7 Search Results for "Zhang, Lichen"


Document
Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time

Authors: Zhao Song, Lichen Zhang, and Ruizhe Zhang

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
We consider the problem of training a multi-layer over-parametrized neural network to minimize the empirical risk induced by a loss function. In the typical setting of over-parametrization, the network width m is much larger than the data dimension d and the number of training samples n (m = poly(n,d)), which induces a prohibitive large weight matrix W ∈ ℝ^{m× m} per layer. Naively, one has to pay O(m²) time to read the weight matrix and evaluate the neural network function in both forward and backward computation. In this work, we show how to reduce the training cost per iteration. Specifically, we propose a framework that uses m² cost only in the initialization phase and achieves a truly subquadratic cost per iteration in terms of m, i.e., m^{2-Ω(1)} per iteration. Our result has implications beyond standard over-parametrization theory, as it can be viewed as designing an efficient data structure on top of a pre-trained large model to further speed up the fine-tuning process, a core procedure to deploy large language models (LLM).

Cite as

Zhao Song, Lichen Zhang, and Ruizhe Zhang. Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 93:1-93:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{song_et_al:LIPIcs.ITCS.2024.93,
  author =	{Song, Zhao and Zhang, Lichen and Zhang, Ruizhe},
  title =	{{Training Multi-Layer Over-Parametrized Neural Network in Subquadratic Time}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{93:1--93:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.93},
  URN =		{urn:nbn:de:0030-drops-196212},
  doi =		{10.4230/LIPIcs.ITCS.2024.93},
  annote =	{Keywords: Deep learning theory, Nonconvex optimization}
}
Document
Track A: Algorithms, Complexity and Games
Space-Efficient Interior Point Method, with Applications to Linear Programming and Maximum Weight Bipartite Matching

Authors: S. Cliff Liu, Zhao Song, Hengjie Zhang, Lichen Zhang, and Tianyi Zhou

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


Abstract
We study the problem of solving linear program in the streaming model. Given a constraint matrix A ∈ ℝ^{m×n} and vectors b ∈ ℝ^m, c ∈ ℝ^n, we develop a space-efficient interior point method that optimizes solely on the dual program. To this end, we obtain efficient algorithms for various different problems: - For general linear programs, we can solve them in Õ(√n log(1/ε)) passes and Õ(n²) space for an ε-approximate solution. To the best of our knowledge, this is the most efficient LP solver in streaming with no polynomial dependence on m for both space and passes. - For bipartite graphs, we can solve the minimum vertex cover and maximum weight matching problem in Õ(√m) passes and Õ(n) space. In addition to our space-efficient IPM, we also give algorithms for solving SDD systems and isolation lemma in Õ(n) spaces, which are the cornerstones for our graph results.

Cite as

S. Cliff Liu, Zhao Song, Hengjie Zhang, Lichen Zhang, and Tianyi Zhou. Space-Efficient Interior Point Method, with Applications to Linear Programming and Maximum Weight Bipartite Matching. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 88:1-88:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{liu_et_al:LIPIcs.ICALP.2023.88,
  author =	{Liu, S. Cliff and Song, Zhao and Zhang, Hengjie and Zhang, Lichen and Zhou, Tianyi},
  title =	{{Space-Efficient Interior Point Method, with Applications to Linear Programming and Maximum Weight Bipartite Matching}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{88:1--88:14},
  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.2023.88},
  URN =		{urn:nbn:de:0030-drops-181408},
  doi =		{10.4230/LIPIcs.ICALP.2023.88},
  annote =	{Keywords: Convex optimization, interior point method, streaming algorithm}
}
Document
Multi-Threshold Asynchronous Reliable Broadcast and Consensus

Authors: Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)


Abstract
Classical protocols for reliable broadcast and consensus provide security guarantees as long as the number of corrupted parties f is bounded by a single given threshold t. If f > t, these protocols are completely deemed insecure. We consider the relaxed notion of multi-threshold reliable broadcast and consensus where validity, consistency and termination are guaranteed as long as f ≤ t_v, f ≤ t_c and f ≤ t_t respectively. For consensus, we consider both variants of (1-ε)-consensus and almost-surely terminating consensus, where termination is guaranteed with probability (1-ε) and 1, respectively. We give a very complete characterization for these primitives in the asynchronous setting and with no signatures: - Multi-threshold reliable broadcast is possible if and only if max{t_c,t_v} + 2t_t < n. - Multi-threshold almost-surely consensus is possible if max{t_c, t_v} + 2t_t < n, 2t_v + t_t < n and t_t < n/3. Assuming a global coin, it is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n. - Multi-threshold (1-ε)-consensus is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n.

Cite as

Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang. Multi-Threshold Asynchronous Reliable Broadcast and Consensus. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 6:1-6:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{hirt_et_al:LIPIcs.OPODIS.2020.6,
  author =	{Hirt, Martin and Kastrati, Ard and Liu-Zhang, Chen-Da},
  title =	{{Multi-Threshold Asynchronous Reliable Broadcast and Consensus}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.6},
  URN =		{urn:nbn:de:0030-drops-134917},
  doi =		{10.4230/LIPIcs.OPODIS.2020.6},
  annote =	{Keywords: broadcast, byzantine agreement, multi-threshold}
}
Document
On Broadcast in Generalized Network and Adversarial Models

Authors: Chen-Da Liu-Zhang, Varun Maram, and Ueli Maurer

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)


Abstract
Broadcast is a primitive which allows a specific party to distribute a message consistently among n parties, even if up to t parties exhibit malicious behaviour. In the classical model with a complete network of bilateral authenticated channels, the seminal result of Pease et al. [Pease et al., 1980] shows that broadcast is achievable if and only if t < n/3. There are two generalizations suggested for the broadcast problem - with respect to the adversarial model and the communication model. Fitzi and Maurer [Fitzi and Maurer, 1998] consider a (non-threshold) general adversary that is characterized by the subsets of parties that could be corrupted, and show that broadcast can be realized from bilateral channels if and only if the union of no three possible corrupted sets equals the entire set of n parties. On the other hand, Considine et al. [Considine et al., 2005] extend the standard model of bilateral channels with the existence of b-minicast channels that allow to locally broadcast among any subset of b parties; the authors show that in this enhanced model of communication, secure broadcast tolerating up to t corrupted parties is possible if and only if t < (b-1)/(b+1)n. These generalizations are unified in the work by Raykov [Raykov P., 2015], where a tight condition on the possible corrupted sets is presented such that broadcast is achievable from a complete set of b-minicasts. This paper investigates the achievability of broadcast in general networks, i.e., networks where only some subsets of minicast channels may be available, thereby addressing open problems posed in [Jaffe et al., 2012; Raykov P., 2015]. To that end, we propose a hierarchy over all possible general adversaries, and identify for each class of general adversaries 1) a set of minicast channels that are necessary to achieve broadcast and 2) a set of minicast channels that are sufficient to achieve broadcast. In particular, this allows us to derive bounds on the amount of b-minicasts that are necessary and that suffice towards constructing broadcast in general b-minicast networks.

Cite as

Chen-Da Liu-Zhang, Varun Maram, and Ueli Maurer. On Broadcast in Generalized Network and Adversarial Models. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 25:1-25:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{liuzhang_et_al:LIPIcs.OPODIS.2020.25,
  author =	{Liu-Zhang, Chen-Da and Maram, Varun and Maurer, Ueli},
  title =	{{On Broadcast in Generalized Network and Adversarial Models}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.25},
  URN =		{urn:nbn:de:0030-drops-135108},
  doi =		{10.4230/LIPIcs.OPODIS.2020.25},
  annote =	{Keywords: broadcast, partial broadcast, minicast, general adversary, general network}
}
Document
From Partial to Global Asynchronous Reliable Broadcast

Authors: Diana Ghinea, Martin Hirt, and Chen-Da Liu-Zhang

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)


Abstract
Broadcast is a fundamental primitive in distributed computing. It allows a sender to consistently distribute a message among n recipients. The seminal result of Pease et al. [JACM'80] shows that in a complete network of synchronous bilateral channels, broadcast is achievable if and only if the number of corruptions is bounded by t < n/3. To overcome this bound, a fascinating line of works, Fitzi and Maurer [STOC'00], Considine et al. [JC'05], and Raykov [ICALP'15], proposed strengthening the communication network by assuming partial synchronous broadcast channels, which guarantee consistency among a subset of recipients. We extend this line of research to the asynchronous setting. We consider reliable broadcast protocols assuming a communication network which provides each subset of b parties with reliable broadcast channels. A natural question is to investigate the trade-off between the size b and the corruption threshold t. We answer this question by showing feasibility and impossibility results: - A reliable broadcast protocol Π_{RBC} that: - For 3 ≤ b ≤ 4, is secure up to t < n/2 corruptions. - For b > 4 even, is secure up to t < ((b-4)/(b-2) n + 8/(b-2)) corruptions. - For b > 4 odd, is secure up to t < ((b-3)/(b-1) n + 6/(b-1)) corruptions. - A nonstop reliable broadcast Π_{nRBC}, where parties are guaranteed to obtain output as in reliable broadcast but may need to run forever, secure up to t < (b-1)/(b+1) n corruptions. - There is no protocol for (nonstop) reliable broadcast secure up to t ≥ (b-1)/(b+1) n corruptions, implying that Π_{RBC} is an asymptotically optimal reliable broadcast protocol, and Π_{nRBC} is an optimal nonstop reliable broadcast protocol.

Cite as

Diana Ghinea, Martin Hirt, and Chen-Da Liu-Zhang. From Partial to Global Asynchronous Reliable Broadcast. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 29:1-29:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{ghinea_et_al:LIPIcs.DISC.2020.29,
  author =	{Ghinea, Diana and Hirt, Martin and Liu-Zhang, Chen-Da},
  title =	{{From Partial to Global Asynchronous Reliable Broadcast}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.29},
  URN =		{urn:nbn:de:0030-drops-131074},
  doi =		{10.4230/LIPIcs.DISC.2020.29},
  annote =	{Keywords: asynchronous broadcast, partial broadcast}
}
Document
Brief Announcement
Brief Announcement: Multi-Threshold Asynchronous Reliable Broadcast and Consensus

Authors: Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)


Abstract
Classical protocols for reliable broadcast and consensus provide security guarantees as long as the number of corrupted parties f is bounded by a single given threshold t. If f > t, these protocols are completely deemed insecure. We consider the relaxed notion of multi-threshold reliable broadcast and consensus where validity, consistency and termination are guaranteed as long as f ≤ t_v, f ≤ t_c and f ≤ t_t respectively. For consensus, we consider both variants of (1-ε)-consensus and almost-surely terminating consensus, where termination is guaranteed with probability (1-ε) and 1, respectively. We give a very complete characterization for these primitives in the asynchronous setting and with no signatures: - Multi-threshold reliable broadcast is possible if and only if max{t_c,t_v} + 2t_t < n. - Multi-threshold almost-surely consensus is possible if max{t_c, t_v} + 2t_t < n, 2t_v + t_t < n and t_t < n/3. Assuming a global coin, it is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n. - Multi-threshold (1-ε)-consensus is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n.

Cite as

Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang. Brief Announcement: Multi-Threshold Asynchronous Reliable Broadcast and Consensus. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 48:1-48:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{hirt_et_al:LIPIcs.DISC.2020.48,
  author =	{Hirt, Martin and Kastrati, Ard and Liu-Zhang, Chen-Da},
  title =	{{Brief Announcement: Multi-Threshold Asynchronous Reliable Broadcast and Consensus}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{48:1--48:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.48},
  URN =		{urn:nbn:de:0030-drops-131267},
  doi =		{10.4230/LIPIcs.DISC.2020.48},
  annote =	{Keywords: broadcast, byzantine agreement, multi-threshold}
}
Document
Brief Announcement
Brief Announcement: Towards Byzantine Broadcast in Generalized Communication and Adversarial Models

Authors: Chen-Da Liu-Zhang, Varun Maram, and Ueli Maurer

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)


Abstract
Byzantine broadcast is a primitive which allows a specific party to distribute a message consistently among n parties, even if up to t parties exhibit malicious behaviour. In the classical model with a complete network of bilateral authenticated channels, the seminal result of Pease et al. [Pease et al., 1980] shows that broadcast is achievable if and only if t < n/3. There are two generalizations suggested for the broadcast problem - w.r.t. the adversarial model and the communication model. Fitzi and Maurer [Fitzi and Maurer, 1998] consider a (non-threshold) general adversary that is characterized by the subsets of parties that could be corrupted, and show that broadcast can be realized from bilateral channels if and only if the union of no three possible corrupted sets equals the entire set of n parties. On the other hand, Considine et al. [Considine et al., 2005] extend the standard model of bilateral channels with the existence of b-minicast channels that allow to locally broadcast among any subset of b parties; the authors show that in this enhanced model of communication, secure broadcast tolerating up to t corrupted parties is possible if and only if t < (b-1)/(b+1) n. These generalizations are unified in the work by Raykov [Raykov P., 2015], where a tight condition on the possible corrupted sets such that broadcast is achievable from a complete set of b-minicasts is shown. This paper investigates the achievability of broadcast in general networks, i.e., networks where only some subsets of minicast channels may be available, thereby addressing open problems posed in [Jaffe et al., 2012; Raykov P., 2015]. Our contributions include: 1) proposing a hierarchy over all possible general adversaries for a clean analysis of the broadcast problem in general networks, 2) showing the infeasibility of a prominent technique - used to achieve broadcast in general 3-minicast networks [Ravikant et al., 2004] - with regard to higher b-minicast networks, and 3) providing some necessary conditions on general networks for broadcast to be possible while tolerating general adversaries.

Cite as

Chen-Da Liu-Zhang, Varun Maram, and Ueli Maurer. Brief Announcement: Towards Byzantine Broadcast in Generalized Communication and Adversarial Models. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 47:1-47:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{liuzhang_et_al:LIPIcs.DISC.2019.47,
  author =	{Liu-Zhang, Chen-Da and Maram, Varun and Maurer, Ueli},
  title =	{{Brief Announcement: Towards Byzantine Broadcast in Generalized Communication and Adversarial Models}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{47:1--47:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.47},
  URN =		{urn:nbn:de:0030-drops-113540},
  doi =		{10.4230/LIPIcs.DISC.2019.47},
  annote =	{Keywords: broadcast, partial broadcast, minicast, general adversary, general network}
}
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