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Documents authored by Cheung, Tsun-Ming


Document
Separation of the Factorization Norm and Randomized Communication Complexity

Authors: Tsun-Ming Cheung, Hamed Hatami, Kaave Hosseini, and Morgan Shirley

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)


Abstract
In an influential paper, Linial and Shraibman (STOC '07) introduced the factorization norm as a powerful tool for proving lower bounds against randomized and quantum communication complexities. They showed that the logarithm of the approximate γ₂-factorization norm is a lower bound for these parameters and asked whether a stronger lower bound that replaces approximate γ₂ norm with the γ₂ norm holds. We answer the question of Linial and Shraibman in the negative by exhibiting a 2ⁿ×2ⁿ Boolean matrix with γ₂ norm 2^Ω(n) and randomized communication complexity O(log n). As a corollary, we recover the recent result of Chattopadhyay, Lovett, and Vinyals (CCC '19) that deterministic protocols with access to an Equality oracle are exponentially weaker than (one-sided error) randomized protocols. In fact, as a stronger consequence, our result implies an exponential separation between the power of unambiguous nondeterministic protocols with access to Equality oracle and (one-sided error) randomized protocols, which answers a question of Pitassi, Shirley, and Shraibman (ITSC '23). Our result also implies a conjecture of Sherif (Ph.D. thesis) that the γ₂ norm of the Integer Inner Product function (IIP) in dimension 3 or higher is exponential in its input size.

Cite as

Tsun-Ming Cheung, Hamed Hatami, Kaave Hosseini, and Morgan Shirley. Separation of the Factorization Norm and Randomized Communication Complexity. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 1:1-1:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{cheung_et_al:LIPIcs.CCC.2023.1,
  author =	{Cheung, Tsun-Ming and Hatami, Hamed and Hosseini, Kaave and Shirley, Morgan},
  title =	{{Separation of the Factorization Norm and Randomized Communication Complexity}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{1:1--1:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.1},
  URN =		{urn:nbn:de:0030-drops-182714},
  doi =		{10.4230/LIPIcs.CCC.2023.1},
  annote =	{Keywords: Factorization norms, randomized communication complexity}
}
Document
Track A: Algorithms, Complexity and Games
Online Learning and Disambiguations of Partial Concept Classes

Authors: Tsun-Ming Cheung, Hamed Hatami, Pooya Hatami, and Kaave Hosseini

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
In a recent article, Alon, Hanneke, Holzman, and Moran (FOCS '21) introduced a unifying framework to study the learnability of classes of partial concepts. One of the central questions studied in their work is whether the learnability of a partial concept class is always inherited from the learnability of some "extension" of it to a total concept class. They showed this is not the case for PAC learning but left the problem open for the stronger notion of online learnability. We resolve this problem by constructing a class of partial concepts that is online learnable, but no extension of it to a class of total concepts is online learnable (or even PAC learnable).

Cite as

Tsun-Ming Cheung, Hamed Hatami, Pooya Hatami, and Kaave Hosseini. Online Learning and Disambiguations of Partial Concept Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 42:1-42:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{cheung_et_al:LIPIcs.ICALP.2023.42,
  author =	{Cheung, Tsun-Ming and Hatami, Hamed and Hatami, Pooya and Hosseini, Kaave},
  title =	{{Online Learning and Disambiguations of Partial Concept Classes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{42:1--42:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.42},
  URN =		{urn:nbn:de:0030-drops-180946},
  doi =		{10.4230/LIPIcs.ICALP.2023.42},
  annote =	{Keywords: Online learning, Littlestone dimension, VC dimension, partial concept class, clique vs independent set, Alon-Saks-Seymour conjecture, Standard Optimal Algorithm, PAC learning}
}
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