--- _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' ...