Malo, France
name: 'ITW: Information Theory Workshop'
start_date: 2023-04-23
date_created: 2023-07-30T22:01:04Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-12-13T11:35:46Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/ITW55543.2023.10160238
external_id:
arxiv:
- '2212.01572'
isi:
- '001031733100053'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2212.01572
month: '05'
oa: 1
oa_version: Preprint
page: 294-298
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 2023 IEEE Information Theory Workshop
publication_identifier:
eissn:
- 2475-4218
isbn:
- '9798350301496'
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Approximate message passing for multi-layer estimation in rotationally invariant
models
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14665'
abstract:
- lang: eng
text: We derive lower bounds on the maximal rates for multiple packings in high-dimensional
Euclidean spaces. For any N > 0 and L ∈ Z ≥2 , a multiple packing is a set C of
points in R n such that any point in R n lies in the intersection of at most L
- 1 balls of radius √ nN around points in C . This is a natural generalization
of the sphere packing problem. We study the multiple packing problem for both
bounded point sets whose points have norm at most √ nP for some constant P > 0,
and unbounded point sets whose points are allowed to be anywhere in R n . Given
a well-known connection with coding theory, multiple packings can be viewed as
the Euclidean analog of list-decodable codes, which are well-studied over finite
fields. We derive the best known lower bounds on the optimal multiple packing
density. This is accomplished by establishing an inequality which relates the
list-decoding error exponent for additive white Gaussian noise channels, a quantity
of average-case nature, to the list-decoding radius, a quantity of worst-case
nature. We also derive novel bounds on the list-decoding error exponent for infinite
constellations and closed-form expressions for the list-decoding error exponents
for the power-constrained AWGN channel, which may be of independent interest beyond
multiple packing.
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. Multiple packing: Lower bounds via error exponents. IEEE
Transactions on Information Theory. 2023. doi:10.1109/TIT.2023.3334032'
apa: 'Zhang, Y., & Vatedka, S. (2023). Multiple packing: Lower bounds via error
exponents. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/TIT.2023.3334032'
chicago: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via
Error Exponents.” IEEE Transactions on Information Theory. IEEE, 2023.
https://doi.org/10.1109/TIT.2023.3334032.'
ieee: 'Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via error exponents,”
IEEE Transactions on Information Theory. IEEE, 2023.'
ista: 'Zhang Y, Vatedka S. 2023. Multiple packing: Lower bounds via error exponents.
IEEE Transactions on Information Theory.'
mla: 'Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Error
Exponents.” IEEE Transactions on Information Theory, IEEE, 2023, doi:10.1109/TIT.2023.3334032.'
short: Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory (2023).
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-16T00:00:00Z
date_updated: 2023-12-18T07:46:45Z
day: '16'
department:
- _id: MaMo
doi: 10.1109/TIT.2023.3334032
external_id:
arxiv:
- '2211.04408'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2211.04408
month: '11'
oa: 1
oa_version: Preprint
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: epub_ahead
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multiple packing: Lower bounds via error exponents'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14751'
abstract:
- lang: eng
text: 'We consider zero-error communication over a two-transmitter deterministic
adversarial multiple access channel (MAC) governed by an adversary who has access
to the transmissions of both senders (hence called omniscient ) and aims to maliciously
corrupt the communication. None of the encoders, jammer and decoder is allowed
to randomize using private or public randomness. This enforces a combinatorial
nature of the problem. Our model covers a large family of channels studied in
the literature, including all deterministic discrete memoryless noisy or noiseless
MACs. In this work, given an arbitrary two-transmitter deterministic omniscient
adversarial MAC, we characterize when the capacity region: 1) has nonempty interior
(in particular, is two-dimensional); 2) consists of two line segments (in particular,
has empty interior); 3) consists of one line segment (in particular, is one-dimensional);
4) or only contains (0,0) (in particular, is zero-dimensional). This extends a
recent result by Wang et al. (201 9) from the point-to-point setting to the multiple
access setting. Indeed, our converse arguments build upon their generalized Plotkin
bound and involve delicate case analysis. One of the technical challenges is to
take care of both “joint confusability” and “marginal confusability”. In particular,
the treatment of marginal confusability does not follow from the point-to-point
results by Wang et al. Our achievability results follow from random coding with
expurgation.'
acknowledgement: "The author would like to thank Amitalok J. Budkuley and Sidharth
Jaggi for many helpful discussions at the early stage of this work. He would also
like to thank Nir Ailon, Qi Cao, and Chandra Nair for discussions on a related problem
regarding zero-error binary adder MACs.\r\nThe work of Yihan Zhang was supported
by the European Union’s Horizon 2020 Research and Innovation Programme under Grant
682203-ERC-[Inf-Speed-Tradeoff]"
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
citation:
ama: Zhang Y. Zero-error communication over adversarial MACs. IEEE Transactions
on Information Theory. 2023;69(7):4093-4127. doi:10.1109/tit.2023.3257239
apa: Zhang, Y. (2023). Zero-error communication over adversarial MACs. IEEE Transactions
on Information Theory. Institute of Electrical and Electronics Engineers.
https://doi.org/10.1109/tit.2023.3257239
chicago: Zhang, Yihan. “Zero-Error Communication over Adversarial MACs.” IEEE
Transactions on Information Theory. Institute of Electrical and Electronics
Engineers, 2023. https://doi.org/10.1109/tit.2023.3257239.
ieee: Y. Zhang, “Zero-error communication over adversarial MACs,” IEEE Transactions
on Information Theory, vol. 69, no. 7. Institute of Electrical and Electronics
Engineers, pp. 4093–4127, 2023.
ista: Zhang Y. 2023. Zero-error communication over adversarial MACs. IEEE Transactions
on Information Theory. 69(7), 4093–4127.
mla: Zhang, Yihan. “Zero-Error Communication over Adversarial MACs.” IEEE Transactions
on Information Theory, vol. 69, no. 7, Institute of Electrical and Electronics
Engineers, 2023, pp. 4093–127, doi:10.1109/tit.2023.3257239.
short: Y. Zhang, IEEE Transactions on Information Theory 69 (2023) 4093–4127.
date_created: 2024-01-08T13:04:54Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2024-01-09T08:45:24Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/tit.2023.3257239
external_id:
arxiv:
- '2101.12426'
intvolume: ' 69'
issue: '7'
keyword:
- Computer Science Applications
- Information Systems
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2101.12426
month: '07'
oa: 1
oa_version: Preprint
page: 4093-4127
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Zero-error communication over adversarial MACs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 69
year: '2023'
...
---
_id: '13269'
abstract:
- lang: eng
text: This paper is a collection of results on combinatorial properties of codes
for the Z-channel . A Z-channel with error fraction τ takes as input a length-
n binary codeword and injects in an adversarial manner up to n τ asymmetric errors,
i.e., errors that only zero out bits but do not flip 0’s to 1’s. It is known that
the largest ( L - 1)-list-decodable code for the Z-channel with error fraction
τ has exponential size (in n ) if τ is less than a critical value that we call
the ( L - 1)- list-decoding Plotkin point and has constant size if τ is larger
than the threshold. The ( L -1)-list-decoding Plotkin point is known to be L -1/L-1
– L -L/ L-1 , which equals 1/4 for unique-decoding with L -1 = 1. In this paper,
we derive various results for the size of the largest codes above and below the
list-decoding Plotkin point. In particular, we show that the largest ( L -1)-list-decodable
code ε-above the Plotkin point, for any given sufficiently small positive constant
ε > 0, has size Θ L (ε -3/2 ) for any L - 1 ≥ 1. We also devise upper and lower
bounds on the exponential size of codes below the list-decoding Plotkin point.
acknowledgement: "Nikita Polyanskii’s research was conducted in part during October
2020 - December 2021 with the Technical University of Munich and the Skolkovo Institute
of Science and Technology. His work was supported by the German Research Foundation
(Deutsche Forschungsgemeinschaft, DFG) under Grant No. WA3907/1-1 and the Russian
Foundation for Basic Research (RFBR)\r\nunder Grant No. 20-01-00559.\r\nYihan Zhang
is supported by funding from the European Union’s Horizon 2020 research and innovation
programme under grant agreement No 682203-ERC-[Inf-Speed-Tradeoff]."
article_processing_charge: No
article_type: original
author:
- first_name: Nikita
full_name: Polyanskii, Nikita
last_name: Polyanskii
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
orcid: 0000-0002-6465-6258
citation:
ama: Polyanskii N, Zhang Y. Codes for the Z-channel. IEEE Transactions on Information
Theory. 2023;69(10):6340-6357. doi:10.1109/TIT.2023.3292219
apa: Polyanskii, N., & Zhang, Y. (2023). Codes for the Z-channel. IEEE Transactions
on Information Theory. Institute of Electrical and Electronics Engineers.
https://doi.org/10.1109/TIT.2023.3292219
chicago: Polyanskii, Nikita, and Yihan Zhang. “Codes for the Z-Channel.” IEEE
Transactions on Information Theory. Institute of Electrical and Electronics
Engineers, 2023. https://doi.org/10.1109/TIT.2023.3292219.
ieee: N. Polyanskii and Y. Zhang, “Codes for the Z-channel,” IEEE Transactions
on Information Theory, vol. 69, no. 10. Institute of Electrical and Electronics
Engineers, pp. 6340–6357, 2023.
ista: Polyanskii N, Zhang Y. 2023. Codes for the Z-channel. IEEE Transactions on
Information Theory. 69(10), 6340–6357.
mla: Polyanskii, Nikita, and Yihan Zhang. “Codes for the Z-Channel.” IEEE Transactions
on Information Theory, vol. 69, no. 10, Institute of Electrical and Electronics
Engineers, 2023, pp. 6340–57, doi:10.1109/TIT.2023.3292219.
short: N. Polyanskii, Y. Zhang, IEEE Transactions on Information Theory 69 (2023)
6340–6357.
date_created: 2023-07-23T22:01:14Z
date_published: 2023-07-04T00:00:00Z
date_updated: 2024-01-29T11:10:54Z
day: '04'
department:
- _id: MaMo
doi: 10.1109/TIT.2023.3292219
external_id:
arxiv:
- '2105.01427'
isi:
- '001069680100011'
intvolume: ' 69'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.01427
month: '07'
oa: 1
oa_version: Preprint
page: 6340-6357
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Codes for the Z-channel
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 69
year: '2023'
...
---
_id: '12859'
abstract:
- lang: eng
text: 'Machine learning models are vulnerable to adversarial perturbations, and
a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through
the lens of over-parameterization: interpolating smoothly the data requires significantly
more parameters than simply memorizing it. However, this "universal" law provides
only a necessary condition for robustness, and it is unable to discriminate between
models. In this paper, we address these gaps by focusing on empirical risk minimization
in two prototypical settings, namely, random features and the neural tangent kernel
(NTK). We prove that, for random features, the model is not robust for any degree
of over-parameterization, even when the necessary condition coming from the universal
law of robustness is satisfied. In contrast, for even activations, the NTK model
meets the universal lower bound, and it is robust as soon as the necessary condition
on over-parameterization is fulfilled. This also addresses a conjecture in prior
work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel
of the model from an "interaction matrix", which describes the interaction with
the test data and captures the effect of the activation. Our theoretical results
are corroborated by numerical evidence on both synthetic and standard datasets
(MNIST, CIFAR-10).'
acknowledgement: "Simone Bombari and Marco Mondelli were partially supported by the
2019 Lopez-Loreta prize, and\r\nthe authors would like to thank Hamed Hassani for
helpful discussions.\r\n"
alternative_title:
- PMLR
article_processing_charge: No
author:
- first_name: Simone
full_name: Bombari, Simone
id: ca726dda-de17-11ea-bc14-f9da834f63aa
last_name: Bombari
- first_name: Shayan
full_name: Kiyani, Shayan
id: f5a2b424-e339-11ed-8435-ff3b4fe70cf8
last_name: Kiyani
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Bombari S, Kiyani S, Mondelli M. Beyond the universal law of robustness: Sharper
laws for random features and neural tangent kernels. In: Proceedings of the
40th International Conference on Machine Learning. Vol 202. ML Research Press;
2023:2738-2776.'
apa: 'Bombari, S., Kiyani, S., & Mondelli, M. (2023). Beyond the universal law
of robustness: Sharper laws for random features and neural tangent kernels. In
Proceedings of the 40th International Conference on Machine Learning (Vol.
202, pp. 2738–2776). Honolulu, HI, United States: ML Research Press.'
chicago: 'Bombari, Simone, Shayan Kiyani, and Marco Mondelli. “Beyond the Universal
Law of Robustness: Sharper Laws for Random Features and Neural Tangent Kernels.”
In Proceedings of the 40th International Conference on Machine Learning,
202:2738–76. ML Research Press, 2023.'
ieee: 'S. Bombari, S. Kiyani, and M. Mondelli, “Beyond the universal law of robustness:
Sharper laws for random features and neural tangent kernels,” in Proceedings
of the 40th International Conference on Machine Learning, Honolulu, HI, United
States, 2023, vol. 202, pp. 2738–2776.'
ista: 'Bombari S, Kiyani S, Mondelli M. 2023. Beyond the universal law of robustness:
Sharper laws for random features and neural tangent kernels. Proceedings of the
40th International Conference on Machine Learning. ICML: International Conference
on Machine Learning, PMLR, vol. 202, 2738–2776.'
mla: 'Bombari, Simone, et al. “Beyond the Universal Law of Robustness: Sharper Laws
for Random Features and Neural Tangent Kernels.” Proceedings of the 40th International
Conference on Machine Learning, vol. 202, ML Research Press, 2023, pp. 2738–76.'
short: S. Bombari, S. Kiyani, M. Mondelli, in:, Proceedings of the 40th International
Conference on Machine Learning, ML Research Press, 2023, pp. 2738–2776.
conference:
end_date: 2023-07-29
location: Honolulu, HI, United States
name: 'ICML: International Conference on Machine Learning'
start_date: 2023-07-23
date_created: 2023-04-23T16:11:03Z
date_published: 2023-10-27T00:00:00Z
date_updated: 2024-02-06T07:42:00Z
day: '27'
department:
- _id: GradSch
- _id: MaMo
external_id:
arxiv:
- '2302.01629'
intvolume: ' 202'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2302.01629
month: '10'
oa: 1
oa_version: Preprint
page: 2738-2776
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 40th International Conference on Machine Learning
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/simone-bombari/beyond-universal-robustness
status: public
title: 'Beyond the universal law of robustness: Sharper laws for random features and
neural tangent kernels'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 202
year: '2023'
...
---
_id: '14921'
abstract:
- lang: eng
text: Neural collapse (NC) refers to the surprising structure of the last layer
of deep neural networks in the terminal phase of gradient descent training. Recently,
an increasing amount of experimental evidence has pointed to the propagation of
NC to earlier layers of neural networks. However, while the NC in the last layer
is well studied theoretically, much less is known about its multi-layered counterpart
- deep neural collapse (DNC). In particular, existing work focuses either on linear
layers or only on the last two layers at the price of an extra assumption. Our
paper fills this gap by generalizing the established analytical framework for
NC - the unconstrained features model - to multiple non-linear layers. Our key
technical contribution is to show that, in a deep unconstrained features model,
the unique global optimum for binary classification exhibits all the properties
typical of DNC. This explains the existing experimental evidence of DNC. We also
empirically show that (i) by optimizing deep unconstrained features models via
gradient descent, the resulting solution agrees well with our theory, and (ii)
trained networks recover the unconstrained features suitable for the occurrence
of DNC, thus supporting the validity of this modeling principle.
acknowledgement: M. M. is partially supported by the 2019 Lopez-Loreta Prize. The
authors would like to thank Eugenia Iofinova, Bernd Prach and Simone Bombari for
valuable feedback on the manuscript.
alternative_title:
- NeurIPS
article_processing_charge: No
author:
- first_name: Peter
full_name: Súkeník, Peter
id: d64d6a8d-eb8e-11eb-b029-96fd216dec3c
last_name: Súkeník
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: 'Súkeník P, Mondelli M, Lampert C. Deep neural collapse is provably optimal
for the deep unconstrained features model. In: 37th Annual Conference on Neural
Information Processing Systems.'
apa: Súkeník, P., Mondelli, M., & Lampert, C. (n.d.). Deep neural collapse is
provably optimal for the deep unconstrained features model. In 37th Annual
Conference on Neural Information Processing Systems. New Orleans, LA, United
States.
chicago: Súkeník, Peter, Marco Mondelli, and Christoph Lampert. “Deep Neural Collapse
Is Provably Optimal for the Deep Unconstrained Features Model.” In 37th Annual
Conference on Neural Information Processing Systems, n.d.
ieee: P. Súkeník, M. Mondelli, and C. Lampert, “Deep neural collapse is provably
optimal for the deep unconstrained features model,” in 37th Annual Conference
on Neural Information Processing Systems, New Orleans, LA, United States.
ista: 'Súkeník P, Mondelli M, Lampert C. Deep neural collapse is provably optimal
for the deep unconstrained features model. 37th Annual Conference on Neural Information
Processing Systems. NeurIPS: Neural Information Processing Systems, NeurIPS, .'
mla: Súkeník, Peter, et al. “Deep Neural Collapse Is Provably Optimal for the Deep
Unconstrained Features Model.” 37th Annual Conference on Neural Information
Processing Systems.
short: P. Súkeník, M. Mondelli, C. Lampert, in:, 37th Annual Conference on Neural
Information Processing Systems, n.d.
conference:
end_date: 2023-12-16
location: New Orleans, LA, United States
name: 'NeurIPS: Neural Information Processing Systems'
start_date: 2023-12-10
date_created: 2024-02-02T11:17:41Z
date_published: 2023-12-15T00:00:00Z
date_updated: 2024-02-06T07:53:26Z
day: '15'
department:
- _id: MaMo
- _id: ChLa
external_id:
arxiv:
- '2305.13165'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2305.13165'
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 37th Annual Conference on Neural Information Processing Systems
publication_status: inpress
quality_controlled: '1'
status: public
title: Deep neural collapse is provably optimal for the deep unconstrained features
model
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14924'
abstract:
- lang: eng
text: "The stochastic heavy ball method (SHB), also known as stochastic gradient
descent (SGD) with Polyak's momentum, is widely used in training neural networks.
However, despite the remarkable success of such algorithm in practice, its theoretical
characterization remains limited. In this paper, we focus on neural networks with
two and three layers and provide a rigorous understanding of the properties of
the solutions found by SHB: \\emph{(i)} stability after dropping out part of the
neurons, \\emph{(ii)} connectivity along a low-loss path, and \\emph{(iii)} convergence
to the global optimum.\r\nTo achieve this goal, we take a mean-field view and
relate the SHB dynamics to a certain partial differential equation in the limit
of large network widths. This mean-field perspective has inspired a recent line
of work focusing on SGD while, in contrast, our paper considers an algorithm with
momentum. More specifically, after proving existence and uniqueness of the limit
differential equations, we show convergence to the global optimum and give a quantitative
bound between the mean-field limit and the SHB dynamics of a finite-width network.
Armed with this last bound, we are able to establish the dropout-stability and
connectivity of SHB solutions."
acknowledgement: D. Wu and M. Mondelli are partially supported by the 2019 Lopez-Loreta
Prize. V. Kungurtsev was supported by the OP VVV project CZ.02.1.01/0.0/0.0/16_019/0000765
"Research Center for Informatics".
alternative_title:
- TMLR
article_processing_charge: No
author:
- first_name: Diyuan
full_name: Wu, Diyuan
id: 1a5914c2-896a-11ed-bdf8-fb80621a0635
last_name: Wu
- first_name: Vyacheslav
full_name: Kungurtsev, Vyacheslav
last_name: Kungurtsev
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Wu D, Kungurtsev V, Mondelli M. Mean-field analysis for heavy ball methods:
Dropout-stability, connectivity, and global convergence. In: Transactions on
Machine Learning Research. ML Research Press; 2023.'
apa: 'Wu, D., Kungurtsev, V., & Mondelli, M. (2023). Mean-field analysis for
heavy ball methods: Dropout-stability, connectivity, and global convergence. In
Transactions on Machine Learning Research. ML Research Press.'
chicago: 'Wu, Diyuan, Vyacheslav Kungurtsev, and Marco Mondelli. “Mean-Field Analysis
for Heavy Ball Methods: Dropout-Stability, Connectivity, and Global Convergence.”
In Transactions on Machine Learning Research. ML Research Press, 2023.'
ieee: 'D. Wu, V. Kungurtsev, and M. Mondelli, “Mean-field analysis for heavy ball
methods: Dropout-stability, connectivity, and global convergence,” in Transactions
on Machine Learning Research, 2023.'
ista: 'Wu D, Kungurtsev V, Mondelli M. 2023. Mean-field analysis for heavy ball
methods: Dropout-stability, connectivity, and global convergence. Transactions
on Machine Learning Research. , TMLR, .'
mla: 'Wu, Diyuan, et al. “Mean-Field Analysis for Heavy Ball Methods: Dropout-Stability,
Connectivity, and Global Convergence.” Transactions on Machine Learning Research,
ML Research Press, 2023.'
short: D. Wu, V. Kungurtsev, M. Mondelli, in:, Transactions on Machine Learning
Research, ML Research Press, 2023.
date_created: 2024-02-02T11:21:56Z
date_published: 2023-02-28T00:00:00Z
date_updated: 2024-02-06T08:53:15Z
day: '28'
department:
- _id: MaMo
external_id:
arxiv:
- '2210.06819'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2210.06819
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Transactions on Machine Learning Research
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
status: public
title: 'Mean-field analysis for heavy ball methods: Dropout-stability, connectivity,
and global convergence'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14923'
abstract:
- lang: eng
text: We study the performance of a Bayesian statistician who estimates a rank-one
signal corrupted by non-symmetric rotationally invariant noise with a generic
distribution of singular values. As the signal-to-noise ratio and the noise structure
are unknown, a Gaussian setup is incorrectly assumed. We derive the exact analytic
expression for the error of the mismatched Bayes estimator and also provide the
analysis of an approximate message passing (AMP) algorithm. The first result exploits
the asymptotic behavior of spherical integrals for rectangular matrices and of
low-rank matrix perturbations; the second one relies on the design and analysis
of an auxiliary AMP. The numerical experiments show that there is a performance
gap between the AMP and Bayes estimators, which is due to the incorrect estimation
of the signal norm.
article_processing_charge: No
author:
- first_name: Teng
full_name: Fu, Teng
last_name: Fu
- first_name: YuHao
full_name: Liu, YuHao
last_name: Liu
- first_name: Jean
full_name: Barbier, Jean
last_name: Barbier
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: ShanSuo
full_name: Liang, ShanSuo
last_name: Liang
- first_name: TianQi
full_name: Hou, TianQi
last_name: Hou
citation:
ama: 'Fu T, Liu Y, Barbier J, Mondelli M, Liang S, Hou T. Mismatched estimation
of non-symmetric rank-one matrices corrupted by structured noise. In: Proceedings
of 2023 IEEE International Symposium on Information Theory. IEEE. doi:10.1109/isit54713.2023.10206671'
apa: 'Fu, T., Liu, Y., Barbier, J., Mondelli, M., Liang, S., & Hou, T. (n.d.).
Mismatched estimation of non-symmetric rank-one matrices corrupted by structured
noise. In Proceedings of 2023 IEEE International Symposium on Information Theory.
Taipei, Taiwan: IEEE. https://doi.org/10.1109/isit54713.2023.10206671'
chicago: Fu, Teng, YuHao Liu, Jean Barbier, Marco Mondelli, ShanSuo Liang, and TianQi
Hou. “Mismatched Estimation of Non-Symmetric Rank-One Matrices Corrupted by Structured
Noise.” In Proceedings of 2023 IEEE International Symposium on Information
Theory. IEEE, n.d. https://doi.org/10.1109/isit54713.2023.10206671.
ieee: T. Fu, Y. Liu, J. Barbier, M. Mondelli, S. Liang, and T. Hou, “Mismatched
estimation of non-symmetric rank-one matrices corrupted by structured noise,”
in Proceedings of 2023 IEEE International Symposium on Information Theory,
Taipei, Taiwan.
ista: 'Fu T, Liu Y, Barbier J, Mondelli M, Liang S, Hou T. Mismatched estimation
of non-symmetric rank-one matrices corrupted by structured noise. Proceedings
of 2023 IEEE International Symposium on Information Theory. ISIT: IEEE International
Symposium on Information Theory.'
mla: Fu, Teng, et al. “Mismatched Estimation of Non-Symmetric Rank-One Matrices
Corrupted by Structured Noise.” Proceedings of 2023 IEEE International Symposium
on Information Theory, IEEE, doi:10.1109/isit54713.2023.10206671.
short: T. Fu, Y. Liu, J. Barbier, M. Mondelli, S. Liang, T. Hou, in:, Proceedings
of 2023 IEEE International Symposium on Information Theory, IEEE, n.d.
conference:
end_date: 2023-06-30
location: Taipei, Taiwan
name: 'ISIT: IEEE International Symposium on Information Theory'
start_date: 2023-06-25
date_created: 2024-02-02T11:20:39Z
date_published: 2023-06-30T00:00:00Z
date_updated: 2024-02-14T14:34:03Z
day: '30'
department:
- _id: MaMo
doi: 10.1109/isit54713.2023.10206671
external_id:
arxiv:
- '2302.03306'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2302.03306
month: '06'
oa: 1
oa_version: Preprint
publication: Proceedings of 2023 IEEE International Symposium on Information Theory
publication_status: inpress
publisher: IEEE
quality_controlled: '1'
status: public
title: Mismatched estimation of non-symmetric rank-one matrices corrupted by structured
noise
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14922'
abstract:
- lang: eng
text: 'We propose a novel approach to concentration for non-independent random variables.
The main idea is to ``pretend'''' that the random variables are independent and
pay a multiplicative price measuring how far they are from actually being independent.
This price is encapsulated in the Hellinger integral between the joint and the
product of the marginals, which is then upper bounded leveraging tensorisation
properties. Our bounds represent a natural generalisation of concentration inequalities
in the presence of dependence: we recover exactly the classical bounds (McDiarmid''s
inequality) when the random variables are independent. Furthermore, in a ``large
deviations'''' regime, we obtain the same decay in the probability as for the
independent case, even when the random variables display non-trivial dependencies.
To show this, we consider a number of applications of interest. First, we provide
a bound for Markov chains with finite state space. Then, we consider the Simple
Symmetric Random Walk, which is a non-contracting Markov chain, and a non-Markovian
setting in which the stochastic process depends on its entire past. To conclude,
we propose an application to Markov Chain Monte Carlo methods, where our approach
leads to an improved lower bound on the minimum burn-in period required to reach
a certain accuracy. In all of these settings, we provide a regime of parameters
in which our bound fares better than what the state of the art can provide.'
acknowledgement: The authors are partially supported by the 2019 Lopez-Loreta Prize.
They would also like to thank Professor Jan Maas for providing valuable suggestions
and comments on an early version of the work.
article_processing_charge: No
author:
- first_name: Amedeo Roberto
full_name: Esposito, Amedeo Roberto
id: 9583e921-e1ad-11ec-9862-cef099626dc9
last_name: Esposito
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Esposito AR, Mondelli M. Concentration without independence via information
measures. In: Proceedings of 2023 IEEE International Symposium on Information
Theory. IEEE; 2023:400-405. doi:10.1109/isit54713.2023.10206899'
apa: 'Esposito, A. R., & Mondelli, M. (2023). Concentration without independence
via information measures. In Proceedings of 2023 IEEE International Symposium
on Information Theory (pp. 400–405). Taipei, Taiwan: IEEE. https://doi.org/10.1109/isit54713.2023.10206899'
chicago: Esposito, Amedeo Roberto, and Marco Mondelli. “Concentration without Independence
via Information Measures.” In Proceedings of 2023 IEEE International Symposium
on Information Theory, 400–405. IEEE, 2023. https://doi.org/10.1109/isit54713.2023.10206899.
ieee: A. R. Esposito and M. Mondelli, “Concentration without independence via information
measures,” in Proceedings of 2023 IEEE International Symposium on Information
Theory, Taipei, Taiwan, 2023, pp. 400–405.
ista: 'Esposito AR, Mondelli M. 2023. Concentration without independence via information
measures. Proceedings of 2023 IEEE International Symposium on Information Theory.
ISIT: IEEE International Symposium on Information Theory, 400–405.'
mla: Esposito, Amedeo Roberto, and Marco Mondelli. “Concentration without Independence
via Information Measures.” Proceedings of 2023 IEEE International Symposium
on Information Theory, IEEE, 2023, pp. 400–05, doi:10.1109/isit54713.2023.10206899.
short: A.R. Esposito, M. Mondelli, in:, Proceedings of 2023 IEEE International Symposium
on Information Theory, IEEE, 2023, pp. 400–405.
conference:
end_date: 2023-06-30
location: Taipei, Taiwan
name: 'ISIT: IEEE International Symposium on Information Theory'
start_date: 2023-06-25
date_created: 2024-02-02T11:18:40Z
date_published: 2023-06-30T00:00:00Z
date_updated: 2024-03-25T07:15:51Z
day: '30'
department:
- _id: MaMo
doi: 10.1109/isit54713.2023.10206899
external_id:
arxiv:
- '2303.07245'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2303.07245
month: '06'
oa: 1
oa_version: Preprint
page: 400-405
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of 2023 IEEE International Symposium on Information Theory
publication_identifier:
eisbn:
- '9781665475549'
eissn:
- 2157-8117
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
record:
- id: '15172'
relation: later_version
status: public
status: public
title: Concentration without independence via information measures
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '11420'
abstract:
- lang: eng
text: 'Understanding the properties of neural networks trained via stochastic gradient
descent (SGD) is at the heart of the theory of deep learning. In this work, we
take a mean-field view, and consider a two-layer ReLU network trained via noisy-SGD
for a univariate regularized regression problem. Our main result is that SGD with
vanishingly small noise injected in the gradients is biased towards a simple solution:
at convergence, the ReLU network implements a piecewise linear map of the inputs,
and the number of “knot” points -- i.e., points where the tangent of the ReLU
network estimator changes -- between two consecutive training inputs is at most
three. In particular, as the number of neurons of the network grows, the SGD dynamics
is captured by the solution of a gradient flow and, at convergence, the distribution
of the weights approaches the unique minimizer of a related free energy, which
has a Gibbs form. Our key technical contribution consists in the analysis of the
estimator resulting from this minimizer: we show that its second derivative vanishes
everywhere, except at some specific locations which represent the “knot” points.
We also provide empirical evidence that knots at locations distinct from the data
points might occur, as predicted by our theory.'
acknowledgement: "We would like to thank Mert Pilanci for several exploratory discussions
in the early stage\r\nof the project, Jan Maas for clarifications about Jordan et
al. (1998), and Max Zimmer for\r\nsuggestive numerical experiments. A. Shevchenko
and M. Mondelli are partially supported\r\nby the 2019 Lopez-Loreta Prize. V. Kungurtsev
acknowledges support to the OP VVV\r\nproject CZ.02.1.01/0.0/0.0/16 019/0000765
Research Center for Informatics.\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Aleksandr
full_name: Shevchenko, Aleksandr
id: F2B06EC2-C99E-11E9-89F0-752EE6697425
last_name: Shevchenko
- first_name: Vyacheslav
full_name: Kungurtsev, Vyacheslav
last_name: Kungurtsev
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: Shevchenko A, Kungurtsev V, Mondelli M. Mean-field analysis of piecewise linear
solutions for wide ReLU networks. Journal of Machine Learning Research.
2022;23(130):1-55.
apa: Shevchenko, A., Kungurtsev, V., & Mondelli, M. (2022). Mean-field analysis
of piecewise linear solutions for wide ReLU networks. Journal of Machine Learning
Research. Journal of Machine Learning Research.
chicago: Shevchenko, Aleksandr, Vyacheslav Kungurtsev, and Marco Mondelli. “Mean-Field
Analysis of Piecewise Linear Solutions for Wide ReLU Networks.” Journal of
Machine Learning Research. Journal of Machine Learning Research, 2022.
ieee: A. Shevchenko, V. Kungurtsev, and M. Mondelli, “Mean-field analysis of piecewise
linear solutions for wide ReLU networks,” Journal of Machine Learning Research,
vol. 23, no. 130. Journal of Machine Learning Research, pp. 1–55, 2022.
ista: Shevchenko A, Kungurtsev V, Mondelli M. 2022. Mean-field analysis of piecewise
linear solutions for wide ReLU networks. Journal of Machine Learning Research.
23(130), 1–55.
mla: Shevchenko, Aleksandr, et al. “Mean-Field Analysis of Piecewise Linear Solutions
for Wide ReLU Networks.” Journal of Machine Learning Research, vol. 23,
no. 130, Journal of Machine Learning Research, 2022, pp. 1–55.
short: A. Shevchenko, V. Kungurtsev, M. Mondelli, Journal of Machine Learning Research
23 (2022) 1–55.
date_created: 2022-05-29T22:01:54Z
date_published: 2022-04-01T00:00:00Z
date_updated: 2022-05-30T08:34:14Z
day: '01'
ddc:
- '000'
department:
- _id: MaMo
- _id: DaAl
external_id:
arxiv:
- '2111.02278'
file:
- access_level: open_access
checksum: d4ff5d1affb34848b5c5e4002483fc62
content_type: application/pdf
creator: cchlebak
date_created: 2022-05-30T08:22:55Z
date_updated: 2022-05-30T08:22:55Z
file_id: '11422'
file_name: 21-1365.pdf
file_size: 1521701
relation: main_file
success: 1
file_date_updated: 2022-05-30T08:22:55Z
has_accepted_license: '1'
intvolume: ' 23'
issue: '130'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 1-55
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Journal of Machine Learning Research
publication_identifier:
eissn:
- 1533-7928
issn:
- 1532-4435
publication_status: published
publisher: Journal of Machine Learning Research
quality_controlled: '1'
related_material:
link:
- relation: other
url: https://www.jmlr.org/papers/v23/21-1365.html
scopus_import: '1'
status: public
title: Mean-field analysis of piecewise linear solutions for wide ReLU networks
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 23
year: '2022'
...
---
_id: '12011'
abstract:
- lang: eng
text: We characterize the capacity for the discrete-time arbitrarily varying channel
with discrete inputs, outputs, and states when (a) the encoder and decoder do
not share common randomness, (b) the input and state are subject to cost constraints,
(c) the transition matrix of the channel is deterministic given the state, and
(d) at each time step the adversary can only observe the current and past channel
inputs when choosing the state at that time. The achievable strategy involves
stochastic encoding together with list decoding and a disambiguation step. The
converse uses a two-phase "babble-and-push" strategy where the adversary chooses
the state randomly in the first phase, list decodes the output, and then chooses
state inputs to symmetrize the channel in the second phase. These results generalize
prior work on specific channels models (additive, erasure) to general discrete
alphabets and models.
acknowledgement: The work of ADS and ML was supported in part by the US National Science
Foundation under awards CCF-1909468 and CCF-1909451.
article_processing_charge: No
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Sidharth
full_name: Jaggi, Sidharth
last_name: Jaggi
- first_name: Michael
full_name: Langberg, Michael
last_name: Langberg
- first_name: Anand D.
full_name: Sarwate, Anand D.
last_name: Sarwate
citation:
ama: 'Zhang Y, Jaggi S, Langberg M, Sarwate AD. The capacity of causal adversarial
channels. In: 2022 IEEE International Symposium on Information Theory.
Vol 2022. IEEE; 2022:2523-2528. doi:10.1109/ISIT50566.2022.9834709'
apa: 'Zhang, Y., Jaggi, S., Langberg, M., & Sarwate, A. D. (2022). The capacity
of causal adversarial channels. In 2022 IEEE International Symposium on Information
Theory (Vol. 2022, pp. 2523–2528). Espoo, Finland: IEEE. https://doi.org/10.1109/ISIT50566.2022.9834709'
chicago: Zhang, Yihan, Sidharth Jaggi, Michael Langberg, and Anand D. Sarwate. “The
Capacity of Causal Adversarial Channels.” In 2022 IEEE International Symposium
on Information Theory, 2022:2523–28. IEEE, 2022. https://doi.org/10.1109/ISIT50566.2022.9834709.
ieee: Y. Zhang, S. Jaggi, M. Langberg, and A. D. Sarwate, “The capacity of causal
adversarial channels,” in 2022 IEEE International Symposium on Information
Theory, Espoo, Finland, 2022, vol. 2022, pp. 2523–2528.
ista: 'Zhang Y, Jaggi S, Langberg M, Sarwate AD. 2022. The capacity of causal adversarial
channels. 2022 IEEE International Symposium on Information Theory. ISIT: Internation
Symposium on Information Theory vol. 2022, 2523–2528.'
mla: Zhang, Yihan, et al. “The Capacity of Causal Adversarial Channels.” 2022
IEEE International Symposium on Information Theory, vol. 2022, IEEE, 2022,
pp. 2523–28, doi:10.1109/ISIT50566.2022.9834709.
short: Y. Zhang, S. Jaggi, M. Langberg, A.D. Sarwate, in:, 2022 IEEE International
Symposium on Information Theory, IEEE, 2022, pp. 2523–2528.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:03Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T09:09:15Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834709
external_id:
arxiv:
- '2205.06708'
intvolume: ' 2022'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2205.06708'
month: '08'
oa: 1
oa_version: Preprint
page: 2523-2528
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: The capacity of causal adversarial channels
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12017'
abstract:
- lang: eng
text: 'In the classic adversarial communication problem, two parties communicate
over a noisy channel in the presence of a malicious jamming adversary. The arbitrarily
varying channels (AVCs) offer an elegant framework to study a wide range of interesting
adversary models. The optimal throughput or capacity over such AVCs is intimately
tied to the underlying adversary model; in some cases, capacity is unknown and
the problem is known to be notoriously hard. The omniscient adversary, one which
knows the sender’s entire channel transmission a priori, is one of such classic
models of interest; the capacity under such an adversary remains an exciting open
problem. The myopic adversary is a generalization of that model where the adversary’s
observation may be corrupted over a noisy discrete memoryless channel. Through
the adversary’s myopicity, one can unify the slew of different adversary models,
ranging from the omniscient adversary to one that is completely blind to the transmission
(the latter is the well known oblivious model where the capacity is fully characterized).In
this work, we present new results on the capacity under both the omniscient and
myopic adversary models. We completely characterize the positive capacity threshold
over general AVCs with omniscient adversaries. The characterization is in terms
of two key combinatorial objects: the set of completely positive distributions
and the CP-confusability set. For omniscient AVCs with positive capacity, we present
non-trivial lower and upper bounds on the capacity; unlike some of the previous
bounds, our bounds hold under fairly general input and jamming constraints. Our
lower bound improves upon the generalized Gilbert-Varshamov bound for general
AVCs while the upper bound generalizes the well known Elias-Bassalygo bound (known
for binary and q-ary alphabets). For the myopic AVCs, we build on prior results
known for the so-called sufficiently myopic model, and present new results on
the positive rate communication threshold over the so-called insufficiently myopic
regime (a completely insufficient myopic adversary specializes to an omniscient
adversary). We present interesting examples for the widely studied models of adversarial
bit-flip and bit-erasure channels. In fact, for the bit-flip AVC with additive
adversarial noise as well as random noise, we completely characterize the omniscient
model capacity when the random noise is sufficiently large vis-a-vis the adversary’s
budget.'
article_processing_charge: No
author:
- first_name: Anuj Kumar
full_name: Yadav, Anuj Kumar
last_name: Yadav
- first_name: Mohammadreza
full_name: Alimohammadi, Mohammadreza
last_name: Alimohammadi
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Amitalok J.
full_name: Budkuley, Amitalok J.
last_name: Budkuley
- first_name: Sidharth
full_name: Jaggi, Sidharth
last_name: Jaggi
citation:
ama: 'Yadav AK, Alimohammadi M, Zhang Y, Budkuley AJ, Jaggi S. New results on AVCs
with omniscient and myopic adversaries. In: 2022 IEEE International Symposium
on Information Theory. Vol 2022. Institute of Electrical and Electronics Engineers;
2022:2535-2540. doi:10.1109/ISIT50566.2022.9834632'
apa: 'Yadav, A. K., Alimohammadi, M., Zhang, Y., Budkuley, A. J., & Jaggi, S.
(2022). New results on AVCs with omniscient and myopic adversaries. In 2022
IEEE International Symposium on Information Theory (Vol. 2022, pp. 2535–2540).
Espoo, Finland: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT50566.2022.9834632'
chicago: Yadav, Anuj Kumar, Mohammadreza Alimohammadi, Yihan Zhang, Amitalok J.
Budkuley, and Sidharth Jaggi. “New Results on AVCs with Omniscient and Myopic
Adversaries.” In 2022 IEEE International Symposium on Information Theory,
2022:2535–40. Institute of Electrical and Electronics Engineers, 2022. https://doi.org/10.1109/ISIT50566.2022.9834632.
ieee: A. K. Yadav, M. Alimohammadi, Y. Zhang, A. J. Budkuley, and S. Jaggi, “New
results on AVCs with omniscient and myopic adversaries,” in 2022 IEEE International
Symposium on Information Theory, Espoo, Finland, 2022, vol. 2022, pp. 2535–2540.
ista: 'Yadav AK, Alimohammadi M, Zhang Y, Budkuley AJ, Jaggi S. 2022. New results
on AVCs with omniscient and myopic adversaries. 2022 IEEE International Symposium
on Information Theory. ISIT: Internation Symposium on Information Theory vol.
2022, 2535–2540.'
mla: Yadav, Anuj Kumar, et al. “New Results on AVCs with Omniscient and Myopic Adversaries.”
2022 IEEE International Symposium on Information Theory, vol. 2022, Institute
of Electrical and Electronics Engineers, 2022, pp. 2535–40, doi:10.1109/ISIT50566.2022.9834632.
short: A.K. Yadav, M. Alimohammadi, Y. Zhang, A.J. Budkuley, S. Jaggi, in:, 2022
IEEE International Symposium on Information Theory, Institute of Electrical and
Electronics Engineers, 2022, pp. 2535–2540.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:06Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2023-02-13T09:00:14Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834632
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 2535-2540
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: New results on AVCs with omniscient and myopic adversaries
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12013'
abstract:
- lang: eng
text: We consider the problem of communication over adversarial channels with feedback.
Two parties comprising sender Alice and receiver Bob seek to communicate reliably.
An adversary James observes Alice's channel transmission entirely and chooses,
maliciously, its additive channel input or jamming state thereby corrupting Bob's
observation. Bob can communicate over a one-way reverse link with Alice; we assume
that transmissions over this feedback link cannot be corrupted by James. Our goal
in this work is to study the optimum throughput or capacity over such channels
with feedback. We first present results for the quadratically-constrained additive
channel where communication is known to be impossible when the noise-to-signal
(power) ratio (NSR) is at least 1. We present a novel achievability scheme to
establish that positive rate communication is possible even when the NSR is as
high as 8/9. We also present new converse upper bounds on the capacity of this
channel under potentially stochastic encoders and decoders. We also study feedback
communication over the more widely studied q-ary alphabet channel under additive
noise. For the q -ary channel, where q > 2, it is well known that capacity is
positive under full feedback if and only if the adversary can corrupt strictly
less than half the transmitted symbols. We generalize this result and show that
the same threshold holds for positive rate communication when the noiseless feedback
may only be partial; our scheme employs a stochastic decoder. We extend this characterization,
albeit partially, to fully deterministic schemes under partial noiseless feedback.
We also present new converse upper bounds for q-ary channels under full feedback,
where the encoder and/or decoder may privately randomize. Our converse results
bring to the fore an interesting alternate expression for the well known converse
bound for the q—ary channel under full feedback which, when specialized to the
binary channel, also equals its known capacity.
article_processing_charge: No
author:
- first_name: Pranav
full_name: Joshi, Pranav
last_name: Joshi
- first_name: Amritakshya
full_name: Purkayastha, Amritakshya
last_name: Purkayastha
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Amitalok J.
full_name: Budkuley, Amitalok J.
last_name: Budkuley
- first_name: Sidharth
full_name: Jaggi, Sidharth
last_name: Jaggi
citation:
ama: 'Joshi P, Purkayastha A, Zhang Y, Budkuley AJ, Jaggi S. On the capacity of
additive AVCs with feedback. In: 2022 IEEE International Symposium on Information
Theory. Vol 2022. IEEE; 2022:504-509. doi:10.1109/ISIT50566.2022.9834850'
apa: 'Joshi, P., Purkayastha, A., Zhang, Y., Budkuley, A. J., & Jaggi, S. (2022).
On the capacity of additive AVCs with feedback. In 2022 IEEE International
Symposium on Information Theory (Vol. 2022, pp. 504–509). Espoo, Finland:
IEEE. https://doi.org/10.1109/ISIT50566.2022.9834850'
chicago: Joshi, Pranav, Amritakshya Purkayastha, Yihan Zhang, Amitalok J. Budkuley,
and Sidharth Jaggi. “On the Capacity of Additive AVCs with Feedback.” In 2022
IEEE International Symposium on Information Theory, 2022:504–9. IEEE, 2022.
https://doi.org/10.1109/ISIT50566.2022.9834850.
ieee: P. Joshi, A. Purkayastha, Y. Zhang, A. J. Budkuley, and S. Jaggi, “On the
capacity of additive AVCs with feedback,” in 2022 IEEE International Symposium
on Information Theory, Espoo, Finland, 2022, vol. 2022, pp. 504–509.
ista: 'Joshi P, Purkayastha A, Zhang Y, Budkuley AJ, Jaggi S. 2022. On the capacity
of additive AVCs with feedback. 2022 IEEE International Symposium on Information
Theory. ISIT: Internation Symposium on Information Theory vol. 2022, 504–509.'
mla: Joshi, Pranav, et al. “On the Capacity of Additive AVCs with Feedback.” 2022
IEEE International Symposium on Information Theory, vol. 2022, IEEE, 2022,
pp. 504–09, doi:10.1109/ISIT50566.2022.9834850.
short: P. Joshi, A. Purkayastha, Y. Zhang, A.J. Budkuley, S. Jaggi, in:, 2022 IEEE
International Symposium on Information Theory, IEEE, 2022, pp. 504–509.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:04Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T10:23:35Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834850
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 504-509
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the capacity of additive AVCs with feedback
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12016'
abstract:
- lang: eng
text: We consider the problem of coded distributed computing using polar codes.
The average execution time of a coded computing system is related to the error
probability for transmission over the binary erasure channel in recent work by
Soleymani, Jamali and Mahdavifar, where the performance of binary linear codes
is investigated. In this paper, we focus on polar codes and unveil a connection
between the average execution time and the scaling exponent μ of the family of
codes. In the finite-length characterization of polar codes, the scaling exponent
is a key object capturing the speed of convergence to capacity. In particular,
we show that (i) the gap between the normalized average execution time of polar
codes and that of optimal MDS codes is O(n –1/μ ), and (ii) this upper bound can
be improved to roughly O(n –1/2 ) by considering polar codes with large kernels.
We conjecture that these bounds could be improved to O(n –2/μ ) and O(n –1 ),
respectively, and provide a heuristic argument as well as numerical evidence supporting
this view.
acknowledgement: D. Fathollahi and M. Mondelli were partially supported by the 2019
Lopez-Loreta Prize. The authors thank Hamed Hassani and Hessam Mahdavifar for helpful
discussions.
article_processing_charge: No
author:
- first_name: Dorsa
full_name: Fathollahi, Dorsa
last_name: Fathollahi
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Fathollahi D, Mondelli M. Polar coded computing: The role of the scaling exponent.
In: 2022 IEEE International Symposium on Information Theory. Vol 2022.
IEEE; 2022:2154-2159. doi:10.1109/ISIT50566.2022.9834712'
apa: 'Fathollahi, D., & Mondelli, M. (2022). Polar coded computing: The role
of the scaling exponent. In 2022 IEEE International Symposium on Information
Theory (Vol. 2022, pp. 2154–2159). Espoo, Finland: IEEE. https://doi.org/10.1109/ISIT50566.2022.9834712'
chicago: 'Fathollahi, Dorsa, and Marco Mondelli. “Polar Coded Computing: The Role
of the Scaling Exponent.” In 2022 IEEE International Symposium on Information
Theory, 2022:2154–59. IEEE, 2022. https://doi.org/10.1109/ISIT50566.2022.9834712.'
ieee: 'D. Fathollahi and M. Mondelli, “Polar coded computing: The role of the scaling
exponent,” in 2022 IEEE International Symposium on Information Theory,
Espoo, Finland, 2022, vol. 2022, pp. 2154–2159.'
ista: 'Fathollahi D, Mondelli M. 2022. Polar coded computing: The role of the scaling
exponent. 2022 IEEE International Symposium on Information Theory. ISIT: Internation
Symposium on Information Theory vol. 2022, 2154–2159.'
mla: 'Fathollahi, Dorsa, and Marco Mondelli. “Polar Coded Computing: The Role of
the Scaling Exponent.” 2022 IEEE International Symposium on Information Theory,
vol. 2022, IEEE, 2022, pp. 2154–59, doi:10.1109/ISIT50566.2022.9834712.'
short: D. Fathollahi, M. Mondelli, in:, 2022 IEEE International Symposium on Information
Theory, IEEE, 2022, pp. 2154–2159.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:05Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T10:35:40Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834712
external_id:
arxiv:
- '2201.10082'
intvolume: ' 2022'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2201.10082
month: '08'
oa: 1
oa_version: Preprint
page: 2154-2159
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Polar coded computing: The role of the scaling exponent'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12012'
abstract:
- lang: eng
text: This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award. We
generalize a previous framework for designing utility-optimal differentially private
(DP) mechanisms via graphs, where datasets are vertices in the graph and edges
represent dataset neighborhood. The boundary set contains datasets where an individual’s
response changes the binary-valued query compared to its neighbors. Previous work
was limited to the homogeneous case where the privacy parameter ε across all datasets
was the same and the mechanism at boundary datasets was identical. In our work,
the mechanism can take different distributions at the boundary and the privacy
parameter ε is a function of neighboring datasets, which recovers an earlier definition
of personalized DP as special case. The problem is how to extend the mechanism,
which is only defined at the boundary set, to other datasets in the graph in a
computationally efficient and utility optimal manner. Using the concept of strongest
induced DP condition we solve this problem efficiently in polynomial time (in
the size of the graph).
article_processing_charge: No
author:
- first_name: Sahel
full_name: Torkamani, Sahel
id: 0503e7f8-2d05-11ed-aa17-db0640c720fc
last_name: Torkamani
- first_name: Javad B.
full_name: Ebrahimi, Javad B.
last_name: Ebrahimi
- first_name: Parastoo
full_name: Sadeghi, Parastoo
last_name: Sadeghi
- first_name: Rafael G.L.
full_name: D'Oliveira, Rafael G.L.
last_name: D'Oliveira
- first_name: Muriel
full_name: Médard, Muriel
last_name: Médard
citation:
ama: 'Torkamani S, Ebrahimi JB, Sadeghi P, D’Oliveira RGL, Médard M. Heterogeneous
differential privacy via graphs. In: 2022 IEEE International Symposium on Information
Theory. Vol 2022. IEEE; 2022:1623-1628. doi:10.1109/ISIT50566.2022.9834711'
apa: 'Torkamani, S., Ebrahimi, J. B., Sadeghi, P., D’Oliveira, R. G. L., & Médard,
M. (2022). Heterogeneous differential privacy via graphs. In 2022 IEEE International
Symposium on Information Theory (Vol. 2022, pp. 1623–1628). Espoo, Finland:
IEEE. https://doi.org/10.1109/ISIT50566.2022.9834711'
chicago: Torkamani, Sahel, Javad B. Ebrahimi, Parastoo Sadeghi, Rafael G.L. D’Oliveira,
and Muriel Médard. “Heterogeneous Differential Privacy via Graphs.” In 2022
IEEE International Symposium on Information Theory, 2022:1623–28. IEEE, 2022.
https://doi.org/10.1109/ISIT50566.2022.9834711.
ieee: S. Torkamani, J. B. Ebrahimi, P. Sadeghi, R. G. L. D’Oliveira, and M. Médard,
“Heterogeneous differential privacy via graphs,” in 2022 IEEE International
Symposium on Information Theory, Espoo, Finland, 2022, vol. 2022, pp. 1623–1628.
ista: 'Torkamani S, Ebrahimi JB, Sadeghi P, D’Oliveira RGL, Médard M. 2022. Heterogeneous
differential privacy via graphs. 2022 IEEE International Symposium on Information
Theory. ISIT: Internation Symposium on Information Theory vol. 2022, 1623–1628.'
mla: Torkamani, Sahel, et al. “Heterogeneous Differential Privacy via Graphs.” 2022
IEEE International Symposium on Information Theory, vol. 2022, IEEE, 2022,
pp. 1623–28, doi:10.1109/ISIT50566.2022.9834711.
short: S. Torkamani, J.B. Ebrahimi, P. Sadeghi, R.G.L. D’Oliveira, M. Médard, in:,
2022 IEEE International Symposium on Information Theory, IEEE, 2022, pp. 1623–1628.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:04Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T10:28:35Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834711
external_id:
arxiv:
- '2203.15429'
intvolume: ' 2022'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2203.15429
month: '08'
oa: 1
oa_version: Preprint
page: 1623-1628
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Heterogeneous differential privacy via graphs
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12018'
abstract:
- lang: eng
text: We study the problem of characterizing the maximal rates of list decoding
in Euclidean spaces for finite list sizes. For any positive integer L ≥ 2 and
real N > 0, we say that a subset C⊂Rn is an (N,L – 1)-multiple packing or an (N,L–
1)-list decodable code if every Euclidean ball of radius nN−−−√ in ℝ n contains
no more than L − 1 points of C. We study this problem with and without ℓ 2 norm
constraints on C, and derive the best-known lower bounds on the maximal rate for
(N,L−1) multiple packing. Our bounds are obtained via error exponents for list
decoding over Additive White Gaussian Noise (AWGN) channels. We establish a curious
inequality which relates the error exponent, a quantity of average-case nature,
to the list-decoding radius, a quantity of worst-case nature. We derive various
bounds on the error exponent for list decoding in both bounded and unbounded settings
which could be of independent interest beyond multiple packing.
article_processing_charge: No
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. Lower bounds on list decoding capacity using error exponents.
In: 2022 IEEE International Symposium on Information Theory. Vol 2022.
Institute of Electrical and Electronics Engineers; 2022:1324-1329. doi:10.1109/ISIT50566.2022.9834815'
apa: 'Zhang, Y., & Vatedka, S. (2022). Lower bounds on list decoding capacity
using error exponents. In 2022 IEEE International Symposium on Information
Theory (Vol. 2022, pp. 1324–1329). Espoo, Finland: Institute of Electrical
and Electronics Engineers. https://doi.org/10.1109/ISIT50566.2022.9834815'
chicago: Zhang, Yihan, and Shashank Vatedka. “Lower Bounds on List Decoding Capacity
Using Error Exponents.” In 2022 IEEE International Symposium on Information
Theory, 2022:1324–29. Institute of Electrical and Electronics Engineers, 2022.
https://doi.org/10.1109/ISIT50566.2022.9834815.
ieee: Y. Zhang and S. Vatedka, “Lower bounds on list decoding capacity using error
exponents,” in 2022 IEEE International Symposium on Information Theory,
Espoo, Finland, 2022, vol. 2022, pp. 1324–1329.
ista: 'Zhang Y, Vatedka S. 2022. Lower bounds on list decoding capacity using error
exponents. 2022 IEEE International Symposium on Information Theory. ISIT: Internation
Symposium on Information Theory vol. 2022, 1324–1329.'
mla: Zhang, Yihan, and Shashank Vatedka. “Lower Bounds on List Decoding Capacity
Using Error Exponents.” 2022 IEEE International Symposium on Information Theory,
vol. 2022, Institute of Electrical and Electronics Engineers, 2022, pp. 1324–29,
doi:10.1109/ISIT50566.2022.9834815.
short: Y. Zhang, S. Vatedka, in:, 2022 IEEE International Symposium on Information
Theory, Institute of Electrical and Electronics Engineers, 2022, pp. 1324–1329.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:06Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2023-02-13T09:02:06Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834815
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 1324-1329
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower bounds on list decoding capacity using error exponents
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12015'
abstract:
- lang: eng
text: We study the problem of high-dimensional multiple packing in Euclidean space.
Multiple packing is a natural generalization of sphere packing and is defined
as follows. Let P, N > 0 and L∈Z≥2. A multiple packing is a set C of points in
Bn(0–,nP−−−√) such that any point in ℝ n lies in the intersection of at most L
– 1 balls of radius nN−−−√ around points in C. 1 In this paper, we derive two
lower bounds on the largest possible density of a multiple packing. These bounds
are obtained through a stronger notion called average-radius multiple packing.
Specifically, we exactly pin down the asymptotics of (expurgated) Gaussian codes
and (expurgated) spherical codes under average-radius multiple packing. To this
end, we apply tools from high-dimensional geometry and large deviation theory.
The bound for spherical codes matches the previous best known bound which was
obtained for the standard (weaker) notion of multiple packing through a curious
connection with error exponents [Bli99], [ZV21]. The bound for Gaussian codes
suggests that they are strictly inferior to spherical codes.
article_processing_charge: No
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. Lower bounds for multiple packing. In: 2022 IEEE International
Symposium on Information Theory. Vol 2022. IEEE; 2022:3085-3090. doi:10.1109/ISIT50566.2022.9834443'
apa: 'Zhang, Y., & Vatedka, S. (2022). Lower bounds for multiple packing. In
2022 IEEE International Symposium on Information Theory (Vol. 2022, pp.
3085–3090). Espoo, Finland: IEEE. https://doi.org/10.1109/ISIT50566.2022.9834443'
chicago: Zhang, Yihan, and Shashank Vatedka. “Lower Bounds for Multiple Packing.”
In 2022 IEEE International Symposium on Information Theory, 2022:3085–90.
IEEE, 2022. https://doi.org/10.1109/ISIT50566.2022.9834443.
ieee: Y. Zhang and S. Vatedka, “Lower bounds for multiple packing,” in 2022 IEEE
International Symposium on Information Theory, Espoo, Finland, 2022, vol.
2022, pp. 3085–3090.
ista: 'Zhang Y, Vatedka S. 2022. Lower bounds for multiple packing. 2022 IEEE International
Symposium on Information Theory. ISIT: Internation Symposium on Information Theory
vol. 2022, 3085–3090.'
mla: Zhang, Yihan, and Shashank Vatedka. “Lower Bounds for Multiple Packing.” 2022
IEEE International Symposium on Information Theory, vol. 2022, IEEE, 2022,
pp. 3085–90, doi:10.1109/ISIT50566.2022.9834443.
short: Y. Zhang, S. Vatedka, in:, 2022 IEEE International Symposium on Information
Theory, IEEE, 2022, pp. 3085–3090.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:05Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T10:39:04Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834443
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 3085-3090
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower bounds for multiple packing
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12014'
abstract:
- lang: eng
text: We study the problem of high-dimensional multiple packing in Euclidean space.
Multiple packing is a natural generalization of sphere packing and is defined
as follows. Let N > 0 and L∈Z≥2. A multiple packing is a set C of points in Rn
such that any point in Rn lies in the intersection of at most L – 1 balls of radius
nN−−−√ around points in C. Given a well-known connection with coding theory, multiple
packings can be viewed as the Euclidean analog of list-decodable codes, which
are well-studied for finite fields. In this paper, we exactly pin down the asymptotic
density of (expurgated) Poisson Point Processes under a stronger notion called
average-radius multiple packing. To this end, we apply tools from high-dimensional
geometry and large deviation theory. This gives rise to the best known lower bound
on the largest multiple packing density. Our result corrects a mistake in a previous
paper by Blinovsky [Bli05].
article_processing_charge: No
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: 'Zhang Y, Vatedka S. List-decodability of Poisson Point Processes. In: 2022
IEEE International Symposium on Information Theory. Vol 2022. IEEE; 2022:2559-2564.
doi:10.1109/ISIT50566.2022.9834512'
apa: 'Zhang, Y., & Vatedka, S. (2022). List-decodability of Poisson Point Processes.
In 2022 IEEE International Symposium on Information Theory (Vol. 2022,
pp. 2559–2564). Espoo, Finland: IEEE. https://doi.org/10.1109/ISIT50566.2022.9834512'
chicago: Zhang, Yihan, and Shashank Vatedka. “List-Decodability of Poisson Point
Processes.” In 2022 IEEE International Symposium on Information Theory,
2022:2559–64. IEEE, 2022. https://doi.org/10.1109/ISIT50566.2022.9834512.
ieee: Y. Zhang and S. Vatedka, “List-decodability of Poisson Point Processes,” in
2022 IEEE International Symposium on Information Theory, Espoo, Finland,
2022, vol. 2022, pp. 2559–2564.
ista: 'Zhang Y, Vatedka S. 2022. List-decodability of Poisson Point Processes. 2022
IEEE International Symposium on Information Theory. ISIT: Internation Symposium
on Information Theory vol. 2022, 2559–2564.'
mla: Zhang, Yihan, and Shashank Vatedka. “List-Decodability of Poisson Point Processes.”
2022 IEEE International Symposium on Information Theory, vol. 2022, IEEE,
2022, pp. 2559–64, doi:10.1109/ISIT50566.2022.9834512.
short: Y. Zhang, S. Vatedka, in:, 2022 IEEE International Symposium on Information
Theory, IEEE, 2022, pp. 2559–2564.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:04Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2022-09-05T09:23:04Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834512
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 2559-2564
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: List-decodability of Poisson Point Processes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12019'
abstract:
- lang: eng
text: This paper studies combinatorial properties of codes for the Z-channel. A
Z-channel with error fraction τ takes as input a length-n binary codeword and
injects in an adversarial manner up to nτ asymmetric errors, i.e., errors that
only zero out bits but do not flip 0’s to 1’s. It is known that the largest (L
− 1)-list-decodable code for the Z-channel with error fraction τ has exponential
(in n) size if τ is less than a critical value that we call the Plotkin point
and has constant size if τ is larger than the threshold. The (L−1)-list-decoding
Plotkin point is known to be L−1L−1−L−LL−1. In this paper, we show that the largest
(L−1)-list-decodable code ε-above the Plotkin point has size Θ L (ε −3/2 ) for
any L − 1 ≥ 1.
article_processing_charge: No
author:
- first_name: Nikita
full_name: Polyanskii, Nikita
last_name: Polyanskii
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
citation:
ama: 'Polyanskii N, Zhang Y. List-decodable zero-rate codes for the Z-channel. In:
2022 IEEE International Symposium on Information Theory. Vol 2022. Institute
of Electrical and Electronics Engineers; 2022:2553-2558. doi:10.1109/ISIT50566.2022.9834829'
apa: 'Polyanskii, N., & Zhang, Y. (2022). List-decodable zero-rate codes for
the Z-channel. In 2022 IEEE International Symposium on Information Theory
(Vol. 2022, pp. 2553–2558). Espoo, Finland: Institute of Electrical and Electronics
Engineers. https://doi.org/10.1109/ISIT50566.2022.9834829'
chicago: Polyanskii, Nikita, and Yihan Zhang. “List-Decodable Zero-Rate Codes for
the Z-Channel.” In 2022 IEEE International Symposium on Information Theory,
2022:2553–58. Institute of Electrical and Electronics Engineers, 2022. https://doi.org/10.1109/ISIT50566.2022.9834829.
ieee: N. Polyanskii and Y. Zhang, “List-decodable zero-rate codes for the Z-channel,”
in 2022 IEEE International Symposium on Information Theory, Espoo, Finland,
2022, vol. 2022, pp. 2553–2558.
ista: 'Polyanskii N, Zhang Y. 2022. List-decodable zero-rate codes for the Z-channel.
2022 IEEE International Symposium on Information Theory. ISIT: Internation Symposium
on Information Theory vol. 2022, 2553–2558.'
mla: Polyanskii, Nikita, and Yihan Zhang. “List-Decodable Zero-Rate Codes for the
Z-Channel.” 2022 IEEE International Symposium on Information Theory, vol.
2022, Institute of Electrical and Electronics Engineers, 2022, pp. 2553–58, doi:10.1109/ISIT50566.2022.9834829.
short: N. Polyanskii, Y. Zhang, in:, 2022 IEEE International Symposium on Information
Theory, Institute of Electrical and Electronics Engineers, 2022, pp. 2553–2558.
conference:
end_date: 2022-07-01
location: Espoo, Finland
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2022-06-26
date_created: 2022-09-04T22:02:07Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2023-02-13T09:02:18Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834829
intvolume: ' 2022'
language:
- iso: eng
month: '08'
oa_version: None
page: 2553-2558
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
isbn:
- '9781665421591'
issn:
- 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: List-decodable zero-rate codes for the Z-channel
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2022
year: '2022'
...
---
_id: '12540'
abstract:
- lang: eng
text: We consider the problem of signal estimation in generalized linear models
defined via rotationally invariant design matrices. Since these matrices can have
an arbitrary spectral distribution, this model is well suited for capturing complex
correlation structures which often arise in applications. We propose a novel family
of approximate message passing (AMP) algorithms for signal estimation, and rigorously
characterize their performance in the high-dimensional limit via a state evolution
recursion. Our rotationally invariant AMP has complexity of the same order as
the existing AMP derived under the restrictive assumption of a Gaussian design;
our algorithm also recovers this existing AMP as a special case. Numerical results
showcase a performance close to Vector AMP (which is conjectured to be Bayes-optimal
in some settings), but obtained with a much lower complexity, as the proposed
algorithm does not require a computationally expensive singular value decomposition.
acknowledgement: The authors would like to thank the anonymous reviewers for their
helpful comments. KK and MM were partially supported by the 2019 Lopez-Loreta Prize.
article_number: '22'
article_processing_charge: No
author:
- first_name: Ramji
full_name: Venkataramanan, Ramji
last_name: Venkataramanan
- first_name: Kevin
full_name: Kögler, Kevin
id: 94ec913c-dc85-11ea-9058-e5051ab2428b
last_name: Kögler
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Venkataramanan R, Kögler K, Mondelli M. Estimation in rotationally invariant
generalized linear models via approximate message passing. In: Proceedings
of the 39th International Conference on Machine Learning. Vol 162. ML Research
Press; 2022.'
apa: 'Venkataramanan, R., Kögler, K., & Mondelli, M. (2022). Estimation in rotationally
invariant generalized linear models via approximate message passing. In Proceedings
of the 39th International Conference on Machine Learning (Vol. 162). Baltimore,
MD, United States: ML Research Press.'
chicago: Venkataramanan, Ramji, Kevin Kögler, and Marco Mondelli. “Estimation in
Rotationally Invariant Generalized Linear Models via Approximate Message Passing.”
In Proceedings of the 39th International Conference on Machine Learning,
Vol. 162. ML Research Press, 2022.
ieee: R. Venkataramanan, K. Kögler, and M. Mondelli, “Estimation in rotationally
invariant generalized linear models via approximate message passing,” in Proceedings
of the 39th International Conference on Machine Learning, Baltimore, MD, United
States, 2022, vol. 162.
ista: 'Venkataramanan R, Kögler K, Mondelli M. 2022. Estimation in rotationally
invariant generalized linear models via approximate message passing. Proceedings
of the 39th International Conference on Machine Learning. ICML: International
Conference on Machine Learning vol. 162, 22.'
mla: Venkataramanan, Ramji, et al. “Estimation in Rotationally Invariant Generalized
Linear Models via Approximate Message Passing.” Proceedings of the 39th International
Conference on Machine Learning, vol. 162, 22, ML Research Press, 2022.
short: R. Venkataramanan, K. Kögler, M. Mondelli, in:, Proceedings of the 39th International
Conference on Machine Learning, ML Research Press, 2022.
conference:
end_date: 2022-07-23
location: Baltimore, MD, United States
name: 'ICML: International Conference on Machine Learning'
start_date: 2022-07-17
date_created: 2023-02-10T13:49:04Z
date_published: 2022-01-01T00:00:00Z
date_updated: 2023-02-13T10:54:58Z
ddc:
- '000'
department:
- _id: MaMo
file:
- access_level: open_access
checksum: 67436eb0a660789514cdf9db79e84683
content_type: application/pdf
creator: dernst
date_created: 2023-02-13T10:53:11Z
date_updated: 2023-02-13T10:53:11Z
file_id: '12547'
file_name: 2022_PMLR_Venkataramanan.pdf
file_size: 2341343
relation: main_file
success: 1
file_date_updated: 2023-02-13T10:53:11Z
has_accepted_license: '1'
intvolume: ' 162'
language:
- iso: eng
oa: 1
oa_version: Published Version
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 39th International Conference on Machine Learning
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
status: public
title: Estimation in rotationally invariant generalized linear models via approximate
message passing
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 162
year: '2022'
...
---
_id: '12536'
abstract:
- lang: eng
text: 'We consider the problem of estimating a rank-1 signal corrupted by structured
rotationally invariant noise, and address the following question: how well do
inference algorithms perform when the noise statistics is unknown and hence Gaussian
noise is assumed? While the matched Bayes-optimal setting with unstructured noise
is well understood, the analysis of this mismatched problem is only at its premises.
In this paper, we make a step towards understanding the effect of the strong source
of mismatch which is the noise statistics. Our main technical contribution is
the rigorous analysis of a Bayes estimator and of an approximate message passing
(AMP) algorithm, both of which incorrectly assume a Gaussian setup. The first
result exploits the theory of spherical integrals and of low-rank matrix perturbations;
the idea behind the second one is to design and analyze an artificial AMP which,
by taking advantage of the flexibility in the denoisers, is able to "correct"
the mismatch. Armed with these sharp asymptotic characterizations, we unveil a
rich and often unexpected phenomenology. For example, despite AMP is in principle
designed to efficiently compute the Bayes estimator, the former is outperformed
by the latter in terms of mean-square error. We show that this performance gap
is due to an incorrect estimation of the signal norm. In fact, when the SNR is
large enough, the overlaps of the AMP and the Bayes estimator coincide, and they
even match those of optimal estimators taking into account the structure of the
noise.'
article_number: '2205.10009'
article_processing_charge: No
author:
- first_name: Jean
full_name: Barbier, Jean
last_name: Barbier
- first_name: TianQi
full_name: Hou, TianQi
last_name: Hou
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Manuel
full_name: Saenz, Manuel
last_name: Saenz
citation:
ama: 'Barbier J, Hou T, Mondelli M, Saenz M. The price of ignorance: How much does
it cost to forget noise structure in low-rank matrix estimation? arXiv.
doi:10.48550/arXiv.2205.10009'
apa: 'Barbier, J., Hou, T., Mondelli, M., & Saenz, M. (n.d.). The price of ignorance:
How much does it cost to forget noise structure in low-rank matrix estimation?
arXiv. https://doi.org/10.48550/arXiv.2205.10009'
chicago: 'Barbier, Jean, TianQi Hou, Marco Mondelli, and Manuel Saenz. “The Price
of Ignorance: How Much Does It Cost to Forget Noise Structure in Low-Rank Matrix
Estimation?” ArXiv, n.d. https://doi.org/10.48550/arXiv.2205.10009.'
ieee: 'J. Barbier, T. Hou, M. Mondelli, and M. Saenz, “The price of ignorance: How
much does it cost to forget noise structure in low-rank matrix estimation?,” arXiv.
.'
ista: 'Barbier J, Hou T, Mondelli M, Saenz M. The price of ignorance: How much does
it cost to forget noise structure in low-rank matrix estimation? arXiv, 2205.10009.'
mla: 'Barbier, Jean, et al. “The Price of Ignorance: How Much Does It Cost to Forget
Noise Structure in Low-Rank Matrix Estimation?” ArXiv, 2205.10009, doi:10.48550/arXiv.2205.10009.'
short: J. Barbier, T. Hou, M. Mondelli, M. Saenz, ArXiv (n.d.).
date_created: 2023-02-10T13:45:41Z
date_published: 2022-05-20T00:00:00Z
date_updated: 2023-02-16T09:41:25Z
day: '20'
department:
- _id: MaMo
doi: 10.48550/arXiv.2205.10009
external_id:
arxiv:
- '2205.10009'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2205.10009
month: '05'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: accepted
status: public
title: 'The price of ignorance: How much does it cost to forget noise structure in
low-rank matrix estimation?'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '12860'
abstract:
- lang: eng
text: 'Memorization of the relation between entities in a dataset can lead to privacy
issues when using a trained model for question answering. We introduce Relational
Memorization (RM) to understand, quantify and control this phenomenon. While bounding
general memorization can have detrimental effects on the performance of a trained
model, bounding RM does not prevent effective learning. The difference is most
pronounced when the data distribution is long-tailed, with many queries having
only few training examples: Impeding general memorization prevents effective learning,
while impeding only relational memorization still allows learning general properties
of the underlying concepts. We formalize the notion of Relational Privacy (RP)
and, inspired by Differential Privacy (DP), we provide a possible definition of
Differential Relational Privacy (DrP). These notions can be used to describe and
compute bounds on the amount of RM in a trained model. We illustrate Relational
Privacy concepts in experiments with large-scale models for Question Answering.'
article_number: '2203.16701'
article_processing_charge: No
author:
- first_name: Simone
full_name: Bombari, Simone
id: ca726dda-de17-11ea-bc14-f9da834f63aa
last_name: Bombari
- first_name: Alessandro
full_name: Achille, Alessandro
last_name: Achille
- first_name: Zijian
full_name: Wang, Zijian
last_name: Wang
- first_name: Yu-Xiang
full_name: Wang, Yu-Xiang
last_name: Wang
- first_name: Yusheng
full_name: Xie, Yusheng
last_name: Xie
- first_name: Kunwar Yashraj
full_name: Singh, Kunwar Yashraj
last_name: Singh
- first_name: Srikar
full_name: Appalaraju, Srikar
last_name: Appalaraju
- first_name: Vijay
full_name: Mahadevan, Vijay
last_name: Mahadevan
- first_name: Stefano
full_name: Soatto, Stefano
last_name: Soatto
citation:
ama: Bombari S, Achille A, Wang Z, et al. Towards differential relational privacy
and its use in question answering. arXiv. doi:10.48550/arXiv.2203.16701
apa: Bombari, S., Achille, A., Wang, Z., Wang, Y.-X., Xie, Y., Singh, K. Y., … Soatto,
S. (n.d.). Towards differential relational privacy and its use in question answering.
arXiv. https://doi.org/10.48550/arXiv.2203.16701
chicago: Bombari, Simone, Alessandro Achille, Zijian Wang, Yu-Xiang Wang, Yusheng
Xie, Kunwar Yashraj Singh, Srikar Appalaraju, Vijay Mahadevan, and Stefano Soatto.
“Towards Differential Relational Privacy and Its Use in Question Answering.” ArXiv,
n.d. https://doi.org/10.48550/arXiv.2203.16701.
ieee: S. Bombari et al., “Towards differential relational privacy and its
use in question answering,” arXiv. .
ista: Bombari S, Achille A, Wang Z, Wang Y-X, Xie Y, Singh KY, Appalaraju S, Mahadevan
V, Soatto S. Towards differential relational privacy and its use in question answering.
arXiv, 2203.16701.
mla: Bombari, Simone, et al. “Towards Differential Relational Privacy and Its Use
in Question Answering.” ArXiv, 2203.16701, doi:10.48550/arXiv.2203.16701.
short: S. Bombari, A. Achille, Z. Wang, Y.-X. Wang, Y. Xie, K.Y. Singh, S. Appalaraju,
V. Mahadevan, S. Soatto, ArXiv (n.d.).
date_created: 2023-04-23T16:11:48Z
date_published: 2022-03-30T00:00:00Z
date_updated: 2023-04-25T07:34:49Z
day: '30'
department:
- _id: GradSch
- _id: MaMo
doi: 10.48550/arXiv.2203.16701
external_id:
arxiv:
- '2203.16701'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2203.16701
month: '03'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
status: public
title: Towards differential relational privacy and its use in question answering
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '11639'
abstract:
- lang: eng
text: We study the list decodability of different ensembles of codes over the real
alphabet under the assumption of an omniscient adversary. It is a well-known result
that when the source and the adversary have power constraints P and N respectively,
the list decoding capacity is equal to 1/2logP/N. Random spherical codes achieve
constant list sizes, and the goal of the present paper is to obtain a better understanding
of the smallest achievable list size as a function of the gap to capacity. We
show a reduction from arbitrary codes to spherical codes, and derive a lower bound
on the list size of typical random spherical codes. We also give an upper bound
on the list size achievable using nested Construction-A lattices and infinite
Construction-A lattices. We then define and study a class of infinite constellations
that generalize Construction-A lattices and prove upper and lower bounds for the
same. Other goodness properties such as packing goodness and AWGN goodness of
infinite constellations are proved along the way. Finally, we consider random
lattices sampled from the Haar distribution and show that if a certain conjecture
that originates in analytic number theory is true, then the list size grows as
a polynomial function of the gap-to-capacity.
acknowledgement: "This work was done when Shashank Vatedka was at the Chinese University
of Hong Kong, where he was supported in part by CUHK Direct Grants 4055039 and 4055077.
He would like to acknowledge funding from a seed grant offered by IIT Hyderabad
and the Start-up Research Grant (SRG/2020/000910) from the Science and Engineering
Board, India. Yihan Zhang has received funding from the European Union’s Horizon
2020 research and innovation programme\r\nunder grant agreement No 682203-ERC-[Inf-Speed-Tradeoff]."
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
citation:
ama: Zhang Y, Vatedka S. List decoding random Euclidean codes and Infinite constellations.
IEEE Transactions on Information Theory. 2022;68(12):7753-7786. doi:10.1109/TIT.2022.3189542
apa: Zhang, Y., & Vatedka, S. (2022). List decoding random Euclidean codes and
Infinite constellations. IEEE Transactions on Information Theory. IEEE.
https://doi.org/10.1109/TIT.2022.3189542
chicago: Zhang, Yihan, and Shashank Vatedka. “List Decoding Random Euclidean Codes
and Infinite Constellations.” IEEE Transactions on Information Theory.
IEEE, 2022. https://doi.org/10.1109/TIT.2022.3189542.
ieee: Y. Zhang and S. Vatedka, “List decoding random Euclidean codes and Infinite
constellations,” IEEE Transactions on Information Theory, vol. 68, no.
12. IEEE, pp. 7753–7786, 2022.
ista: Zhang Y, Vatedka S. 2022. List decoding random Euclidean codes and Infinite
constellations. IEEE Transactions on Information Theory. 68(12), 7753–7786.
mla: Zhang, Yihan, and Shashank Vatedka. “List Decoding Random Euclidean Codes and
Infinite Constellations.” IEEE Transactions on Information Theory, vol.
68, no. 12, IEEE, 2022, pp. 7753–86, doi:10.1109/TIT.2022.3189542.
short: Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory 68 (2022) 7753–7786.
date_created: 2022-07-24T22:01:42Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-03T12:12:19Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TIT.2022.3189542
external_id:
arxiv:
- '1901.03790'
isi:
- '000891796100007'
intvolume: ' 68'
isi: 1
issue: '12'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1901.03790
month: '12'
oa: 1
oa_version: Preprint
page: 7753-7786
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: List decoding random Euclidean codes and Infinite constellations
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 68
year: '2022'
...
---
_id: '12233'
abstract:
- lang: eng
text: A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes
based on successive permutations (SP) of the codeword is presented. A low-complexity
SP scheme applied to a subset of the symmetry group of RM codes is first proposed
to carefully select a good codeword permutation on the fly. Then, the proposed
SP technique is integrated into an improved RLD algorithm that initializes different
decoding paths with random codeword permutations, which are sampled from the full
symmetry group of RM codes. Finally, efficient latency and complexity reduction
schemes are introduced that virtually preserve the error-correction performance
of the proposed decoder. Simulation results demonstrate that at the target frame
error rate of 10−3 for the RM code of length 256 with 163 information bits, the
proposed decoder reduces 6% of the computational complexity and 22% of the decoding
latency of the state-of-the-art semi-parallel simplified successive-cancellation
decoder with fast Hadamard transform (SSC-FHT) that uses 96 permutations from
the full symmetry group of RM codes, while relatively maintaining the error-correction
performance and memory consumption of the semi-parallel permuted SSC-FHT decoder.
article_processing_charge: No
article_type: original
author:
- first_name: Nghia
full_name: Doan, Nghia
last_name: Doan
- first_name: Seyyed Ali
full_name: Hashemi, Seyyed Ali
last_name: Hashemi
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Warren J.
full_name: Gross, Warren J.
last_name: Gross
citation:
ama: Doan N, Hashemi SA, Mondelli M, Gross WJ. Decoding Reed-Muller codes with successive
codeword permutations. IEEE Transactions on Communications. 2022;70(11):7134-7145.
doi:10.1109/tcomm.2022.3211101
apa: Doan, N., Hashemi, S. A., Mondelli, M., & Gross, W. J. (2022). Decoding
Reed-Muller codes with successive codeword permutations. IEEE Transactions
on Communications. Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/tcomm.2022.3211101
chicago: Doan, Nghia, Seyyed Ali Hashemi, Marco Mondelli, and Warren J. Gross. “Decoding
Reed-Muller Codes with Successive Codeword Permutations.” IEEE Transactions
on Communications. Institute of Electrical and Electronics Engineers, 2022.
https://doi.org/10.1109/tcomm.2022.3211101.
ieee: N. Doan, S. A. Hashemi, M. Mondelli, and W. J. Gross, “Decoding Reed-Muller
codes with successive codeword permutations,” IEEE Transactions on Communications,
vol. 70, no. 11. Institute of Electrical and Electronics Engineers, pp. 7134–7145,
2022.
ista: Doan N, Hashemi SA, Mondelli M, Gross WJ. 2022. Decoding Reed-Muller codes
with successive codeword permutations. IEEE Transactions on Communications. 70(11),
7134–7145.
mla: Doan, Nghia, et al. “Decoding Reed-Muller Codes with Successive Codeword Permutations.”
IEEE Transactions on Communications, vol. 70, no. 11, Institute of Electrical
and Electronics Engineers, 2022, pp. 7134–45, doi:10.1109/tcomm.2022.3211101.
short: N. Doan, S.A. Hashemi, M. Mondelli, W.J. Gross, IEEE Transactions on Communications
70 (2022) 7134–7145.
date_created: 2023-01-16T09:50:38Z
date_published: 2022-11-01T00:00:00Z
date_updated: 2023-08-04T09:34:43Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/tcomm.2022.3211101
external_id:
arxiv:
- '2109.02122'
isi:
- '000937284600006'
intvolume: ' 70'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2109.02122'
month: '11'
oa: 1
oa_version: Preprint
page: 7134-7145
publication: IEEE Transactions on Communications
publication_identifier:
eissn:
- 1558-0857
issn:
- 0090-6778
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Decoding Reed-Muller codes with successive codeword permutations
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 70
year: '2022'
...
---
_id: '12273'
abstract:
- lang: eng
text: We study communication in the presence of a jamming adversary where quadratic
power constraints are imposed on the transmitter and the jammer. The jamming signal
is allowed to be a function of the codebook, and a noncausal but noisy observation
of the transmitted codeword. For a certain range of the noise-to-signal ratios
(NSRs) of the transmitter and the jammer, we are able to characterize the capacity
of this channel under deterministic encoding or stochastic encoding, i.e., with
no common randomness between the encoder/decoder pair. For the remaining NSR regimes,
we determine the capacity under the assumption of a small amount of common randomness
(at most 2log(n) bits in one sub-regime, and at most Ω(n) bits in the other sub-regime)
available to the encoder-decoder pair. Our proof techniques involve a novel myopic
list-decoding result for achievability, and a Plotkin-type push attack for the
converse in a subregion of the NSRs, both of which may be of independent interest.
We also give bounds on the strong secrecy capacity of this channel assuming that
the jammer is simultaneously eavesdropping.
article_processing_charge: No
article_type: original
author:
- first_name: Yihan
full_name: Zhang, Yihan
id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
last_name: Zhang
- first_name: Shashank
full_name: Vatedka, Shashank
last_name: Vatedka
- first_name: Sidharth
full_name: Jaggi, Sidharth
last_name: Jaggi
- first_name: Anand D.
full_name: Sarwate, Anand D.
last_name: Sarwate
citation:
ama: Zhang Y, Vatedka S, Jaggi S, Sarwate AD. Quadratically constrained myopic adversarial
channels. IEEE Transactions on Information Theory. 2022;68(8):4901-4948.
doi:10.1109/tit.2022.3167554
apa: Zhang, Y., Vatedka, S., Jaggi, S., & Sarwate, A. D. (2022). Quadratically
constrained myopic adversarial channels. IEEE Transactions on Information Theory.
Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/tit.2022.3167554
chicago: Zhang, Yihan, Shashank Vatedka, Sidharth Jaggi, and Anand D. Sarwate. “Quadratically
Constrained Myopic Adversarial Channels.” IEEE Transactions on Information
Theory. Institute of Electrical and Electronics Engineers, 2022. https://doi.org/10.1109/tit.2022.3167554.
ieee: Y. Zhang, S. Vatedka, S. Jaggi, and A. D. Sarwate, “Quadratically constrained
myopic adversarial channels,” IEEE Transactions on Information Theory,
vol. 68, no. 8. Institute of Electrical and Electronics Engineers, pp. 4901–4948,
2022.
ista: Zhang Y, Vatedka S, Jaggi S, Sarwate AD. 2022. Quadratically constrained myopic
adversarial channels. IEEE Transactions on Information Theory. 68(8), 4901–4948.
mla: Zhang, Yihan, et al. “Quadratically Constrained Myopic Adversarial Channels.”
IEEE Transactions on Information Theory, vol. 68, no. 8, Institute of Electrical
and Electronics Engineers, 2022, pp. 4901–48, doi:10.1109/tit.2022.3167554.
short: Y. Zhang, S. Vatedka, S. Jaggi, A.D. Sarwate, IEEE Transactions on Information
Theory 68 (2022) 4901–4948.
date_created: 2023-01-16T10:01:19Z
date_published: 2022-08-01T00:00:00Z
date_updated: 2023-08-04T10:08:49Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/tit.2022.3167554
external_id:
arxiv:
- '1801.05951'
isi:
- '000838527100004'
intvolume: ' 68'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1801.05951
month: '08'
oa: 1
oa_version: Preprint
page: 4901-4948
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quadratically constrained myopic adversarial channels
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 68
year: '2022'
...
---
_id: '10364'
abstract:
- lang: eng
text: 'This paper characterizes the latency of the simplified successive-cancellation
(SSC) decoding scheme for polar codes under hardware resource constraints. In
particular, when the number of processing elements P that can perform SSC decoding
operations in parallel is limited, as is the case in practice, the latency of
SSC decoding is O(N1-1/μ + N/P log2 log2 N/P), where N is the block length of
the code and μ is the scaling exponent of the channel. Three direct consequences
of this bound are presented. First, in a fully-parallel implementation where P
= N/2, the latency of SSC decoding is O(N1-1/μ), which is sublinear in the block
length. This recovers a result from our earlier work. Second, in a fully-serial
implementation where P = 1, the latency of SSC decoding scales as O(N log2 log2
N). The multiplicative constant is also calculated: we show that the latency of
SSC decoding when P = 1 is given by (2 + o(1))N log2 log2 N. Third, in a semi-parallel
implementation, the smallest P that gives the same latency as that of the fully-parallel
implementation is P = N1/μ. The tightness of our bound on SSC decoding latency
and the applicability of the foregoing results is validated through extensive
simulations.'
acknowledgement: "S. A. Hashemi is supported by a Postdoctoral Fellowship from the
Natural Sciences and\r\nEngineering Research Council of Canada (NSERC) and by Huawei.
M. Mondelli is partially\r\nsupported by the 2019 Lopez-Loreta Prize. A. Fazeli
and A. Vardy were supported in part by\r\nthe National Science Foundation under
Grant CCF-1764104."
article_processing_charge: No
article_type: original
author:
- first_name: Seyyed Ali
full_name: Hashemi, Seyyed Ali
last_name: Hashemi
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Arman
full_name: Fazeli, Arman
last_name: Fazeli
- first_name: Alexander
full_name: Vardy, Alexander
last_name: Vardy
- first_name: John
full_name: Cioffi, John
last_name: Cioffi
- first_name: Andrea
full_name: Goldsmith, Andrea
last_name: Goldsmith
citation:
ama: Hashemi SA, Mondelli M, Fazeli A, Vardy A, Cioffi J, Goldsmith A. Parallelism
versus latency in simplified successive-cancellation decoding of polar codes.
IEEE Transactions on Wireless Communications. 2022;21(6):3909-3920. doi:10.1109/TWC.2021.3125626
apa: Hashemi, S. A., Mondelli, M., Fazeli, A., Vardy, A., Cioffi, J., & Goldsmith,
A. (2022). Parallelism versus latency in simplified successive-cancellation decoding
of polar codes. IEEE Transactions on Wireless Communications. Institute
of Electrical and Electronics Engineers. https://doi.org/10.1109/TWC.2021.3125626
chicago: Hashemi, Seyyed Ali, Marco Mondelli, Arman Fazeli, Alexander Vardy, John
Cioffi, and Andrea Goldsmith. “Parallelism versus Latency in Simplified Successive-Cancellation
Decoding of Polar Codes.” IEEE Transactions on Wireless Communications.
Institute of Electrical and Electronics Engineers, 2022. https://doi.org/10.1109/TWC.2021.3125626.
ieee: S. A. Hashemi, M. Mondelli, A. Fazeli, A. Vardy, J. Cioffi, and A. Goldsmith,
“Parallelism versus latency in simplified successive-cancellation decoding of
polar codes,” IEEE Transactions on Wireless Communications, vol. 21, no.
6. Institute of Electrical and Electronics Engineers, pp. 3909–3920, 2022.
ista: Hashemi SA, Mondelli M, Fazeli A, Vardy A, Cioffi J, Goldsmith A. 2022. Parallelism
versus latency in simplified successive-cancellation decoding of polar codes.
IEEE Transactions on Wireless Communications. 21(6), 3909–3920.
mla: Hashemi, Seyyed Ali, et al. “Parallelism versus Latency in Simplified Successive-Cancellation
Decoding of Polar Codes.” IEEE Transactions on Wireless Communications,
vol. 21, no. 6, Institute of Electrical and Electronics Engineers, 2022, pp. 3909–20,
doi:10.1109/TWC.2021.3125626.
short: S.A. Hashemi, M. Mondelli, A. Fazeli, A. Vardy, J. Cioffi, A. Goldsmith,
IEEE Transactions on Wireless Communications 21 (2022) 3909–3920.
date_created: 2021-11-28T23:01:29Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-08-14T06:55:57Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TWC.2021.3125626
external_id:
arxiv:
- '2012.13378'
isi:
- '000809406400028'
intvolume: ' 21'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2012.13378
month: '06'
oa: 1
oa_version: Preprint
page: 3909-3920
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: IEEE Transactions on Wireless Communications
publication_identifier:
eissn:
- 1558-2248
issn:
- 1536-1276
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
related_material:
record:
- id: '10053'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Parallelism versus latency in simplified successive-cancellation decoding of
polar codes
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 21
year: '2022'
...
---
_id: '12538'
abstract:
- lang: eng
text: In this paper, we study the compression of a target two-layer neural network
with N nodes into a compressed network with MIEEE Information Theory Workshop.
2022:588-593. doi:10.1109/ITW54588.2022.9965870
apa: 'Amani, M. H., Bombari, S., Mondelli, M., Pukdee, R., & Rini, S. (2022).
Sharp asymptotics on the compression of two-layer neural networks. IEEE Information
Theory Workshop. Mumbai, India: IEEE. https://doi.org/10.1109/ITW54588.2022.9965870'
chicago: Amani, Mohammad Hossein, Simone Bombari, Marco Mondelli, Rattana Pukdee,
and Stefano Rini. “Sharp Asymptotics on the Compression of Two-Layer Neural Networks.”
IEEE Information Theory Workshop. IEEE, 2022. https://doi.org/10.1109/ITW54588.2022.9965870.
ieee: M. H. Amani, S. Bombari, M. Mondelli, R. Pukdee, and S. Rini, “Sharp asymptotics
on the compression of two-layer neural networks,” IEEE Information Theory Workshop.
IEEE, pp. 588–593, 2022.
ista: Amani MH, Bombari S, Mondelli M, Pukdee R, Rini S. 2022. Sharp asymptotics
on the compression of two-layer neural networks. IEEE Information Theory Workshop.,
588–593.
mla: Amani, Mohammad Hossein, et al. “Sharp Asymptotics on the Compression of Two-Layer
Neural Networks.” IEEE Information Theory Workshop, IEEE, 2022, pp. 588–93,
doi:10.1109/ITW54588.2022.9965870.
short: M.H. Amani, S. Bombari, M. Mondelli, R. Pukdee, S. Rini, IEEE Information
Theory Workshop (2022) 588–593.
conference:
end_date: 2022-11-09
location: Mumbai, India
name: 'ITW: Information Theory Workshop'
start_date: 2022-11-01
date_created: 2023-02-10T13:47:56Z
date_published: 2022-11-16T00:00:00Z
date_updated: 2023-12-18T11:31:47Z
day: '16'
department:
- _id: MaMo
doi: 10.1109/ITW54588.2022.9965870
external_id:
arxiv:
- '2205.08199'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2205.08199'
month: '11'
oa: 1
oa_version: Preprint
page: 588-593
publication: IEEE Information Theory Workshop
publication_identifier:
isbn:
- '9781665483414'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sharp asymptotics on the compression of two-layer neural networks
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '12537'
abstract:
- lang: eng
text: 'The Neural Tangent Kernel (NTK) has emerged as a powerful tool to provide
memorization, optimization and generalization guarantees in deep neural networks.
A line of work has studied the NTK spectrum for two-layer and deep networks with
at least a layer with Ω(N) neurons, N being the number of training samples. Furthermore,
there is increasing evidence suggesting that deep networks with sub-linear layer
widths are powerful memorizers and optimizers, as long as the number of parameters
exceeds the number of samples. Thus, a natural open question is whether the NTK
is well conditioned in such a challenging sub-linear setup. In this paper, we
answer this question in the affirmative. Our key technical contribution is a lower
bound on the smallest NTK eigenvalue for deep networks with the minimum possible
over-parameterization: the number of parameters is roughly Ω(N) and, hence, the
number of neurons is as little as Ω(N−−√). To showcase the applicability of our
NTK bounds, we provide two results concerning memorization capacity and optimization
guarantees for gradient descent training.'
acknowledgement: "The authors were partially supported by the 2019 Lopez-Loreta prize,
and they would like to thank\r\nQuynh Nguyen, Mahdi Soltanolkotabi and Adel Javanmard
for helpful discussions.\r\n"
article_processing_charge: No
author:
- first_name: Simone
full_name: Bombari, Simone
id: ca726dda-de17-11ea-bc14-f9da834f63aa
last_name: Bombari
- first_name: Mohammad Hossein
full_name: Amani, Mohammad Hossein
last_name: Amani
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Bombari S, Amani MH, Mondelli M. Memorization and optimization in deep neural
networks with minimum over-parameterization. In: 36th Conference on Neural
Information Processing Systems. Vol 35. Curran Associates; 2022:7628-7640.'
apa: Bombari, S., Amani, M. H., & Mondelli, M. (2022). Memorization and optimization
in deep neural networks with minimum over-parameterization. In 36th Conference
on Neural Information Processing Systems (Vol. 35, pp. 7628–7640). Curran
Associates.
chicago: Bombari, Simone, Mohammad Hossein Amani, and Marco Mondelli. “Memorization
and Optimization in Deep Neural Networks with Minimum Over-Parameterization.”
In 36th Conference on Neural Information Processing Systems, 35:7628–40.
Curran Associates, 2022.
ieee: S. Bombari, M. H. Amani, and M. Mondelli, “Memorization and optimization in
deep neural networks with minimum over-parameterization,” in 36th Conference
on Neural Information Processing Systems, 2022, vol. 35, pp. 7628–7640.
ista: Bombari S, Amani MH, Mondelli M. 2022. Memorization and optimization in deep
neural networks with minimum over-parameterization. 36th Conference on Neural
Information Processing Systems. vol. 35, 7628–7640.
mla: Bombari, Simone, et al. “Memorization and Optimization in Deep Neural Networks
with Minimum Over-Parameterization.” 36th Conference on Neural Information
Processing Systems, vol. 35, Curran Associates, 2022, pp. 7628–40.
short: S. Bombari, M.H. Amani, M. Mondelli, in:, 36th Conference on Neural Information
Processing Systems, Curran Associates, 2022, pp. 7628–7640.
date_created: 2023-02-10T13:46:37Z
date_published: 2022-07-24T00:00:00Z
date_updated: 2023-12-18T11:39:09Z
day: '24'
department:
- _id: MaMo
external_id:
arxiv:
- '2205.10217'
intvolume: ' 35'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2205.10217'
month: '07'
oa: 1
oa_version: Preprint
page: 7628-7640
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 36th Conference on Neural Information Processing Systems
publication_identifier:
isbn:
- '9781713871088'
publication_status: published
publisher: Curran Associates
quality_controlled: '1'
status: public
title: Memorization and optimization in deep neural networks with minimum over-parameterization
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2022'
...
---
_id: '12480'
abstract:
- lang: eng
text: 'We consider the problem of estimating a signal from measurements obtained
via a generalized linear model. We focus on estimators based on approximate message
passing (AMP), a family of iterative algorithms with many appealing features:
the performance of AMP in the high-dimensional limit can be succinctly characterized
under suitable model assumptions; AMP can also be tailored to the empirical distribution
of the signal entries, and for a wide class of estimation problems, AMP is conjectured
to be optimal among all polynomial-time algorithms. However, a major issue of
AMP is that in many models (such as phase retrieval), it requires an initialization
correlated with the ground-truth signal and independent from the measurement matrix.
Assuming that such an initialization is available is typically not realistic.
In this paper, we solve this problem by proposing an AMP algorithm initialized
with a spectral estimator. With such an initialization, the standard AMP analysis
fails since the spectral estimator depends in a complicated way on the design
matrix. Our main contribution is a rigorous characterization of the performance
of AMP with spectral initialization in the high-dimensional limit. The key technical
idea is to define and analyze a two-phase artificial AMP algorithm that first
produces the spectral estimator, and then closely approximates the iterates of
the true AMP. We also provide numerical results that demonstrate the validity
of the proposed approach.'
acknowledgement: "The authors would like to thank Andrea Montanari for helpful discussions.\r\nM
Mondelli was partially supported by the 2019 Lopez-Loreta Prize. R Venkataramanan
was partially supported by the Alan Turing Institute under the EPSRC Grant\r\nEP/N510129/1."
article_number: '114003'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Ramji
full_name: Venkataramanan, Ramji
last_name: Venkataramanan
citation:
ama: 'Mondelli M, Venkataramanan R. Approximate message passing with spectral initialization
for generalized linear models. Journal of Statistical Mechanics: Theory and
Experiment. 2022;2022(11). doi:10.1088/1742-5468/ac9828'
apa: 'Mondelli, M., & Venkataramanan, R. (2022). Approximate message passing
with spectral initialization for generalized linear models. Journal of Statistical
Mechanics: Theory and Experiment. IOP Publishing. https://doi.org/10.1088/1742-5468/ac9828'
chicago: 'Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing
with Spectral Initialization for Generalized Linear Models.” Journal of Statistical
Mechanics: Theory and Experiment. IOP Publishing, 2022. https://doi.org/10.1088/1742-5468/ac9828.'
ieee: 'M. Mondelli and R. Venkataramanan, “Approximate message passing with spectral
initialization for generalized linear models,” Journal of Statistical Mechanics:
Theory and Experiment, vol. 2022, no. 11. IOP Publishing, 2022.'
ista: 'Mondelli M, Venkataramanan R. 2022. Approximate message passing with spectral
initialization for generalized linear models. Journal of Statistical Mechanics:
Theory and Experiment. 2022(11), 114003.'
mla: 'Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing with
Spectral Initialization for Generalized Linear Models.” Journal of Statistical
Mechanics: Theory and Experiment, vol. 2022, no. 11, 114003, IOP Publishing,
2022, doi:10.1088/1742-5468/ac9828.'
short: 'M. Mondelli, R. Venkataramanan, Journal of Statistical Mechanics: Theory
and Experiment 2022 (2022).'
date_created: 2023-02-02T08:31:57Z
date_published: 2022-11-24T00:00:00Z
date_updated: 2024-03-07T10:36:52Z
day: '24'
ddc:
- '510'
- '530'
department:
- _id: MaMo
doi: 10.1088/1742-5468/ac9828
external_id:
isi:
- '000889589900001'
file:
- access_level: open_access
checksum: 01411ffa76d3e380a0446baeb89b1ef7
content_type: application/pdf
creator: dernst
date_created: 2023-02-02T08:35:52Z
date_updated: 2023-02-02T08:35:52Z
file_id: '12481'
file_name: 2022_JourStatisticalMechanics_Mondelli.pdf
file_size: 1729997
relation: main_file
success: 1
file_date_updated: 2023-02-02T08:35:52Z
has_accepted_license: '1'
intvolume: ' 2022'
isi: 1
issue: '11'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
issn:
- 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
related_material:
record:
- id: '10598'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Approximate message passing with spectral initialization for generalized linear
models
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2022
year: '2022'
...
---
_id: '10595'
abstract:
- lang: eng
text: 'A recent line of work has analyzed the theoretical properties of deep neural
networks via the Neural Tangent Kernel (NTK). In particular, the smallest eigenvalue
of the NTK has been related to the memorization capacity, the global convergence
of gradient descent algorithms and the generalization of deep nets. However, existing
results either provide bounds in the two-layer setting or assume that the spectrum
of the NTK matrices is bounded away from 0 for multi-layer networks. In this paper,
we provide tight bounds on the smallest eigenvalue of NTK matrices for deep ReLU
nets, both in the limiting case of infinite widths and for finite widths. In the
finite-width setting, the network architectures we consider are fairly general:
we require the existence of a wide layer with roughly order of $N$ neurons, $N$
being the number of data samples; and the scaling of the remaining layer widths
is arbitrary (up to logarithmic factors). To obtain our results, we analyze various
quantities of independent interest: we give lower bounds on the smallest singular
value of hidden feature matrices, and upper bounds on the Lipschitz constant of
input-output feature maps.'
acknowledgement: "The authors would like to thank the anonymous reviewers for their
helpful comments. MM was partially supported\r\nby the 2019 Lopez-Loreta Prize.
QN and GM acknowledge support from the European Research Council (ERC) under\r\nthe
European Union’s Horizon 2020 research and innovation programme (grant agreement
no 757983)."
alternative_title:
- Proceedings of Machine Learning Research
article_processing_charge: No
author:
- first_name: Quynh
full_name: Nguyen, Quynh
last_name: Nguyen
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Guido F
full_name: Montufar, Guido F
last_name: Montufar
citation:
ama: 'Nguyen Q, Mondelli M, Montufar GF. Tight bounds on the smallest eigenvalue
of the neural tangent kernel for deep ReLU networks. In: Meila M, Zhang T, eds.
Proceedings of the 38th International Conference on Machine Learning. Vol
139. ML Research Press; 2021:8119-8129.'
apa: 'Nguyen, Q., Mondelli, M., & Montufar, G. F. (2021). Tight bounds on the
smallest eigenvalue of the neural tangent kernel for deep ReLU networks. In M.
Meila & T. Zhang (Eds.), Proceedings of the 38th International Conference
on Machine Learning (Vol. 139, pp. 8119–8129). Virtual: ML Research Press.'
chicago: Nguyen, Quynh, Marco Mondelli, and Guido F Montufar. “Tight Bounds on the
Smallest Eigenvalue of the Neural Tangent Kernel for Deep ReLU Networks.” In Proceedings
of the 38th International Conference on Machine Learning, edited by Marina
Meila and Tong Zhang, 139:8119–29. ML Research Press, 2021.
ieee: Q. Nguyen, M. Mondelli, and G. F. Montufar, “Tight bounds on the smallest
eigenvalue of the neural tangent kernel for deep ReLU networks,” in Proceedings
of the 38th International Conference on Machine Learning, Virtual, 2021, vol.
139, pp. 8119–8129.
ista: 'Nguyen Q, Mondelli M, Montufar GF. 2021. Tight bounds on the smallest eigenvalue
of the neural tangent kernel for deep ReLU networks. Proceedings of the 38th International
Conference on Machine Learning. ICML: International Conference on Machine Learning,
Proceedings of Machine Learning Research, vol. 139, 8119–8129.'
mla: Nguyen, Quynh, et al. “Tight Bounds on the Smallest Eigenvalue of the Neural
Tangent Kernel for Deep ReLU Networks.” Proceedings of the 38th International
Conference on Machine Learning, edited by Marina Meila and Tong Zhang, vol.
139, ML Research Press, 2021, pp. 8119–29.
short: Q. Nguyen, M. Mondelli, G.F. Montufar, in:, M. Meila, T. Zhang (Eds.), Proceedings
of the 38th International Conference on Machine Learning, ML Research Press, 2021,
pp. 8119–8129.
conference:
end_date: 2021-07-24
location: Virtual
name: 'ICML: International Conference on Machine Learning'
start_date: 2021-07-18
date_created: 2022-01-03T10:57:49Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2022-01-04T09:59:21Z
department:
- _id: MaMo
editor:
- first_name: Marina
full_name: Meila, Marina
last_name: Meila
- first_name: Tong
full_name: Zhang, Tong
last_name: Zhang
external_id:
arxiv:
- '2012.11654'
intvolume: ' 139'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://proceedings.mlr.press/v139/nguyen21g.html
oa: 1
oa_version: Published Version
page: 8119-8129
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 38th International Conference on Machine Learning
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
status: public
title: Tight bounds on the smallest eigenvalue of the neural tangent kernel for deep
ReLU networks
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 139
year: '2021'
...
---
_id: '10599'
abstract:
- lang: eng
text: A two-part successive syndrome-check decoding of polar codes is proposed with
the first part successively refining the received codeword and the second part
checking its syndrome. A new formulation of the successive-cancellation (SC) decoding
algorithm is presented that allows for successively refining the received codeword
by comparing the log-likelihood ratio value of a frozen bit with its predefined
value. The syndrome of the refined received codeword is then checked for possible
errors. In case there are no errors, the decoding process is terminated. Otherwise,
the decoder continues to refine the received codeword. The proposed method is
extended to the case of SC list (SCL) decoding by terminating the decoding process
when the syndrome of the best candidate in the list indicates no errors. Simulation
results show that the proposed method reduces the time-complexity of SC and SCL
decoders and their fast variants, especially at high signal-to-noise ratios.
acknowledgement: This work is supported in part by ONR grant N00014-18-1-2191. S.
A. Hashemi was supported by a Postdoctoral Fellowship from the Natural Sciences
and Engineering Research Council of Canada (NSERC) and by Huawei. M. Mondelli was
partially supported by the 2019 Lopez-Loreta Prize.
article_processing_charge: No
author:
- first_name: Seyyed Ali
full_name: Hashemi, Seyyed Ali
last_name: Hashemi
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: John
full_name: Cioffi, John
last_name: Cioffi
- first_name: Andrea
full_name: Goldsmith, Andrea
last_name: Goldsmith
citation:
ama: 'Hashemi SA, Mondelli M, Cioffi J, Goldsmith A. Successive syndrome-check decoding
of polar codes. In: Proceedings of the 55th Asilomar Conference on Signals,
Systems, and Computers. Vol 2021-October. Institute of Electrical and Electronics
Engineers; 2021:943-947. doi:10.1109/IEEECONF53345.2021.9723394'
apa: 'Hashemi, S. A., Mondelli, M., Cioffi, J., & Goldsmith, A. (2021). Successive
syndrome-check decoding of polar codes. In Proceedings of the 55th Asilomar
Conference on Signals, Systems, and Computers (Vol. 2021–October, pp. 943–947).
Virtual, Pacific Grove, CA, United States: Institute of Electrical and Electronics
Engineers. https://doi.org/10.1109/IEEECONF53345.2021.9723394'
chicago: Hashemi, Seyyed Ali, Marco Mondelli, John Cioffi, and Andrea Goldsmith.
“Successive Syndrome-Check Decoding of Polar Codes.” In Proceedings of the
55th Asilomar Conference on Signals, Systems, and Computers, 2021–October:943–47.
Institute of Electrical and Electronics Engineers, 2021. https://doi.org/10.1109/IEEECONF53345.2021.9723394.
ieee: S. A. Hashemi, M. Mondelli, J. Cioffi, and A. Goldsmith, “Successive syndrome-check
decoding of polar codes,” in Proceedings of the 55th Asilomar Conference on
Signals, Systems, and Computers, Virtual, Pacific Grove, CA, United States,
2021, vol. 2021–October, pp. 943–947.
ista: 'Hashemi SA, Mondelli M, Cioffi J, Goldsmith A. 2021. Successive syndrome-check
decoding of polar codes. Proceedings of the 55th Asilomar Conference on Signals,
Systems, and Computers. ACSSC: Asilomar Conference on Signals, Systems, and Computers
vol. 2021–October, 943–947.'
mla: Hashemi, Seyyed Ali, et al. “Successive Syndrome-Check Decoding of Polar Codes.”
Proceedings of the 55th Asilomar Conference on Signals, Systems, and Computers,
vol. 2021–October, Institute of Electrical and Electronics Engineers, 2021, pp.
943–47, doi:10.1109/IEEECONF53345.2021.9723394.
short: S.A. Hashemi, M. Mondelli, J. Cioffi, A. Goldsmith, in:, Proceedings of the
55th Asilomar Conference on Signals, Systems, and Computers, Institute of Electrical
and Electronics Engineers, 2021, pp. 943–947.
conference:
end_date: 2021-11-03
location: Virtual, Pacific Grove, CA, United States
name: 'ACSSC: Asilomar Conference on Signals, Systems, and Computers'
start_date: 2021-10-31
date_created: 2022-01-03T11:39:51Z
date_published: 2021-11-01T00:00:00Z
date_updated: 2023-02-13T10:44:16Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/IEEECONF53345.2021.9723394
external_id:
arxiv:
- '2112.00057'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2112.00057'
month: '11'
oa: 1
oa_version: Preprint
page: 943-947
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 55th Asilomar Conference on Signals, Systems, and
Computers
publication_identifier:
isbn:
- '9781665458283'
issn:
- 1058-6393
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Successive syndrome-check decoding of polar codes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2021-October
year: '2021'
...
---
_id: '13146'
abstract:
- lang: eng
text: 'A recent line of work has analyzed the theoretical properties of deep neural
networks via the Neural Tangent Kernel (NTK). In particular, the smallest eigenvalue
of the NTK has been related to the memorization capacity, the global convergence
of gradient descent algorithms and the generalization of deep nets. However, existing
results either provide bounds in the two-layer setting or assume that the spectrum
of the NTK matrices is bounded away from 0 for multi-layer networks. In this paper,
we provide tight bounds on the smallest eigenvalue of NTK matrices for deep ReLU
nets, both in the limiting case of infinite widths and for finite widths. In the
finite-width setting, the network architectures we consider are fairly general:
we require the existence of a wide layer with roughly order of N neurons, N being
the number of data samples; and the scaling of the remaining layer widths is arbitrary
(up to logarithmic factors). To obtain our results, we analyze various quantities
of independent interest: we give lower bounds on the smallest singular value of
hidden feature matrices, and upper bounds on the Lipschitz constant of input-output
feature maps.'
acknowledgement: The authors would like to thank the anonymous reviewers for their
helpful comments. MM was partially supported by the 2019 Lopez-Loreta Prize. QN
and GM acknowledge support from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (grant agreement no 757983).
article_processing_charge: No
author:
- first_name: Quynh
full_name: Nguyen, Quynh
last_name: Nguyen
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Guido
full_name: Montufar, Guido
last_name: Montufar
citation:
ama: 'Nguyen Q, Mondelli M, Montufar G. Tight bounds on the smallest Eigenvalue
of the neural tangent kernel for deep ReLU networks. In: Proceedings of the
38th International Conference on Machine Learning. Vol 139. ML Research Press;
2021:8119-8129.'
apa: 'Nguyen, Q., Mondelli, M., & Montufar, G. (2021). Tight bounds on the smallest
Eigenvalue of the neural tangent kernel for deep ReLU networks. In Proceedings
of the 38th International Conference on Machine Learning (Vol. 139, pp. 8119–8129).
Virtual: ML Research Press.'
chicago: Nguyen, Quynh, Marco Mondelli, and Guido Montufar. “Tight Bounds on the
Smallest Eigenvalue of the Neural Tangent Kernel for Deep ReLU Networks.” In Proceedings
of the 38th International Conference on Machine Learning, 139:8119–29. ML
Research Press, 2021.
ieee: Q. Nguyen, M. Mondelli, and G. Montufar, “Tight bounds on the smallest Eigenvalue
of the neural tangent kernel for deep ReLU networks,” in Proceedings of the
38th International Conference on Machine Learning, Virtual, 2021, vol. 139,
pp. 8119–8129.
ista: Nguyen Q, Mondelli M, Montufar G. 2021. Tight bounds on the smallest Eigenvalue
of the neural tangent kernel for deep ReLU networks. Proceedings of the 38th International
Conference on Machine Learning. International Conference on Machine Learning vol.
139, 8119–8129.
mla: Nguyen, Quynh, et al. “Tight Bounds on the Smallest Eigenvalue of the Neural
Tangent Kernel for Deep ReLU Networks.” Proceedings of the 38th International
Conference on Machine Learning, vol. 139, ML Research Press, 2021, pp. 8119–29.
short: Q. Nguyen, M. Mondelli, G. Montufar, in:, Proceedings of the 38th International
Conference on Machine Learning, ML Research Press, 2021, pp. 8119–8129.
conference:
end_date: 2021-07-24
location: Virtual
name: International Conference on Machine Learning
start_date: 2021-07-18
date_created: 2023-06-18T22:00:48Z
date_published: 2021-07-01T00:00:00Z
date_updated: 2023-06-19T10:52:51Z
day: '01'
ddc:
- '000'
department:
- _id: MaMo
external_id:
arxiv:
- '2012.11654'
file:
- access_level: open_access
checksum: 19489cf5e16a0596b1f92e317d97c9b0
content_type: application/pdf
creator: dernst
date_created: 2023-06-19T10:49:12Z
date_updated: 2023-06-19T10:49:12Z
file_id: '13155'
file_name: 2021_PMLR_Nguyen.pdf
file_size: 591332
relation: main_file
success: 1
file_date_updated: 2023-06-19T10:49:12Z
has_accepted_license: '1'
intvolume: ' 139'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 8119-8129
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 38th International Conference on Machine Learning
publication_identifier:
eissn:
- 2640-3498
isbn:
- '9781713845065'
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tight bounds on the smallest Eigenvalue of the neural tangent kernel for deep
ReLU networks
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 139
year: '2021'
...
---
_id: '9047'
abstract:
- lang: eng
text: This work analyzes the latency of the simplified successive cancellation (SSC)
decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It
is shown that, unlike conventional successive cancellation decoding, where latency
is linear in the block length, the latency of SSC decoding is sublinear. More
specifically, the latency of SSC decoding is O(N1−1/μ) , where N is the block
length and μ is the scaling exponent of the channel, which captures the speed
of convergence of the rate to capacity. Numerical results demonstrate the tightness
of the bound and show that most of the latency reduction arises from the parallel
decoding of subcodes of rate 0 or 1.
acknowledgement: M. Mondelli was partially supported by grants NSF DMS-1613091, CCF-1714305,
IIS-1741162, and ONR N00014-18-1-2729. S. A. Hashemi is supported by a Postdoctoral
Fellowship from the Natural Sciences and Engineering Research Council of Canada
(NSERC) and by Huawei. The authors would like to thank the anonymous reviewers for
their comments that helped improving the quality of the manuscript.
article_processing_charge: No
article_type: original
author:
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Seyyed Ali
full_name: Hashemi, Seyyed Ali
last_name: Hashemi
- first_name: John M.
full_name: Cioffi, John M.
last_name: Cioffi
- first_name: Andrea
full_name: Goldsmith, Andrea
last_name: Goldsmith
citation:
ama: Mondelli M, Hashemi SA, Cioffi JM, Goldsmith A. Sublinear latency for simplified
successive cancellation decoding of polar codes. IEEE Transactions on Wireless
Communications. 2021;20(1):18-27. doi:10.1109/TWC.2020.3022922
apa: Mondelli, M., Hashemi, S. A., Cioffi, J. M., & Goldsmith, A. (2021). Sublinear
latency for simplified successive cancellation decoding of polar codes. IEEE
Transactions on Wireless Communications. IEEE. https://doi.org/10.1109/TWC.2020.3022922
chicago: Mondelli, Marco, Seyyed Ali Hashemi, John M. Cioffi, and Andrea Goldsmith.
“Sublinear Latency for Simplified Successive Cancellation Decoding of Polar Codes.”
IEEE Transactions on Wireless Communications. IEEE, 2021. https://doi.org/10.1109/TWC.2020.3022922.
ieee: M. Mondelli, S. A. Hashemi, J. M. Cioffi, and A. Goldsmith, “Sublinear latency
for simplified successive cancellation decoding of polar codes,” IEEE Transactions
on Wireless Communications, vol. 20, no. 1. IEEE, pp. 18–27, 2021.
ista: Mondelli M, Hashemi SA, Cioffi JM, Goldsmith A. 2021. Sublinear latency for
simplified successive cancellation decoding of polar codes. IEEE Transactions
on Wireless Communications. 20(1), 18–27.
mla: Mondelli, Marco, et al. “Sublinear Latency for Simplified Successive Cancellation
Decoding of Polar Codes.” IEEE Transactions on Wireless Communications,
vol. 20, no. 1, IEEE, 2021, pp. 18–27, doi:10.1109/TWC.2020.3022922.
short: M. Mondelli, S.A. Hashemi, J.M. Cioffi, A. Goldsmith, IEEE Transactions on
Wireless Communications 20 (2021) 18–27.
date_created: 2021-01-31T23:01:21Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-07T13:36:25Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TWC.2020.3022922
external_id:
arxiv:
- '1909.04892'
isi:
- '000607808800002'
intvolume: ' 20'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1909.04892
month: '01'
oa: 1
oa_version: Preprint
page: 18-27
publication: IEEE Transactions on Wireless Communications
publication_identifier:
eissn:
- '15582248'
issn:
- '15361276'
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
record:
- id: '8536'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Sublinear latency for simplified successive cancellation decoding of polar
codes
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 20
year: '2021'
...
---
_id: '10053'
abstract:
- lang: eng
text: 'This paper characterizes the latency of the simplified successive-cancellation
(SSC) decoding scheme for polar codes under hardware resource constraints. In
particular, when the number of processing elements P that can perform SSC decoding
operations in parallel is limited, as is the case in practice, the latency of
SSC decoding is O(N1−1 μ+NPlog2log2NP), where N is the block length of the code
and μ is the scaling exponent of polar codes for the channel. Three direct consequences
of this bound are presented. First, in a fully-parallel implementation where P=N2
, the latency of SSC decoding is O(N1−1/μ) , which is sublinear in the block length.
This recovers a result from an earlier work. Second, in a fully-serial implementation
where P=1 , the latency of SSC decoding scales as O(Nlog2log2N) . The multiplicative
constant is also calculated: we show that the latency of SSC decoding when P=1
is given by (2+o(1))Nlog2log2N . Third, in a semi-parallel implementation, the
smallest P that gives the same latency as that of the fully-parallel implementation
is P=N1/μ . The tightness of our bound on SSC decoding latency and the applicability
of the foregoing results is validated through extensive simulations.'
acknowledgement: "S. A. Hashemi is supported by a Postdoctoral Fellowship from the
Natural Sciences and Engineering Research Council\r\nof Canada (NSERC) and by Huawei.
M. Mondelli is partially supported by the 2019 Lopez-Loreta Prize. A. Fazeli and
A. Vardy were supported in part by the National Science Foundation under Grant CCF-1764104."
article_processing_charge: No
author:
- first_name: Seyyed Ali
full_name: Hashemi, Seyyed Ali
last_name: Hashemi
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Arman
full_name: Fazeli, Arman
last_name: Fazeli
- first_name: Alexander
full_name: Vardy, Alexander
last_name: Vardy
- first_name: John
full_name: Cioffi, John
last_name: Cioffi
- first_name: Andrea
full_name: Goldsmith, Andrea
last_name: Goldsmith
citation:
ama: 'Hashemi SA, Mondelli M, Fazeli A, Vardy A, Cioffi J, Goldsmith A. Parallelism
versus latency in simplified successive-cancellation decoding of polar codes.
In: 2021 IEEE International Symposium on Information Theory. Institute
of Electrical and Electronics Engineers; 2021:2369-2374. doi:10.1109/ISIT45174.2021.9518153'
apa: 'Hashemi, S. A., Mondelli, M., Fazeli, A., Vardy, A., Cioffi, J., & Goldsmith,
A. (2021). Parallelism versus latency in simplified successive-cancellation decoding
of polar codes. In 2021 IEEE International Symposium on Information Theory
(pp. 2369–2374). Melbourne, Australia: Institute of Electrical and Electronics
Engineers. https://doi.org/10.1109/ISIT45174.2021.9518153'
chicago: Hashemi, Seyyed Ali, Marco Mondelli, Arman Fazeli, Alexander Vardy, John
Cioffi, and Andrea Goldsmith. “Parallelism versus Latency in Simplified Successive-Cancellation
Decoding of Polar Codes.” In 2021 IEEE International Symposium on Information
Theory, 2369–74. Institute of Electrical and Electronics Engineers, 2021.
https://doi.org/10.1109/ISIT45174.2021.9518153.
ieee: S. A. Hashemi, M. Mondelli, A. Fazeli, A. Vardy, J. Cioffi, and A. Goldsmith,
“Parallelism versus latency in simplified successive-cancellation decoding of
polar codes,” in 2021 IEEE International Symposium on Information Theory,
Melbourne, Australia, 2021, pp. 2369–2374.
ista: 'Hashemi SA, Mondelli M, Fazeli A, Vardy A, Cioffi J, Goldsmith A. 2021. Parallelism
versus latency in simplified successive-cancellation decoding of polar codes.
2021 IEEE International Symposium on Information Theory. ISIT: International Symposium
on Information Theory, 2369–2374.'
mla: Hashemi, Seyyed Ali, et al. “Parallelism versus Latency in Simplified Successive-Cancellation
Decoding of Polar Codes.” 2021 IEEE International Symposium on Information
Theory, Institute of Electrical and Electronics Engineers, 2021, pp. 2369–74,
doi:10.1109/ISIT45174.2021.9518153.
short: S.A. Hashemi, M. Mondelli, A. Fazeli, A. Vardy, J. Cioffi, A. Goldsmith,
in:, 2021 IEEE International Symposium on Information Theory, Institute of Electrical
and Electronics Engineers, 2021, pp. 2369–2374.
conference:
end_date: 2021-07-20
location: Melbourne, Australia
name: 'ISIT: International Symposium on Information Theory'
start_date: 2021-07-12
date_created: 2021-09-27T14:33:14Z
date_published: 2021-09-01T00:00:00Z
date_updated: 2023-08-14T06:55:58Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/ISIT45174.2021.9518153
external_id:
arxiv:
- '2012.13378'
isi:
- '000701502202078'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2012.13378
month: '09'
oa: 1
oa_version: Preprint
page: 2369-2374
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 2021 IEEE International Symposium on Information Theory
publication_identifier:
eisbn:
- 978-1-5386-8209-8
isbn:
- 978-1-5386-8210-4
issn:
- 2157-8095
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
related_material:
record:
- id: '10364'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Parallelism versus latency in simplified successive-cancellation decoding of
polar codes
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '10597'
abstract:
- lang: eng
text: We thank Emmanuel Abbe and Min Ye for providing us the implementation of RPA
decoding. D. Fathollahi and M. Mondelli are partially supported by the 2019 Lopez-Loreta
Prize. N. Farsad is supported by Discovery Grant from the Natural Sciences and
Engineering Research Council of Canada (NSERC) and Canada Foundation for Innovation
(CFI), John R. Evans Leader Fund. S. A. Hashemi is supported by a Postdoctoral
Fellowship from NSERC.
article_processing_charge: No
author:
- first_name: Dorsa
full_name: Fathollahi, Dorsa
last_name: Fathollahi
- first_name: Nariman
full_name: Farsad, Nariman
last_name: Farsad
- first_name: Seyyed Ali
full_name: Hashemi, Seyyed Ali
last_name: Hashemi
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Fathollahi D, Farsad N, Hashemi SA, Mondelli M. Sparse multi-decoder recursive
projection aggregation for Reed-Muller codes. In: 2021 IEEE International Symposium
on Information Theory. Institute of Electrical and Electronics Engineers;
2021:1082-1087. doi:10.1109/isit45174.2021.9517887'
apa: 'Fathollahi, D., Farsad, N., Hashemi, S. A., & Mondelli, M. (2021). Sparse
multi-decoder recursive projection aggregation for Reed-Muller codes. In 2021
IEEE International Symposium on Information Theory (pp. 1082–1087). Virtual,
Melbourne, Australia: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/isit45174.2021.9517887'
chicago: Fathollahi, Dorsa, Nariman Farsad, Seyyed Ali Hashemi, and Marco Mondelli.
“Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes.”
In 2021 IEEE International Symposium on Information Theory, 1082–87. Institute
of Electrical and Electronics Engineers, 2021. https://doi.org/10.1109/isit45174.2021.9517887.
ieee: D. Fathollahi, N. Farsad, S. A. Hashemi, and M. Mondelli, “Sparse multi-decoder
recursive projection aggregation for Reed-Muller codes,” in 2021 IEEE International
Symposium on Information Theory, Virtual, Melbourne, Australia, 2021, pp.
1082–1087.
ista: 'Fathollahi D, Farsad N, Hashemi SA, Mondelli M. 2021. Sparse multi-decoder
recursive projection aggregation for Reed-Muller codes. 2021 IEEE International
Symposium on Information Theory. ISIT: International Symposium on Information
Theory, 1082–1087.'
mla: Fathollahi, Dorsa, et al. “Sparse Multi-Decoder Recursive Projection Aggregation
for Reed-Muller Codes.” 2021 IEEE International Symposium on Information Theory,
Institute of Electrical and Electronics Engineers, 2021, pp. 1082–87, doi:10.1109/isit45174.2021.9517887.
short: D. Fathollahi, N. Farsad, S.A. Hashemi, M. Mondelli, in:, 2021 IEEE International
Symposium on Information Theory, Institute of Electrical and Electronics Engineers,
2021, pp. 1082–1087.
conference:
end_date: 2021-07-20
location: Virtual, Melbourne, Australia
name: 'ISIT: International Symposium on Information Theory'
start_date: 2021-07-12
date_created: 2022-01-03T11:31:26Z
date_published: 2021-09-01T00:00:00Z
date_updated: 2023-08-17T06:32:06Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/isit45174.2021.9517887
external_id:
arxiv:
- '2011.12882'
isi:
- '000701502201029'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2011.12882
month: '09'
oa: 1
oa_version: Preprint
page: 1082-1087
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 2021 IEEE International Symposium on Information Theory
publication_identifier:
eisbn:
- 978-1-5386-8209-8
isbn:
- 978-1-5386-8210-4
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sparse multi-decoder recursive projection aggregation for Reed-Muller codes
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '10211'
abstract:
- lang: eng
text: "We study the problem of recovering an unknown signal \U0001D465\U0001D465
given measurements obtained from a generalized linear model with a Gaussian sensing
matrix. Two popular solutions are based on a linear estimator \U0001D465\U0001D465^L
and a spectral estimator \U0001D465\U0001D465^s. The former is a data-dependent
linear combination of the columns of the measurement matrix, and its analysis
is quite simple. The latter is the principal eigenvector of a data-dependent matrix,
and a recent line of work has studied its performance. In this paper, we show
how to optimally combine \U0001D465\U0001D465^L and \U0001D465\U0001D465^s. At
the heart of our analysis is the exact characterization of the empirical joint
distribution of (\U0001D465\U0001D465,\U0001D465\U0001D465^L,\U0001D465\U0001D465^s)
in the high-dimensional limit. This allows us to compute the Bayes-optimal combination
of \U0001D465\U0001D465^L and \U0001D465\U0001D465^s, given the limiting distribution
of the signal \U0001D465\U0001D465. When the distribution of the signal is Gaussian,
then the Bayes-optimal combination has the form \U0001D703\U0001D465\U0001D465^L+\U0001D465\U0001D465^s
and we derive the optimal combination coefficient. In order to establish the limiting
distribution of (\U0001D465\U0001D465,\U0001D465\U0001D465^L,\U0001D465\U0001D465^s),
we design and analyze an approximate message passing algorithm whose iterates
give \U0001D465\U0001D465^L and approach \U0001D465\U0001D465^s. Numerical simulations
demonstrate the improvement of the proposed combination with respect to the two
methods considered separately."
acknowledgement: M. Mondelli would like to thank Andrea Montanari for helpful discussions.
All the authors would like to thank the anonymous reviewers for their helpful comments.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Christos
full_name: Thrampoulidis, Christos
last_name: Thrampoulidis
- first_name: Ramji
full_name: Venkataramanan, Ramji
last_name: Venkataramanan
citation:
ama: Mondelli M, Thrampoulidis C, Venkataramanan R. Optimal combination of linear
and spectral estimators for generalized linear models. Foundations of Computational
Mathematics. 2021. doi:10.1007/s10208-021-09531-x
apa: Mondelli, M., Thrampoulidis, C., & Venkataramanan, R. (2021). Optimal combination
of linear and spectral estimators for generalized linear models. Foundations
of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-021-09531-x
chicago: Mondelli, Marco, Christos Thrampoulidis, and Ramji Venkataramanan. “Optimal
Combination of Linear and Spectral Estimators for Generalized Linear Models.”
Foundations of Computational Mathematics. Springer, 2021. https://doi.org/10.1007/s10208-021-09531-x.
ieee: M. Mondelli, C. Thrampoulidis, and R. Venkataramanan, “Optimal combination
of linear and spectral estimators for generalized linear models,” Foundations
of Computational Mathematics. Springer, 2021.
ista: Mondelli M, Thrampoulidis C, Venkataramanan R. 2021. Optimal combination of
linear and spectral estimators for generalized linear models. Foundations of Computational
Mathematics.
mla: Mondelli, Marco, et al. “Optimal Combination of Linear and Spectral Estimators
for Generalized Linear Models.” Foundations of Computational Mathematics,
Springer, 2021, doi:10.1007/s10208-021-09531-x.
short: M. Mondelli, C. Thrampoulidis, R. Venkataramanan, Foundations of Computational
Mathematics (2021).
date_created: 2021-11-03T10:59:08Z
date_published: 2021-08-17T00:00:00Z
date_updated: 2023-09-05T14:13:57Z
day: '17'
ddc:
- '510'
department:
- _id: MaMo
doi: 10.1007/s10208-021-09531-x
external_id:
arxiv:
- '2008.03326'
isi:
- '000685721000001'
file:
- access_level: open_access
checksum: 9ea12dd8045a0678000a3a59295221cb
content_type: application/pdf
creator: alisjak
date_created: 2021-12-13T15:47:54Z
date_updated: 2021-12-13T15:47:54Z
file_id: '10542'
file_name: 2021_Springer_Mondelli.pdf
file_size: 2305731
relation: main_file
success: 1
file_date_updated: 2021-12-13T15:47:54Z
has_accepted_license: '1'
isi: 1
keyword:
- Applied Mathematics
- Computational Theory and Mathematics
- Computational Mathematics
- Analysis
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal combination of linear and spectral estimators for generalized linear
models
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2021'
...
---
_id: '10593'
abstract:
- lang: eng
text: 'We study the problem of estimating a rank-$1$ signal in the presence of rotationally
invariant noise-a class of perturbations more general than Gaussian noise. Principal
Component Analysis (PCA) provides a natural estimator, and sharp results on its
performance have been obtained in the high-dimensional regime. Recently, an Approximate
Message Passing (AMP) algorithm has been proposed as an alternative estimator
with the potential to improve the accuracy of PCA. However, the existing analysis
of AMP requires an initialization that is both correlated with the signal and
independent of the noise, which is often unrealistic in practice. In this work,
we combine the two methods, and propose to initialize AMP with PCA. Our main result
is a rigorous asymptotic characterization of the performance of this estimator.
Both the AMP algorithm and its analysis differ from those previously derived in
the Gaussian setting: at every iteration, our AMP algorithm requires a specific
term to account for PCA initialization, while in the Gaussian case, PCA initialization
affects only the first iteration of AMP. The proof is based on a two-phase artificial
AMP that first approximates the PCA estimator and then mimics the true AMP. Our
numerical simulations show an excellent agreement between AMP results and theoretical
predictions, and suggest an interesting open direction on achieving Bayes-optimal
performance.'
acknowledgement: "M. Mondelli would like to thank László Erdős for helpful discussions.
M. Mondelli was partially supported by the 2019 Lopez-Loreta Prize. R. Venkataramanan
was partially supported by the Alan Turing Institute under the EPSRC grant EP/N510129/1.\r\n"
article_processing_charge: No
author:
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Ramji
full_name: Venkataramanan, Ramji
last_name: Venkataramanan
citation:
ama: 'Mondelli M, Venkataramanan R. PCA initialization for approximate message passing
in rotationally invariant models. In: 35th Conference on Neural Information
Processing Systems. Vol 35. Neural Information Processing Systems Foundation;
2021:29616-29629.'
apa: 'Mondelli, M., & Venkataramanan, R. (2021). PCA initialization for approximate
message passing in rotationally invariant models. In 35th Conference on Neural
Information Processing Systems (Vol. 35, pp. 29616–29629). Virtual: Neural
Information Processing Systems Foundation.'
chicago: Mondelli, Marco, and Ramji Venkataramanan. “PCA Initialization for Approximate
Message Passing in Rotationally Invariant Models.” In 35th Conference on Neural
Information Processing Systems, 35:29616–29. Neural Information Processing
Systems Foundation, 2021.
ieee: M. Mondelli and R. Venkataramanan, “PCA initialization for approximate message
passing in rotationally invariant models,” in 35th Conference on Neural Information
Processing Systems, Virtual, 2021, vol. 35, pp. 29616–29629.
ista: 'Mondelli M, Venkataramanan R. 2021. PCA initialization for approximate message
passing in rotationally invariant models. 35th Conference on Neural Information
Processing Systems. NeurIPS: Neural Information Processing Systems vol. 35, 29616–29629.'
mla: Mondelli, Marco, and Ramji Venkataramanan. “PCA Initialization for Approximate
Message Passing in Rotationally Invariant Models.” 35th Conference on Neural
Information Processing Systems, vol. 35, Neural Information Processing Systems
Foundation, 2021, pp. 29616–29.
short: M. Mondelli, R. Venkataramanan, in:, 35th Conference on Neural Information
Processing Systems, Neural Information Processing Systems Foundation, 2021, pp.
29616–29629.
conference:
end_date: 2021-12-14
location: Virtual
name: 'NeurIPS: Neural Information Processing Systems'
start_date: 2021-12-06
date_created: 2022-01-03T10:50:02Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2023-10-17T11:48:23Z
day: '01'
department:
- _id: MaMo
external_id:
arxiv:
- '2106.02356'
intvolume: ' 35'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2106.02356
month: '12'
oa: 1
oa_version: Preprint
page: 29616-29629
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 35th Conference on Neural Information Processing Systems
publication_identifier:
isbn:
- '9781713845393'
issn:
- 1049-5258
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
scopus_import: '1'
status: public
title: PCA initialization for approximate message passing in rotationally invariant
models
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2021'
...
---
_id: '10594'
abstract:
- lang: eng
text: 'The question of how and why the phenomenon of mode connectivity occurs in
training deep neural networks has gained remarkable attention in the research
community. From a theoretical perspective, two possible explanations have been
proposed: (i) the loss function has connected sublevel sets, and (ii) the solutions
found by stochastic gradient descent are dropout stable. While these explanations
provide insights into the phenomenon, their assumptions are not always satisfied
in practice. In particular, the first approach requires the network to have one
layer with order of N neurons (N being the number of training samples), while
the second one requires the loss to be almost invariant after removing half of
the neurons at each layer (up to some rescaling of the remaining ones). In this
work, we improve both conditions by exploiting the quality of the features at
every intermediate layer together with a milder over-parameterization condition.
More specifically, we show that: (i) under generic assumptions on the features
of intermediate layers, it suffices that the last two hidden layers have order
of N−−√ neurons, and (ii) if subsets of features at each layer are linearly separable,
then no over-parameterization is needed to show the connectivity. Our experiments
confirm that the proposed condition ensures the connectivity of solutions found
by stochastic gradient descent, even in settings where the previous requirements
do not hold.'
acknowledgement: MM was partially supported by the 2019 Lopez-Loreta Prize. QN and
PB acknowledge support from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (grant agreement no 757983).
article_processing_charge: No
author:
- first_name: Quynh
full_name: Nguyen, Quynh
last_name: Nguyen
- first_name: Pierre
full_name: Bréchet, Pierre
last_name: Bréchet
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Nguyen Q, Bréchet P, Mondelli M. When are solutions connected in deep networks?
In: 35th Conference on Neural Information Processing Systems. Vol 35. Neural
Information Processing Systems Foundation; 2021.'
apa: 'Nguyen, Q., Bréchet, P., & Mondelli, M. (2021). When are solutions connected
in deep networks? In 35th Conference on Neural Information Processing Systems
(Vol. 35). Virtual: Neural Information Processing Systems Foundation.'
chicago: Nguyen, Quynh, Pierre Bréchet, and Marco Mondelli. “When Are Solutions
Connected in Deep Networks?” In 35th Conference on Neural Information Processing
Systems, Vol. 35. Neural Information Processing Systems Foundation, 2021.
ieee: Q. Nguyen, P. Bréchet, and M. Mondelli, “When are solutions connected in deep
networks?,” in 35th Conference on Neural Information Processing Systems,
Virtual, 2021, vol. 35.
ista: Nguyen Q, Bréchet P, Mondelli M. 2021. When are solutions connected in deep
networks? 35th Conference on Neural Information Processing Systems. 35th Conference
on Neural Information Processing Systems vol. 35.
mla: Nguyen, Quynh, et al. “When Are Solutions Connected in Deep Networks?” 35th
Conference on Neural Information Processing Systems, vol. 35, Neural Information
Processing Systems Foundation, 2021.
short: Q. Nguyen, P. Bréchet, M. Mondelli, in:, 35th Conference on Neural Information
Processing Systems, Neural Information Processing Systems Foundation, 2021.
conference:
end_date: 2021-12-14
location: Virtual
name: 35th Conference on Neural Information Processing Systems
start_date: 2021-12-06
date_created: 2022-01-03T10:56:20Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2023-10-17T11:48:40Z
day: '01'
department:
- _id: MaMo
external_id:
arxiv:
- '2102.09671'
intvolume: ' 35'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2102.09671
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 35th Conference on Neural Information Processing Systems
publication_identifier:
isbn:
- '9781713845393'
issn:
- 1049-5258
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
status: public
title: When are solutions connected in deep networks?
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2021'
...
---
_id: '10598'
abstract:
- lang: eng
text: ' We consider the problem of estimating a signal from measurements obtained
via a generalized linear model. We focus on estimators based on approximate message
passing (AMP), a family of iterative algorithms with many appealing features:
the performance of AMP in the high-dimensional limit can be succinctly characterized
under suitable model assumptions; AMP can also be tailored to the empirical distribution
of the signal entries, and for a wide class of estimation problems, AMP is conjectured
to be optimal among all polynomial-time algorithms. However, a major issue of
AMP is that in many models (such as phase retrieval), it requires an initialization
correlated with the ground-truth signal and independent from the measurement matrix.
Assuming that such an initialization is available is typically not realistic.
In this paper, we solve this problem by proposing an AMP algorithm initialized
with a spectral estimator. With such an initialization, the standard AMP analysis
fails since the spectral estimator depends in a complicated way on the design
matrix. Our main contribution is a rigorous characterization of the performance
of AMP with spectral initialization in the high-dimensional limit. The key technical
idea is to define and analyze a two-phase artificial AMP algorithm that first
produces the spectral estimator, and then closely approximates the iterates of
the true AMP. We also provide numerical results that demonstrate the validity
of the proposed approach. '
acknowledgement: The authors would like to thank Andrea Montanari for helpful discussions.
M. Mondelli was partially supported by the 2019 Lopez-Loreta Prize. R. Venkataramanan
was partially supported by the Alan Turing Institute under the EPSRC grant EP/N510129/1.
alternative_title:
- Proceedings of Machine Learning Research
article_processing_charge: Yes (via OA deal)
author:
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Ramji
full_name: Venkataramanan, Ramji
last_name: Venkataramanan
citation:
ama: 'Mondelli M, Venkataramanan R. Approximate message passing with spectral initialization
for generalized linear models. In: Banerjee A, Fukumizu K, eds. Proceedings
of The 24th International Conference on Artificial Intelligence and Statistics.
Vol 130. ML Research Press; 2021:397-405.'
apa: 'Mondelli, M., & Venkataramanan, R. (2021). Approximate message passing
with spectral initialization for generalized linear models. In A. Banerjee &
K. Fukumizu (Eds.), Proceedings of The 24th International Conference on Artificial
Intelligence and Statistics (Vol. 130, pp. 397–405). Virtual, San Diego, CA,
United States: ML Research Press.'
chicago: Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing
with Spectral Initialization for Generalized Linear Models.” In Proceedings
of The 24th International Conference on Artificial Intelligence and Statistics,
edited by Arindam Banerjee and Kenji Fukumizu, 130:397–405. ML Research Press,
2021.
ieee: M. Mondelli and R. Venkataramanan, “Approximate message passing with spectral
initialization for generalized linear models,” in Proceedings of The 24th International
Conference on Artificial Intelligence and Statistics, Virtual, San Diego,
CA, United States, 2021, vol. 130, pp. 397–405.
ista: 'Mondelli M, Venkataramanan R. 2021. Approximate message passing with spectral
initialization for generalized linear models. Proceedings of The 24th International
Conference on Artificial Intelligence and Statistics. AISTATS: Artificial Intelligence
and Statistics, Proceedings of Machine Learning Research, vol. 130, 397–405.'
mla: Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing with
Spectral Initialization for Generalized Linear Models.” Proceedings of The
24th International Conference on Artificial Intelligence and Statistics, edited
by Arindam Banerjee and Kenji Fukumizu, vol. 130, ML Research Press, 2021, pp.
397–405.
short: M. Mondelli, R. Venkataramanan, in:, A. Banerjee, K. Fukumizu (Eds.), Proceedings
of The 24th International Conference on Artificial Intelligence and Statistics,
ML Research Press, 2021, pp. 397–405.
conference:
end_date: 2021-04-15
location: Virtual, San Diego, CA, United States
name: 'AISTATS: Artificial Intelligence and Statistics'
start_date: 2021-04-13
date_created: 2022-01-03T11:34:22Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2024-03-07T10:36:53Z
day: '01'
department:
- _id: MaMo
editor:
- first_name: Arindam
full_name: Banerjee, Arindam
last_name: Banerjee
- first_name: Kenji
full_name: Fukumizu, Kenji
last_name: Fukumizu
external_id:
arxiv:
- '2010.03460'
intvolume: ' 130'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://proceedings.mlr.press/v130/mondelli21a.html
month: '04'
oa: 1
oa_version: Preprint
page: 397-405
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of The 24th International Conference on Artificial Intelligence
and Statistics
publication_identifier:
issn:
- 2640-3498
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
related_material:
record:
- id: '12480'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Approximate message passing with spectral initialization for generalized linear
models
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 130
year: '2021'
...
---
_id: '9002'
abstract:
- lang: eng
text: ' We prove that, for the binary erasure channel (BEC), the polar-coding paradigm
gives rise to codes that not only approach the Shannon limit but do so under the
best possible scaling of their block length as a function of the gap to capacity.
This result exhibits the first known family of binary codes that attain both optimal
scaling and quasi-linear complexity of encoding and decoding. Our proof is based
on the construction and analysis of binary polar codes with large kernels. When
communicating reliably at rates within ε>0 of capacity, the code length n often
scales as O(1/εμ), where the constant μ is called the scaling exponent. It is
known that the optimal scaling exponent is μ=2, and it is achieved by random linear
codes. The scaling exponent of conventional polar codes (based on the 2×2 kernel)
on the BEC is μ=3.63. This falls far short of the optimal scaling guaranteed by
random codes. Our main contribution is a rigorous proof of the following result:
for the BEC, there exist ℓ×ℓ binary kernels, such that polar codes constructed
from these kernels achieve scaling exponent μ(ℓ) that tends to the optimal value
of 2 as ℓ grows. We furthermore characterize precisely how large ℓ needs to be
as a function of the gap between μ(ℓ) and 2. The resulting binary codes maintain
the recursive structure of conventional polar codes, and thereby achieve construction
complexity O(n) and encoding/decoding complexity O(nlogn).'
article_processing_charge: No
article_type: original
author:
- first_name: Arman
full_name: Fazeli, Arman
last_name: Fazeli
- first_name: Hamed
full_name: Hassani, Hamed
last_name: Hassani
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Alexander
full_name: Vardy, Alexander
last_name: Vardy
citation:
ama: 'Fazeli A, Hassani H, Mondelli M, Vardy A. Binary linear codes with optimal
scaling: Polar codes with large kernels. IEEE Transactions on Information Theory.
2021;67(9):5693-5710. doi:10.1109/TIT.2020.3038806'
apa: 'Fazeli, A., Hassani, H., Mondelli, M., & Vardy, A. (2021). Binary linear
codes with optimal scaling: Polar codes with large kernels. IEEE Transactions
on Information Theory. IEEE. https://doi.org/10.1109/TIT.2020.3038806'
chicago: 'Fazeli, Arman, Hamed Hassani, Marco Mondelli, and Alexander Vardy. “Binary
Linear Codes with Optimal Scaling: Polar Codes with Large Kernels.” IEEE Transactions
on Information Theory. IEEE, 2021. https://doi.org/10.1109/TIT.2020.3038806.'
ieee: 'A. Fazeli, H. Hassani, M. Mondelli, and A. Vardy, “Binary linear codes with
optimal scaling: Polar codes with large kernels,” IEEE Transactions on Information
Theory, vol. 67, no. 9. IEEE, pp. 5693–5710, 2021.'
ista: 'Fazeli A, Hassani H, Mondelli M, Vardy A. 2021. Binary linear codes with
optimal scaling: Polar codes with large kernels. IEEE Transactions on Information
Theory. 67(9), 5693–5710.'
mla: 'Fazeli, Arman, et al. “Binary Linear Codes with Optimal Scaling: Polar Codes
with Large Kernels.” IEEE Transactions on Information Theory, vol. 67,
no. 9, IEEE, 2021, pp. 5693–710, doi:10.1109/TIT.2020.3038806.'
short: A. Fazeli, H. Hassani, M. Mondelli, A. Vardy, IEEE Transactions on Information
Theory 67 (2021) 5693–5710.
date_created: 2021-01-10T23:01:18Z
date_published: 2021-09-01T00:00:00Z
date_updated: 2024-03-07T12:18:50Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TIT.2020.3038806
external_id:
arxiv:
- '1711.01339'
intvolume: ' 67'
issue: '9'
language:
- iso: eng
month: '09'
oa_version: Preprint
page: 5693-5710
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1557-9654
issn:
- 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
record:
- id: '6665'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: 'Binary linear codes with optimal scaling: Polar codes with large kernels'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 67
year: '2021'
...
---
_id: '9221'
abstract:
- lang: eng
text: "Recent works have shown that gradient descent can find a global minimum for
over-parameterized neural networks where the widths of all the hidden layers scale
polynomially with N (N being the number of training samples). In this paper, we
prove that, for deep networks, a single layer of width N following the input layer
suffices to ensure a similar guarantee. In particular, all the remaining layers
are allowed to have constant widths, and form a pyramidal topology. We show an
application of our result to the widely used LeCun’s initialization and obtain
an over-parameterization requirement for the single wide layer of order N2.\r\n"
acknowledgement: The authors would like to thank Jan Maas, Mahdi Soltanolkotabi, and
Daniel Soudry for the helpful discussions, Marius Kloft, Matthias Hein and Quoc
Dinh Tran for proofreading portions of a prior version of this paper, and James
Martens for a clarification concerning LeCun’s initialization. M. Mondelli was partially
supported by the 2019 Lopez-Loreta Prize. Q. Nguyen was partially supported by the
German Research Foundation (DFG) award KL 2698/2-1.
article_processing_charge: No
author:
- first_name: Quynh
full_name: Nguyen, Quynh
last_name: Nguyen
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Nguyen Q, Mondelli M. Global convergence of deep networks with one wide layer
followed by pyramidal topology. In: 34th Conference on Neural Information Processing
Systems. Vol 33. Curran Associates; 2020:11961–11972.'
apa: 'Nguyen, Q., & Mondelli, M. (2020). Global convergence of deep networks
with one wide layer followed by pyramidal topology. In 34th Conference on Neural
Information Processing Systems (Vol. 33, pp. 11961–11972). Vancouver, Canada:
Curran Associates.'
chicago: Nguyen, Quynh, and Marco Mondelli. “Global Convergence of Deep Networks
with One Wide Layer Followed by Pyramidal Topology.” In 34th Conference on
Neural Information Processing Systems, 33:11961–11972. Curran Associates,
2020.
ieee: Q. Nguyen and M. Mondelli, “Global convergence of deep networks with one wide
layer followed by pyramidal topology,” in 34th Conference on Neural Information
Processing Systems, Vancouver, Canada, 2020, vol. 33, pp. 11961–11972.
ista: 'Nguyen Q, Mondelli M. 2020. Global convergence of deep networks with one
wide layer followed by pyramidal topology. 34th Conference on Neural Information
Processing Systems. NeurIPS: Neural Information Processing Systems vol. 33, 11961–11972.'
mla: Nguyen, Quynh, and Marco Mondelli. “Global Convergence of Deep Networks with
One Wide Layer Followed by Pyramidal Topology.” 34th Conference on Neural Information
Processing Systems, vol. 33, Curran Associates, 2020, pp. 11961–11972.
short: Q. Nguyen, M. Mondelli, in:, 34th Conference on Neural Information Processing
Systems, Curran Associates, 2020, pp. 11961–11972.
conference:
end_date: 2020-12-12
location: Vancouver, Canada
name: 'NeurIPS: Neural Information Processing Systems'
start_date: 2020-12-06
date_created: 2021-03-03T12:06:02Z
date_published: 2020-07-07T00:00:00Z
date_updated: 2022-01-04T09:24:41Z
day: '07'
department:
- _id: MaMo
external_id:
arxiv:
- '2002.07867'
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2002.07867
month: '07'
oa: 1
oa_version: Preprint
page: 11961–11972
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 34th Conference on Neural Information Processing Systems
publication_status: published
publisher: Curran Associates
quality_controlled: '1'
status: public
title: Global convergence of deep networks with one wide layer followed by pyramidal
topology
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 33
year: '2020'
...
---
_id: '8536'
abstract:
- lang: eng
text: This work analyzes the latency of the simplified successive cancellation (SSC)
decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It
is shown that, unlike conventional successive cancellation decoding, where latency
is linear in the block length, the latency of SSC decoding is sublinear. More
specifically, the latency of SSC decoding is O(N 1−1/µ ), where N is the block
length and µ is the scaling exponent of the channel, which captures the speed
of convergence of the rate to capacity. Numerical results demonstrate the tightness
of the bound and show that most of the latency reduction arises from the parallel
decoding of subcodes of rate 0 and 1.
acknowledgement: M. Mondelli was partially supported by grants NSF DMS-1613091, CCF-1714305,
IIS-1741162 and ONR N00014-18-1-2729. S. A. Hashemi is supported by a Postdoctoral
Fellowship from the Natural Sciences and Engineering Research Council of Canada
(NSERC) and by Huawei.
article_number: 401-406
article_processing_charge: No
author:
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Seyyed Ali
full_name: Hashemi, Seyyed Ali
last_name: Hashemi
- first_name: John
full_name: Cioffi, John
last_name: Cioffi
- first_name: Andrea
full_name: Goldsmith, Andrea
last_name: Goldsmith
citation:
ama: 'Mondelli M, Hashemi SA, Cioffi J, Goldsmith A. Simplified successive cancellation
decoding of polar codes has sublinear latency. In: IEEE International Symposium
on Information Theory - Proceedings. Vol 2020-June. IEEE; 2020. doi:10.1109/ISIT44484.2020.9174141'
apa: 'Mondelli, M., Hashemi, S. A., Cioffi, J., & Goldsmith, A. (2020). Simplified
successive cancellation decoding of polar codes has sublinear latency. In IEEE
International Symposium on Information Theory - Proceedings (Vol. 2020–June).
Los Angeles, CA, United States: IEEE. https://doi.org/10.1109/ISIT44484.2020.9174141'
chicago: Mondelli, Marco, Seyyed Ali Hashemi, John Cioffi, and Andrea Goldsmith.
“Simplified Successive Cancellation Decoding of Polar Codes Has Sublinear Latency.”
In IEEE International Symposium on Information Theory - Proceedings, Vol.
2020–June. IEEE, 2020. https://doi.org/10.1109/ISIT44484.2020.9174141.
ieee: M. Mondelli, S. A. Hashemi, J. Cioffi, and A. Goldsmith, “Simplified successive
cancellation decoding of polar codes has sublinear latency,” in IEEE International
Symposium on Information Theory - Proceedings, Los Angeles, CA, United States,
2020, vol. 2020–June.
ista: 'Mondelli M, Hashemi SA, Cioffi J, Goldsmith A. 2020. Simplified successive
cancellation decoding of polar codes has sublinear latency. IEEE International
Symposium on Information Theory - Proceedings. ISIT: Internation Symposium on
Information Theory vol. 2020–June, 401–406.'
mla: Mondelli, Marco, et al. “Simplified Successive Cancellation Decoding of Polar
Codes Has Sublinear Latency.” IEEE International Symposium on Information Theory
- Proceedings, vol. 2020–June, 401–406, IEEE, 2020, doi:10.1109/ISIT44484.2020.9174141.
short: M. Mondelli, S.A. Hashemi, J. Cioffi, A. Goldsmith, in:, IEEE International
Symposium on Information Theory - Proceedings, IEEE, 2020.
conference:
end_date: 2020-06-26
location: Los Angeles, CA, United States
name: 'ISIT: Internation Symposium on Information Theory'
start_date: 2020-06-21
date_created: 2020-09-20T22:01:37Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-07T13:36:24Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/ISIT44484.2020.9174141
external_id:
arxiv:
- '1909.04892'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1909.04892
month: '06'
oa: 1
oa_version: Preprint
publication: IEEE International Symposium on Information Theory - Proceedings
publication_identifier:
isbn:
- '9781728164328'
issn:
- '21578095'
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
record:
- id: '9047'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Simplified successive cancellation decoding of polar codes has sublinear latency
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2020-June
year: '2020'
...
---
_id: '9198'
abstract:
- lang: eng
text: "The optimization of multilayer neural networks typically leads to a solution\r\nwith
zero training error, yet the landscape can exhibit spurious local minima\r\nand
the minima can be disconnected. In this paper, we shed light on this\r\nphenomenon:
we show that the combination of stochastic gradient descent (SGD)\r\nand over-parameterization
makes the landscape of multilayer neural networks\r\napproximately connected and
thus more favorable to optimization. More\r\nspecifically, we prove that SGD solutions
are connected via a piecewise linear\r\npath, and the increase in loss along this
path vanishes as the number of\r\nneurons grows large. This result is a consequence
of the fact that the\r\nparameters found by SGD are increasingly dropout stable
as the network becomes\r\nwider. We show that, if we remove part of the neurons
(and suitably rescale the\r\nremaining ones), the change in loss is independent
of the total number of\r\nneurons, and it depends only on how many neurons are
left. Our results exhibit\r\na mild dependence on the input dimension: they are
dimension-free for two-layer\r\nnetworks and depend linearly on the dimension
for multilayer networks. We\r\nvalidate our theoretical findings with numerical
experiments for different\r\narchitectures and classification tasks."
acknowledgement: M. Mondelli was partially supported by the 2019 LopezLoreta Prize.
The authors thank Phan-Minh Nguyen for helpful discussions and the IST Distributed
Algorithms and Systems Lab for providing computational resources.
article_processing_charge: No
author:
- first_name: Alexander
full_name: Shevchenko, Alexander
last_name: Shevchenko
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Shevchenko A, Mondelli M. Landscape connectivity and dropout stability of
SGD solutions for over-parameterized neural networks. In: Proceedings of the
37th International Conference on Machine Learning. Vol 119. ML Research Press;
2020:8773-8784.'
apa: Shevchenko, A., & Mondelli, M. (2020). Landscape connectivity and dropout
stability of SGD solutions for over-parameterized neural networks. In Proceedings
of the 37th International Conference on Machine Learning (Vol. 119, pp. 8773–8784).
ML Research Press.
chicago: Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and
Dropout Stability of SGD Solutions for Over-Parameterized Neural Networks.” In
Proceedings of the 37th International Conference on Machine Learning, 119:8773–84.
ML Research Press, 2020.
ieee: A. Shevchenko and M. Mondelli, “Landscape connectivity and dropout stability
of SGD solutions for over-parameterized neural networks,” in Proceedings of
the 37th International Conference on Machine Learning, 2020, vol. 119, pp.
8773–8784.
ista: Shevchenko A, Mondelli M. 2020. Landscape connectivity and dropout stability
of SGD solutions for over-parameterized neural networks. Proceedings of the 37th
International Conference on Machine Learning. vol. 119, 8773–8784.
mla: Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and Dropout
Stability of SGD Solutions for Over-Parameterized Neural Networks.” Proceedings
of the 37th International Conference on Machine Learning, vol. 119, ML Research
Press, 2020, pp. 8773–84.
short: A. Shevchenko, M. Mondelli, in:, Proceedings of the 37th International Conference
on Machine Learning, ML Research Press, 2020, pp. 8773–8784.
date_created: 2021-02-25T09:36:22Z
date_published: 2020-07-13T00:00:00Z
date_updated: 2023-10-17T12:43:19Z
day: '13'
ddc:
- '000'
department:
- _id: MaMo
external_id:
arxiv:
- '1912.10095'
file:
- access_level: open_access
checksum: f042c8d4316bd87c6361aa76f1fbdbbe
content_type: application/pdf
creator: dernst
date_created: 2021-03-02T15:38:14Z
date_updated: 2021-03-02T15:38:14Z
file_id: '9217'
file_name: 2020_PMLR_Shevchenko.pdf
file_size: 5336380
relation: main_file
success: 1
file_date_updated: 2021-03-02T15:38:14Z
has_accepted_license: '1'
intvolume: ' 119'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 8773-8784
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 37th International Conference on Machine Learning
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
status: public
title: Landscape connectivity and dropout stability of SGD solutions for over-parameterized
neural networks
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 119
year: '2020'
...
---
_id: '6748'
abstract:
- lang: eng
text: "Fitting a function by using linear combinations of a large number N of `simple'
components is one of the most fruitful ideas in statistical learning. This idea
lies at the core of a variety of methods, from two-layer neural networks to kernel
regression, to boosting. In general, the resulting risk minimization problem is
non-convex and is solved by gradient descent or its variants. Unfortunately, little
is known about global convergence properties of these approaches.\r\nHere we consider
the problem of learning a concave function f on a compact convex domain Ω⊆ℝd,
using linear combinations of `bump-like' components (neurons). The parameters
to be fitted are the centers of N bumps, and the resulting empirical risk minimization
problem is highly non-convex. We prove that, in the limit in which the number
of neurons diverges, the evolution of gradient descent converges to a Wasserstein
gradient flow in the space of probability distributions over Ω. Further, when
the bump width δ tends to 0, this gradient flow has a limit which is a viscous
porous medium equation. Remarkably, the cost function optimized by this gradient
flow exhibits a special property known as displacement convexity, which implies
exponential convergence rates for N→∞, δ→0. Surprisingly, this asymptotic theory
appears to capture well the behavior for moderate values of δ,N. Explaining this
phenomenon, and understanding the dependence on δ,N in a quantitative manner remains
an outstanding challenge."
article_processing_charge: No
article_type: original
author:
- first_name: Adel
full_name: Javanmard, Adel
last_name: Javanmard
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Andrea
full_name: Montanari, Andrea
last_name: Montanari
citation:
ama: Javanmard A, Mondelli M, Montanari A. Analysis of a two-layer neural network
via displacement convexity. Annals of Statistics. 2020;48(6):3619-3642.
doi:10.1214/20-AOS1945
apa: Javanmard, A., Mondelli, M., & Montanari, A. (2020). Analysis of a two-layer
neural network via displacement convexity. Annals of Statistics. Institute
of Mathematical Statistics. https://doi.org/10.1214/20-AOS1945
chicago: Javanmard, Adel, Marco Mondelli, and Andrea Montanari. “Analysis of a Two-Layer
Neural Network via Displacement Convexity.” Annals of Statistics. Institute
of Mathematical Statistics, 2020. https://doi.org/10.1214/20-AOS1945.
ieee: A. Javanmard, M. Mondelli, and A. Montanari, “Analysis of a two-layer neural
network via displacement convexity,” Annals of Statistics, vol. 48, no.
6. Institute of Mathematical Statistics, pp. 3619–3642, 2020.
ista: Javanmard A, Mondelli M, Montanari A. 2020. Analysis of a two-layer neural
network via displacement convexity. Annals of Statistics. 48(6), 3619–3642.
mla: Javanmard, Adel, et al. “Analysis of a Two-Layer Neural Network via Displacement
Convexity.” Annals of Statistics, vol. 48, no. 6, Institute of Mathematical
Statistics, 2020, pp. 3619–42, doi:10.1214/20-AOS1945.
short: A. Javanmard, M. Mondelli, A. Montanari, Annals of Statistics 48 (2020) 3619–3642.
date_created: 2019-07-31T09:39:42Z
date_published: 2020-12-11T00:00:00Z
date_updated: 2024-03-06T08:28:50Z
day: '11'
department:
- _id: MaMo
doi: 10.1214/20-AOS1945
external_id:
arxiv:
- '1901.01375'
isi:
- '000598369200021'
intvolume: ' 48'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1901.01375
month: '12'
oa: 1
oa_version: Preprint
page: 3619-3642
publication: Annals of Statistics
publication_identifier:
eissn:
- 1941-7330
issn:
- 1932-6157
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
status: public
title: Analysis of a two-layer neural network via displacement convexity
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2020'
...
---
_id: '6750'
abstract:
- lang: eng
text: 'Polar codes have gained extensive attention during the past few years and
recently they have been selected for the next generation of wireless communications
standards (5G). Successive-cancellation-based (SC-based) decoders, such as SC
list (SCL) and SC flip (SCF), provide a reasonable error performance for polar
codes at the cost of low decoding speed. Fast SC-based decoders, such as Fast-SSC,
Fast-SSCL, and Fast-SSCF, identify the special constituent codes in a polar code
graph off-line, produce a list of operations, store the list in memory, and feed
the list to the decoder to decode the constituent codes in order efficiently,
thus increasing the decoding speed. However, the list of operations is dependent
on the code rate and as the rate changes, a new list is produced, making fast
SC-based decoders not rate-flexible. In this paper, we propose a completely rate-flexible
fast SC-based decoder by creating the list of operations directly in hardware,
with low implementation complexity. We further propose a hardware architecture
implementing the proposed method and show that the area occupation of the rate-flexible
fast SC-based decoder in this paper is only 38% of the total area of the memory-based
base-line decoder when 5G code rates are supported. '
article_number: '8854897'
article_processing_charge: No
article_type: original
author:
- first_name: Seyyed Ali
full_name: Hashemi, Seyyed Ali
last_name: Hashemi
- first_name: Carlo
full_name: Condo, Carlo
last_name: Condo
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Warren J
full_name: Gross, Warren J
last_name: Gross
citation:
ama: Hashemi SA, Condo C, Mondelli M, Gross WJ. Rate-flexible fast polar decoders.
IEEE Transactions on Signal Processing. 2019;67(22). doi:10.1109/TSP.2019.2944738
apa: Hashemi, S. A., Condo, C., Mondelli, M., & Gross, W. J. (2019). Rate-flexible
fast polar decoders. IEEE Transactions on Signal Processing. IEEE. https://doi.org/10.1109/TSP.2019.2944738
chicago: Hashemi, Seyyed Ali, Carlo Condo, Marco Mondelli, and Warren J Gross. “Rate-Flexible
Fast Polar Decoders.” IEEE Transactions on Signal Processing. IEEE, 2019.
https://doi.org/10.1109/TSP.2019.2944738.
ieee: S. A. Hashemi, C. Condo, M. Mondelli, and W. J. Gross, “Rate-flexible fast
polar decoders,” IEEE Transactions on Signal Processing, vol. 67, no. 22.
IEEE, 2019.
ista: Hashemi SA, Condo C, Mondelli M, Gross WJ. 2019. Rate-flexible fast polar
decoders. IEEE Transactions on Signal Processing. 67(22), 8854897.
mla: Hashemi, Seyyed Ali, et al. “Rate-Flexible Fast Polar Decoders.” IEEE Transactions
on Signal Processing, vol. 67, no. 22, 8854897, IEEE, 2019, doi:10.1109/TSP.2019.2944738.
short: S.A. Hashemi, C. Condo, M. Mondelli, W.J. Gross, IEEE Transactions on Signal
Processing 67 (2019).
date_created: 2019-07-31T09:51:14Z
date_published: 2019-11-15T00:00:00Z
date_updated: 2021-01-12T08:08:51Z
day: '15'
department:
- _id: MaMo
doi: 10.1109/TSP.2019.2944738
external_id:
arxiv:
- '1903.09203'
intvolume: ' 67'
issue: '22'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1903.09203
month: '11'
oa: 1
oa_version: Preprint
publication: IEEE Transactions on Signal Processing
publication_identifier:
issn:
- 1053587X
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: 1
status: public
title: Rate-flexible fast polar decoders
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 67
year: '2019'
...
---
_id: '7007'
abstract:
- lang: eng
text: 'We consider the primitive relay channel, where the source sends a message
to the relay and to the destination, and the relay helps the communication by
transmitting an additional message to the destination via a separate channel.
Two well-known coding techniques have been introduced for this setting: decode-and-forward
and compress-and-forward. In decode-and-forward, the relay completely decodes
the message and sends some information to the destination; in compress-and-forward,
the relay does not decode, and it sends a compressed version of the received signal
to the destination using Wyner–Ziv coding. In this paper, we present a novel coding
paradigm that provides an improved achievable rate for the primitive relay channel.
The idea is to combine compress-and-forward and decode-and-forward via a chaining
construction. We transmit over pairs of blocks: in the first block, we use compress-and-forward;
and, in the second block, we use decode-and-forward. More specifically, in the
first block, the relay does not decode, it compresses the received signal via
Wyner–Ziv, and it sends only part of the compression to the destination. In the
second block, the relay completely decodes the message, it sends some information
to the destination, and it also sends the remaining part of the compression coming
from the first block. By doing so, we are able to strictly outperform both compress-and-forward
and decode-and-forward. Note that the proposed coding scheme can be implemented
with polar codes. As such, it has the typical attractive properties of polar coding
schemes, namely, quasi-linear encoding and decoding complexity, and error probability
that decays at super-polynomial speed. As a running example, we take into account
the special case of the erasure relay channel, and we provide a comparison between
the rates achievable by our proposed scheme and the existing upper and lower bounds.'
article_number: '218'
article_type: original
author:
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: S. Hamed
full_name: Hassani, S. Hamed
last_name: Hassani
- first_name: Rüdiger
full_name: Urbanke, Rüdiger
last_name: Urbanke
citation:
ama: Mondelli M, Hassani SH, Urbanke R. A new coding paradigm for the primitive
relay channel. Algorithms. 2019;12(10). doi:10.3390/a12100218
apa: Mondelli, M., Hassani, S. H., & Urbanke, R. (2019). A new coding paradigm
for the primitive relay channel. Algorithms. MDPI. https://doi.org/10.3390/a12100218
chicago: Mondelli, Marco, S. Hamed Hassani, and Rüdiger Urbanke. “A New Coding Paradigm
for the Primitive Relay Channel.” Algorithms. MDPI, 2019. https://doi.org/10.3390/a12100218.
ieee: M. Mondelli, S. H. Hassani, and R. Urbanke, “A new coding paradigm for the
primitive relay channel,” Algorithms, vol. 12, no. 10. MDPI, 2019.
ista: Mondelli M, Hassani SH, Urbanke R. 2019. A new coding paradigm for the primitive
relay channel. Algorithms. 12(10), 218.
mla: Mondelli, Marco, et al. “A New Coding Paradigm for the Primitive Relay Channel.”
Algorithms, vol. 12, no. 10, 218, MDPI, 2019, doi:10.3390/a12100218.
short: M. Mondelli, S.H. Hassani, R. Urbanke, Algorithms 12 (2019).
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