---
_id: '6747'
abstract:
- lang: eng
text: "We establish connections between the problem of learning a two-layer neural
network and tensor decomposition. We consider a model with feature vectors x∈ℝd,
r hidden units with weights {wi}1≤i≤r and output y∈ℝ, i.e., y=∑ri=1σ(w\U0001D5B3ix),
with activation functions given by low-degree polynomials. In particular, if σ(x)=a0+a1x+a3x3,
we prove that no polynomial-time learning algorithm can outperform the trivial
predictor that assigns to each example the response variable \U0001D53C(y), when
d3/2≪r≪d2. Our conclusion holds for a `natural data distribution', namely standard
Gaussian feature vectors x, and output distributed according to a two-layer neural
network with random isotropic weights, and under a certain complexity-theoretic
assumption on tensor decomposition. Roughly speaking, we assume that no polynomial-time
algorithm can substantially outperform current methods for tensor decomposition
based on the sum-of-squares hierarchy. We also prove generalizations of this statement
for higher degree polynomial activations, and non-random weight vectors. Remarkably,
several existing algorithms for learning two-layer networks with rigorous guarantees
are based on tensor decomposition. Our results support the idea that this is indeed
the core computational difficulty in learning such networks, under the stated
generative model for the data. As a side result, we show that under this model
learning the network requires accurate learning of its weights, a property that
does not hold in a more general setting. "
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: Andrea
full_name: Montanari, Andrea
last_name: Montanari
citation:
ama: 'Mondelli M, Montanari A. On the connection between learning two-layers neural
networks and tensor decomposition. In: Proceedings of the 22nd International
Conference on Artificial Intelligence and Statistics. Vol 89. Proceedings
of Machine Learning Research; 2019:1051-1060.'
apa: 'Mondelli, M., & Montanari, A. (2019). On the connection between learning
two-layers neural networks and tensor decomposition. In Proceedings of the
22nd International Conference on Artificial Intelligence and Statistics (Vol.
89, pp. 1051–1060). Naha, Okinawa, Japan: Proceedings of Machine Learning Research.'
chicago: Mondelli, Marco, and Andrea Montanari. “On the Connection between Learning
Two-Layers Neural Networks and Tensor Decomposition.” In Proceedings of the
22nd International Conference on Artificial Intelligence and Statistics, 89:1051–60.
Proceedings of Machine Learning Research, 2019.
ieee: M. Mondelli and A. Montanari, “On the connection between learning two-layers
neural networks and tensor decomposition,” in Proceedings of the 22nd International
Conference on Artificial Intelligence and Statistics, Naha, Okinawa, Japan,
2019, vol. 89, pp. 1051–1060.
ista: 'Mondelli M, Montanari A. 2019. On the connection between learning two-layers
neural networks and tensor decomposition. Proceedings of the 22nd International
Conference on Artificial Intelligence and Statistics. AISTATS: Artificial Intelligence
and Statistics vol. 89, 1051–1060.'
mla: Mondelli, Marco, and Andrea Montanari. “On the Connection between Learning
Two-Layers Neural Networks and Tensor Decomposition.” Proceedings of the 22nd
International Conference on Artificial Intelligence and Statistics, vol. 89,
Proceedings of Machine Learning Research, 2019, pp. 1051–60.
short: M. Mondelli, A. Montanari, in:, Proceedings of the 22nd International Conference
on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research,
2019, pp. 1051–1060.
conference:
end_date: 2019-04-18
location: Naha, Okinawa, Japan
name: 'AISTATS: Artificial Intelligence and Statistics'
start_date: 2019-04-16
date_created: 2019-07-31T09:31:26Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2021-01-12T08:08:49Z
day: '01'
extern: '1'
external_id:
arxiv:
- '1802.07301'
intvolume: ' 89'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1802.07301
month: '04'
oa: 1
oa_version: Preprint
page: 1051-1060
publication: Proceedings of the 22nd International Conference on Artificial Intelligence
and Statistics
publication_status: published
publisher: Proceedings of Machine Learning Research
quality_controlled: '1'
status: public
title: On the connection between learning two-layers neural networks and tensor decomposition
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 89
year: '2019'
...
---
_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: '6759'
abstract:
- lang: eng
text: "We consider the graph class Grounded-L corresponding to graphs that admit
an intersection representation by L-shaped curves, where additionally the topmost
points of each curve are assumed to belong to a common horizontal line. We prove
that Grounded-L graphs admit an equivalent characterisation in terms of vertex
ordering with forbidden patterns. \r\nWe also compare this class to related intersection
classes, such as the grounded segment graphs, the monotone L-graphs (a.k.a. max
point-tolerance graphs), or the outer-1-string graphs. We give constructions showing
that these classes are all distinct and satisfy only trivial or previously known
inclusions."
article_number: P3.17
article_processing_charge: No
article_type: original
author:
- first_name: Vít
full_name: Jelínek, Vít
last_name: Jelínek
- first_name: Martin
full_name: Töpfer, Martin
id: 4B865388-F248-11E8-B48F-1D18A9856A87
last_name: Töpfer
citation:
ama: Jelínek V, Töpfer M. On grounded L-graphs and their relatives. Electronic
Journal of Combinatorics. 2019;26(3). doi:10.37236/8096
apa: Jelínek, V., & Töpfer, M. (2019). On grounded L-graphs and their relatives.
Electronic Journal of Combinatorics. Electronic Journal of Combinatorics.
https://doi.org/10.37236/8096
chicago: Jelínek, Vít, and Martin Töpfer. “On Grounded L-Graphs and Their Relatives.”
Electronic Journal of Combinatorics. Electronic Journal of Combinatorics,
2019. https://doi.org/10.37236/8096.
ieee: V. Jelínek and M. Töpfer, “On grounded L-graphs and their relatives,” Electronic
Journal of Combinatorics, vol. 26, no. 3. Electronic Journal of Combinatorics,
2019.
ista: Jelínek V, Töpfer M. 2019. On grounded L-graphs and their relatives. Electronic
Journal of Combinatorics. 26(3), P3.17.
mla: Jelínek, Vít, and Martin Töpfer. “On Grounded L-Graphs and Their Relatives.”
Electronic Journal of Combinatorics, vol. 26, no. 3, P3.17, Electronic
Journal of Combinatorics, 2019, doi:10.37236/8096.
short: V. Jelínek, M. Töpfer, Electronic Journal of Combinatorics 26 (2019).
date_created: 2019-08-04T21:59:20Z
date_published: 2019-07-19T00:00:00Z
date_updated: 2022-03-18T12:32:02Z
day: '19'
ddc:
- '510'
department:
- _id: DaAl
doi: 10.37236/8096
ec_funded: 1
external_id:
arxiv:
- '1808.04148'
file:
- access_level: open_access
checksum: 20fc366fc6683ef0b074a019b73a663a
content_type: application/pdf
creator: dernst
date_created: 2019-08-05T06:46:55Z
date_updated: 2020-07-14T12:47:39Z
file_id: '6764'
file_name: 2019_eJourCombinatorics_Jelinek.pdf
file_size: 533697
relation: main_file
file_date_updated: 2020-07-14T12:47:39Z
has_accepted_license: '1'
intvolume: ' 26'
issue: '3'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Electronic Journal of Combinatorics
publication_identifier:
eissn:
- '10778926'
publication_status: published
publisher: Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On grounded L-graphs and their relatives
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: 26
year: '2019'
...
---
_id: '6822'
abstract:
- lang: eng
text: "In two-player games on graphs, the players move a token through a graph to
produce an infinite path, which determines the qualitative winner or quantitative
payoff of the game. In bidding games, in each turn, we hold an auction between
the two players to determine which player moves the token. Bidding games have
largely been studied with concrete bidding mechanisms that are variants of a first-price
auction: in each turn both players simultaneously submit bids, the higher\r\nbidder
moves the token, and pays his bid to the lower bidder in Richman bidding, to the
bank in poorman bidding, and in taxman bidding, the bid is split between the other
player and the bank according to a predefined constant factor. Bidding games are
deterministic games. They have an intriguing connection with a fragment of stochastic
games called \r\n randomturn games. We study, for the first time, a combination
of bidding games with probabilistic behavior; namely, we study bidding games that
are played on Markov decision processes, where the players bid for the right to
choose the next action, which determines the probability distribution according
to which the next vertex is chosen. We study parity and meanpayoff bidding games
on MDPs and extend results from the deterministic bidding setting to the probabilistic
one."
alternative_title:
- LNCS
author:
- first_name: Guy
full_name: Avni, Guy
id: 463C8BC2-F248-11E8-B48F-1D18A9856A87
last_name: Avni
orcid: 0000-0001-5588-8287
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
- first_name: Petr
full_name: Novotny, Petr
last_name: Novotny
citation:
ama: 'Avni G, Henzinger TA, Ibsen-Jensen R, Novotny P. Bidding games on Markov decision
processes. In: Proceedings of the 13th International Conference of Reachability
Problems. Vol 11674. Springer; 2019:1-12. doi:10.1007/978-3-030-30806-3_1'
apa: 'Avni, G., Henzinger, T. A., Ibsen-Jensen, R., & Novotny, P. (2019). Bidding
games on Markov decision processes. In Proceedings of the 13th International
Conference of Reachability Problems (Vol. 11674, pp. 1–12). Brussels, Belgium:
Springer. https://doi.org/10.1007/978-3-030-30806-3_1'
chicago: Avni, Guy, Thomas A Henzinger, Rasmus Ibsen-Jensen, and Petr Novotny. “Bidding
Games on Markov Decision Processes.” In Proceedings of the 13th International
Conference of Reachability Problems, 11674:1–12. Springer, 2019. https://doi.org/10.1007/978-3-030-30806-3_1.
ieee: G. Avni, T. A. Henzinger, R. Ibsen-Jensen, and P. Novotny, “Bidding games
on Markov decision processes,” in Proceedings of the 13th International Conference
of Reachability Problems, Brussels, Belgium, 2019, vol. 11674, pp. 1–12.
ista: 'Avni G, Henzinger TA, Ibsen-Jensen R, Novotny P. 2019. Bidding games on Markov
decision processes. Proceedings of the 13th International Conference of Reachability
Problems. RP: Reachability Problems, LNCS, vol. 11674, 1–12.'
mla: Avni, Guy, et al. “Bidding Games on Markov Decision Processes.” Proceedings
of the 13th International Conference of Reachability Problems, vol. 11674,
Springer, 2019, pp. 1–12, doi:10.1007/978-3-030-30806-3_1.
short: G. Avni, T.A. Henzinger, R. Ibsen-Jensen, P. Novotny, in:, Proceedings of
the 13th International Conference of Reachability Problems, Springer, 2019, pp.
1–12.
conference:
end_date: 2019-09-13
location: Brussels, Belgium
name: 'RP: Reachability Problems'
start_date: 2019-09-11
date_created: 2019-08-19T07:58:10Z
date_published: 2019-09-06T00:00:00Z
date_updated: 2021-01-12T08:09:12Z
day: '06'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/978-3-030-30806-3_1
file:
- access_level: open_access
checksum: 45ebbc709af2b247d28c7c293c01504b
content_type: application/pdf
creator: gavni
date_created: 2019-08-19T07:56:40Z
date_updated: 2020-07-14T12:47:41Z
file_id: '6823'
file_name: prob.pdf
file_size: 436635
relation: main_file
file_date_updated: 2020-07-14T12:47:41Z
has_accepted_license: '1'
intvolume: ' 11674'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Submitted Version
page: 1-12
project:
- _id: 264B3912-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02369
name: Formal Methods meets Algorithmic Game Theory
- _id: 25F2ACDE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11402-N23
name: Rigorous Systems Engineering
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication: ' Proceedings of the 13th International Conference of Reachability Problems'
publication_identifier:
isbn:
- 978-303030805-6
issn:
- 0302-9743
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: 1
status: public
title: Bidding games on Markov decision processes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11674
year: '2019'
...
---
_id: '6887'
abstract:
- lang: eng
text: 'The fundamental model-checking problem, given as input a model and a specification,
asks for the algorithmic verification of whether the model satisfies the specification.
Two classical models for reactive systems are graphs and Markov decision processes
(MDPs). A basic specification formalism in the verification of reactive systems
is the strong fairness (aka Streett) objective, where given different types of
requests and corresponding grants, the requirement is that for each type, if the
request event happens infinitely often, then the corresponding grant event must
also happen infinitely often. All omega-regular objectives can be expressed as
Streett objectives and hence they are canonical in verification. Consider graphs/MDPs
with n vertices, m edges, and a Streett objectives with k pairs, and let b denote
the size of the description of the Streett objective for the sets of requests
and grants. The current best-known algorithm for the problem requires time O(min(n^2,
m sqrt{m log n}) + b log n). In this work we present randomized near-linear time
algorithms, with expected running time O~(m + b), where the O~ notation hides
poly-log factors. Our randomized algorithms are near-linear in the size of the
input, and hence optimal up to poly-log factors. '
alternative_title:
- LIPIcs
article_number: '7'
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Wolfgang
full_name: Dvorák, Wolfgang
last_name: Dvorák
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Alexander
full_name: Svozil, Alexander
last_name: Svozil
citation:
ama: 'Chatterjee K, Dvorák W, Henzinger MH, Svozil A. Near-linear time algorithms
for Streett objectives in graphs and MDPs. In: Leibniz International Proceedings
in Informatics. Vol 140. Schloss Dagstuhl - Leibniz-Zentrum für Informatik;
2019. doi:10.4230/LIPICS.CONCUR.2019.7'
apa: 'Chatterjee, K., Dvorák, W., Henzinger, M. H., & Svozil, A. (2019). Near-linear
time algorithms for Streett objectives in graphs and MDPs. In Leibniz International
Proceedings in Informatics (Vol. 140). Amsterdam, Netherlands: Schloss Dagstuhl
- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.CONCUR.2019.7'
chicago: Chatterjee, Krishnendu, Wolfgang Dvorák, Monika H Henzinger, and Alexander
Svozil. “Near-Linear Time Algorithms for Streett Objectives in Graphs and MDPs.”
In Leibniz International Proceedings in Informatics, Vol. 140. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.CONCUR.2019.7.
ieee: K. Chatterjee, W. Dvorák, M. H. Henzinger, and A. Svozil, “Near-linear time
algorithms for Streett objectives in graphs and MDPs,” in Leibniz International
Proceedings in Informatics, Amsterdam, Netherlands, 2019, vol. 140.
ista: 'Chatterjee K, Dvorák W, Henzinger MH, Svozil A. 2019. Near-linear time algorithms
for Streett objectives in graphs and MDPs. Leibniz International Proceedings in
Informatics. CONCUR: International Conference on Concurrency Theory, LIPIcs, vol.
140, 7.'
mla: Chatterjee, Krishnendu, et al. “Near-Linear Time Algorithms for Streett Objectives
in Graphs and MDPs.” Leibniz International Proceedings in Informatics,
vol. 140, 7, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, doi:10.4230/LIPICS.CONCUR.2019.7.
short: K. Chatterjee, W. Dvorák, M.H. Henzinger, A. Svozil, in:, Leibniz International
Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2019.
conference:
end_date: 2019-08-30
location: Amsterdam, Netherlands
name: 'CONCUR: International Conference on Concurrency Theory'
start_date: 2019-08-27
date_created: 2019-09-18T08:07:58Z
date_published: 2019-08-01T00:00:00Z
date_updated: 2022-08-12T10:54:34Z
day: '01'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPICS.CONCUR.2019.7
ec_funded: 1
file:
- access_level: open_access
checksum: e1f0e4061212454574f34a1368d018ec
content_type: application/pdf
creator: kschuh
date_created: 2019-10-01T08:20:30Z
date_updated: 2020-07-14T12:47:43Z
file_id: '6922'
file_name: 2019_LIPIcs_Chatterjee.pdf
file_size: 730112
relation: main_file
file_date_updated: 2020-07-14T12:47:43Z
has_accepted_license: '1'
intvolume: ' 140'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
publication: Leibniz International Proceedings in Informatics
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Near-linear time algorithms for Streett objectives in graphs and MDPs
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: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 140
year: '2019'
...