5 Search Results for "Lu, Chi-Jen"

Document
DOI: 10.4230/LIPIcs.CCC.2024.1
A Technique for Hardness Amplification Against AC⁰

Authors: William M. Hoza

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
We study hardness amplification in the context of two well-known "moderate" average-case hardness results for AC⁰ circuits. First, we investigate the extent to which AC⁰ circuits of depth d can approximate AC⁰ circuits of some larger depth d + k. The case k = 1 is resolved by Håstad, Rossman, Servedio, and Tan’s celebrated average-case depth hierarchy theorem (JACM 2017). Our contribution is a significantly stronger correlation bound when k ≥ 3. Specifically, we show that there exists a linear-size AC⁰_{d + k} circuit h : {0, 1}ⁿ → {0, 1} such that for every AC⁰_d circuit g, either g has size exp(n^{Ω(1/d)}), or else g agrees with h on at most a (1/2 + ε)-fraction of inputs where ε = exp(-(1/d) ⋅ Ω(log n)^{k-1}). For comparison, Håstad, Rossman, Servedio, and Tan’s result has ε = n^{-Θ(1/d)}. Second, we consider the majority function. It is well known that the majority function is moderately hard for AC⁰ circuits (and stronger classes). Our contribution is a stronger correlation bound for the XOR of t copies of the n-bit majority function, denoted MAJ_n^{⊕ t}. We show that if g is an AC⁰_d circuit of size S, then g agrees with MAJ_n^{⊕ t} on at most a (1/2 + ε)-fraction of inputs, where ε = (O(log S)^{d - 1} / √n)^t. To prove these results, we develop a hardness amplification technique that is tailored to a specific type of circuit lower bound proof. In particular, one way to show that a function h is moderately hard for AC⁰ circuits is to (a) design some distribution over random restrictions or random projections, (b) show that AC⁰ circuits simplify to shallow decision trees under these restrictions/projections, and finally (c) show that after applying the restriction/projection, h is moderately hard for shallow decision trees with respect to an appropriate distribution. We show that (roughly speaking) if h can be proven to be moderately hard by a proof with that structure, then XORing multiple copies of h amplifies its hardness. Our analysis involves a new kind of XOR lemma for decision trees, which might be of independent interest.
Cite as

William M. Hoza. A Technique for Hardness Amplification Against AC⁰. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{hoza:LIPIcs.CCC.2024.1,
  author =	{Hoza, William M.},
  title =	{{A Technique for Hardness Amplification Against AC⁰}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.1},
  URN =		{urn:nbn:de:0030-drops-203977},
  doi =		{10.4230/LIPIcs.CCC.2024.1},
  annote =	{Keywords: Bounded-depth circuits, average-case lower bounds, hardness amplification, XOR lemmas}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.20
Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks

Authors: Kenneth Langedal, Demian Hespe, and Peter Sanders

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Identifying a maximum independent set is a fundamental NP-hard problem. This problem has several real-world applications and requires finding the largest possible set of vertices not adjacent to each other in an undirected graph. Over the past few years, branch-and-bound and branch-and-reduce algorithms have emerged as some of the most effective methods for solving the problem exactly. Specifically, the branch-and-reduce approach, which combines branch-and-bound principles with reduction rules, has proven particularly successful in tackling previously unmanageable real-world instances. This progress was largely made possible by the development of more effective reduction rules. Nevertheless, other key components that can impact the efficiency of these algorithms have not received the same level of interest. Among these is the branching strategy, which determines which vertex to branch on next. Until recently, the most widely used strategy was to choose the vertex of the highest degree. In this work, we present a graph neural network approach for selecting the next branching vertex. The intricate nature of current branch-and-bound solvers makes supervised and reinforcement learning difficult. Therefore, we use a population-based genetic algorithm to evolve the model’s parameters instead. Our proposed approach results in a speedup on 73% of the benchmark instances with a median speedup of 24%.
Cite as

Kenneth Langedal, Demian Hespe, and Peter Sanders. Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{langedal_et_al:LIPIcs.SEA.2024.20,
  author =	{Langedal, Kenneth and Hespe, Demian and Sanders, Peter},
  title =	{{Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{20:1--20:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.20},
  URN =		{urn:nbn:de:0030-drops-203853},
  doi =		{10.4230/LIPIcs.SEA.2024.20},
  annote =	{Keywords: Graphs, Independent Set, Vertex Cover, Graph Neural Networks, Branch-and-Reduce}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2024.12
Autonomy Today: Many Delay-Prone Black Boxes

Authors: Sizhe Liu, Rohan Wagle, James H. Anderson, Ming Yang, Chi Zhang, and Yunhua Li

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract
Machine-learning (ML) technology has been a key enabler in the push towards realizing ever more sophisticated autonomous-driving features. In deploying such technology, the automotive industry has relied heavily on using "black-box" software and hardware components that were originally intended for non-safety-critical contexts, without a full understanding of their real-time capabilities. A prime example of such a component is CUDA, which is fundamental to the acceleration of ML algorithms using NVIDIA GPUs. In this paper, evidence is presented demonstrating that CUDA can cause unbounded task delays. Such delays are the result of CUDA’s usage of synchronization mechanisms in the POSIX thread (pthread) library, so the latter is implicated as a delay-prone component as well. Such synchronization delays are shown to be the source of a system failure that occurred in an actual autonomous vehicle system during testing at WeRide. Motivated by these findings, a broader experimental study is presented that demonstrates several real-time deficiencies in CUDA, the glibc pthread library, Linux, and the POSIX interface of the safety-certified QNX Operating System for Safety. Partial mitigations for these deficiencies are presented and further actions are proposed for real-time researchers and developers to integrate more complete mitigations.
Cite as

Sizhe Liu, Rohan Wagle, James H. Anderson, Ming Yang, Chi Zhang, and Yunhua Li. Autonomy Today: Many Delay-Prone Black Boxes. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 12:1-12:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{liu_et_al:LIPIcs.ECRTS.2024.12,
  author =	{Liu, Sizhe and Wagle, Rohan and Anderson, James H. and Yang, Ming and Zhang, Chi and Li, Yunhua},
  title =	{{Autonomy Today: Many Delay-Prone Black Boxes}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{12:1--12:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.12},
  URN =		{urn:nbn:de:0030-drops-203152},
  doi =		{10.4230/LIPIcs.ECRTS.2024.12},
  annote =	{Keywords: autonomous driving, CUDA programming, locking protocols, POSIX thread, operating systems, machine learning systems, real-time systems}
}
Document
DOI: 10.4230/DagMan.10.1.1
Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter

Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)

Abstract
Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022,sser a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade.
Cite as

James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@Article{delgrande_et_al:DagMan.10.1.1,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}},
  pages =	{1--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2024},
  volume =	{10},
  number =	{1},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1},
  URN =		{urn:nbn:de:0030-drops-201403},
  doi =		{10.4230/DagMan.10.1.1},
  annote =	{Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.26
On the Algorithmic Power of Spiking Neural Networks

Authors: Chi-Ning Chou, Kai-Min Chung, and Chi-Jen Lu

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
Spiking Neural Networks (SNN) are mathematical models in neuroscience to describe the dynamics among a set of neurons that interact with each other by firing instantaneous signals, a.k.a., spikes. Interestingly, a recent advance in neuroscience [Barrett-Denève-Machens, NIPS 2013] showed that the neurons' firing rate, i.e., the average number of spikes fired per unit of time, can be characterized by the optimal solution of a quadratic program defined by the parameters of the dynamics. This indicated that SNN potentially has the computational power to solve non-trivial quadratic programs. However, the results were justified empirically without rigorous analysis. We put this into the context of natural algorithms and aim to investigate the algorithmic power of SNN. Especially, we emphasize on giving rigorous asymptotic analysis on the performance of SNN in solving optimization problems. To enforce a theoretical study, we first identify a simplified SNN model that is tractable for analysis. Next, we confirm the empirical observation in the work of Barrett et al. by giving an upper bound on the convergence rate of SNN in solving the quadratic program. Further, we observe that in the case where there are infinitely many optimal solutions, SNN tends to converge to the one with smaller l_1 norm. We give an affirmative answer to our finding by showing that SNN can solve the l_1 minimization problem under some regular conditions. Our main technical insight is a dual view of the SNN dynamics, under which SNN can be viewed as a new natural primal-dual algorithm for the l_1 minimization problem. We believe that the dual view is of independent interest and may potentially find interesting interpretation in neuroscience.
Cite as

Chi-Ning Chou, Kai-Min Chung, and Chi-Jen Lu. On the Algorithmic Power of Spiking Neural Networks. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{chou_et_al:LIPIcs.ITCS.2019.26,
  author =	{Chou, Chi-Ning and Chung, Kai-Min and Lu, Chi-Jen},
  title =	{{On the Algorithmic Power of Spiking Neural Networks}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{26:1--26:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.26},
  URN =		{urn:nbn:de:0030-drops-101191},
  doi =		{10.4230/LIPIcs.ITCS.2019.26},
  annote =	{Keywords: Spiking Neural Networks, Natural Algorithms, l\underline1 Minimization}
}
  • Refine by Author
  • 1 Anderson, James H.
  • 1 Chou, Chi-Ning
  • 1 Chung, Kai-Min
  • 1 Delgrande, James P.
  • 1 Glimm, Birte
  • Show More...

  • Refine by Classification
  • 1 Computer systems organization → Real-time operating systems
  • 1 Computing methodologies → Artificial intelligence
  • 1 Computing methodologies → Knowledge representation and reasoning
  • 1 Computing methodologies → Neural networks
  • 1 Information systems → Information integration
  • Show More...

  • Refine by Keyword
  • 1 Applications of logics
  • 1 Bounded-depth circuits
  • 1 Branch-and-Reduce
  • 1 CUDA programming
  • 1 Declarative representations
  • Show More...

  • Refine by Type
  • 5 document

  • Refine by Publication Year
  • 4 2024
  • 1 2019

© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact