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arXiv 2024年

作者： Dinur, Irit Lin, Ting-Chun Vidick, Thomas Department of Applied Math and Computer Science The Weizmann Institute of Science Department of Physics University of California San Diego CA United States Hon Hai Research Institute Taipei Taiwan

We introduce a high-dimensional cubical complex, for any dimension t ∈ N, and apply it to the design of quantum locally testable codes. Our complex is a natural generalization of the constructions by Panteleev and Kalachev and by Dinur et. al of a square complex (case t = 2), which have been applied to the design of classical locally testable codes (LTC) and quantum low-density parity check codes (qLDPC) respectively. We turn the geometric (cubical) complex into a chain complex by relying on constant-sized local codes h1, . . . , ht as gadgets. A recent result of Panteleev and Kalachev on existence of tuples of codes that are product expanding enables us to prove lower bounds on the cycle and co-cycle expansion of our chain complex. For t = 4 our construction gives a new family of "almost-good" quantum LTCs — with constant relative rate, inverse-polylogarithmic relative distance and soundness, and constant-size parity checks. Both the distance of the quantum code and its local testability are proven directly from the cycle and co-cycle expansion of our chain complex. Copyright © 2024, The Authors. All rights reserved.

关键词： Expansion

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Nullspacenet: Nullspace convoluional neural network with differentiable loss function

arXiv

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arXiv 2020年

作者： Abdelpakey, Mohamed H. Shehata, Mohamed S. University of British Columbia Department of Computer Science Math Physics and Statistics KelownaBC Canada Memorial University of Newfoundland Computer Engineering and Applied Science St. John’sNL Canada

We propose NullSpaceNet, a novel network that maps from the pixel level input to a joint-nullspace (as opposed to the traditional feature space), where the newly learned joint-nullspace features have clearer interpretation and are more separable. NullSpaceNet ensures that all inputs from the same class are collapsed into one point in this new joint-nullspace, and the different classes are collapsed into different points with high separation margins. Moreover, a novel differentiable loss function is proposed that has a closed-form solution with no free-parameters. NullSpaceNet exhibits superior performance when tested against VGG16 with fully-connected layer over 4 different datasets, with accuracy gain of up to 4.55%, a reduction in learnable parameters from ∼ 135Mto ∼ 19M, and reduction in inference time of ∼ 99% in favor of NullSpaceNet. This means that NullSpaceNet needs less than 1% of the time it takes a traditional CNN to classify a batch of images with better accuracy. Copyright © 2020, The Authors. All rights reserved.

关键词： Machine learning

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Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 12th InternationalWorkshop, APPROX 2009 and 13th International Workshop, RANDOM 2009 Berkeley, CA, USA, August 21-23, 2009 Proceedings. Preface

Lecture Notes in Computer Science (including subseries Lectu...

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Lecture Notes in computer science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2009年 5687 LNCS卷 V-VII页

作者： Dinur, Irit Jansen, Klaus Naor, Joseph Rolim, José Weizmann Institute of Science Dept. of Applied Math and Computer Science Rehovot 76100 Israel University of Kiel Institute for Computer Science and Applied Mathematics Olshausenstr. 40 24098 Kiel Germany Technion Computer Science Department Haifa 32000 Israel University of Geneva Centre Universitaire d'Informatique Battelle Bat. A 7 rte de Drize 1227 Carouge Switzerland

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Green's function contact maps for accurate real time collisions

Green's function contact maps for accurate real time collisi...

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IEEE International Conference on Robotics and Automation (ICRA)

作者： C. Ullrich D.K. Pai Institute of Applied Math University of British Columbia Vancouver BC Canada Department of Computer Science University of British Columbia Vancouver BC Canada

In this article, we discuss the application, of a Green's function approach to contact maps. We apply the contact map algorithm to the case of an elastic bar impacting on a massive foundation. It is demonstrated t... 详细信息

关键词： Green's function methods Solid modeling Computational modeling Energy loss Boundary element methods Telerobotics Virtual environment Partial differential equations Iris computer science

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Impossibility results for recycling random bits in two-prover proof systems 95

Impossibility results for recycling random bits in two-prove...

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Proceedings of the twenty-seventh annual ACM symposium on Theory of computing

作者： Uriel Feige Joe Kilian Department of Applied Math and Computer Science the Weizmann Institute Rehovot 76100 Israel NEC Research Institute 4 Independence Way Princeton NJ

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Noisy Circumnutations Facilitate Self-Organized Shade Avoidance in Sunflowers

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Physical Review X 2024年第3期14卷 031027-031027页

作者： Chantal Nguyen Imri Dromi Ahron Kempinski Gabriella E. C. Gall Orit Peleg Yasmine Meroz BioFrontiers Institute School of Plant Science and Food Security The Center for Physics and Chemistry of Living Systems Zukunftskolleg Department of Biology Centre for the Advanced Study of Collective Behaviour Konstanz Germany Department of Computer Science Department of Physics Department of Applied Math Department of Ecology and Evolutionary Biology Santa Fe New Mexico USA

Circumnutations are widespread in plants and typically associated with exploratory movements; however, a quantitative understanding of their role remains elusive. In this study we report, for the first time, the role of noisy circumnutations in facilitating an optimal growth pattern within a crowded group of mutually shading plants. We revisit the problem of self-organization observed for sunflowers, mediated by shade response interactions. Our analysis reveals that circumnutation movements conform to a bounded random walk characterized by a remarkably broad distribution of velocities, covering 3 orders of magnitude. In motile animal systems such wide distributions of movement velocities are frequently identified with enhancement of behavioral processes, suggesting that circumnutations may serve as a source of functional noise. To test our hypothesis, we developed a Langevin-type parsimonious model of interacting growing disks, informed by experiments, successfully capturing the characteristic dynamics of individual and multiple interacting plants. Employing our simulation framework we examine the role of circumnutations in the system, and find that the observed breadth of the velocity distribution represents a sharp transition in the force-noise ratio, conferring advantageous effects by facilitating exploration of potential configurations, leading to an optimized arrangement with minimal shading. These findings represent the first report of functional noise in plant movements and establish a theoretical foundation for investigating how plants navigate their environment by employing computational processes such as task-oriented processes, optimization, and active sensing. Since plants move by growing, space and time are coupled, and dynamics of self-organization lead to emergent 3D patterns. As such, this system provides conceptual insight for other interacting growth-driven systems such as fungal hyphae, neurons and self-growing robots, as well as active matter sys

关键词： Animal behavior, social interactions & emergent phenomena Biological self-organization Emergence of patterns Emergent biological functions from complex interactions Foraging Patterns in complex systems Plant development Scaling laws of complex systems

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Clustering appearances of 3D objects

Clustering appearances of 3D objects

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Conference on computer Vision and Pattern Recognition (CVPR)

作者： R. Basri D. Roth D. Jacobs Department of Applied Math Weizmann Institute of Science Rehovoth Israel Department of Computer Science University of Illinois Urbana IL USA NEC Research Institute Inc. Princeton NJ USA

We introduce a method for unsupervised clustering of images of 3D objects. Our method examines the space of all images and partitions the images into sets that form smooth and parallel surfaces in this space. It further uses sequences of images to obtain more reliable clustering. Finally, since our method relies on a non-Euclidean similarity measure we introduce algebraic techniques for estimating local properties of these surfaces without first embedding the images in a Euclidean space. We demonstrate our method by applying it to a large database of images.

关键词： Distortion measurement Image databases Shape Jacobian matrices computer science National electric code Extraterrestrial measurements computer vision Humans Visual system

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BUZZ: Beehive-structured Sparse KV Cache with Segmented Heavy Hitters for Efficient LLM Inference

arXiv

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arXiv 2024年

作者： Zhao, Junqi Fang, Zhijin Li, Shu Yang, Shaohui He, Shichao Department of Computer Science New York University New York United States Department of Statistics and Data Science University of California Los Angeles United States Department of Mathematical Science Beihang University Beijing China School of Computer Science University of Leed Leeds United Kingdom Department of Computer Science and Applied Math Brandeis University Boston United States

Large language models (LLMs) are essential in natural language processing but often struggle with inference speed and computational efficiency, limiting real-time deployment. The key-value (KV) cache mechanism reduces computational overhead in transformer models, but challenges in maintaining contextual understanding remain. In this paper, we propose BUZZ, a novel KV caching algorithm that leverages structured contextual information to minimize cache memory usage while enhancing inference speed. BUZZ employs a beehive-structured sparse cache, incorporating a sliding window to capture recent information and dynamically segmenting historical tokens into chunks to prioritize important tokens in local neighborhoods. We evaluate BUZZ on four real-world datasets: CNN/Daily Mail, XSUM, Wikitext, and 10-QA. Our results demonstrate that BUZZ (1) reduces cache memory usage by 2.5× in LLM inference while maintaining over 99% accuracy in long-text summarization, and (2) surpasses state-of-the-art performance in multi-document question answering by 7.69% under the same memory limit, where full cache methods encounter out-of-memory issues. Additionally, BUZZ achieves significant inference speedup with a log n time complexity. The code is available at: https://***/JunqiZhao888/buzz-llm. Copyright © 2024, The Authors. All rights reserved.

关键词： Cache memory

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The estimate for the cost of a search tree constructed on an arbitrary set of binary words

The estimate for the cost of a search tree constructed on an...

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IEEE International Symposium on Information Theory

作者： A. Fedotov B. Ryabko Department of Information Technologies Institute of Computational Technologies SB RAS Novosibirsk Russia Department of Applied math and Cybernetics Siberian State University of Computer Science Novosibirsk Russia

Simple algorithm constructing search trees for the given set of binary words is presented. It is shown that the average cost of result of this algorithm, and, hence, the average cost of the optimum search tree is near... 详细信息

关键词： Cost function Binary search trees computer science Information technology Electronic mail Application software Biology NP-hard problem Cybernetics Art

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Strong edge coloring for channel assignment in wireless radio networks

Strong edge coloring for channel assignment in wireless radi...

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IEEE Annual Conference on Pervasive Computing and Communications Workshops (PerCom)

作者： C.L. Barrett G. Istrate V.S.A. Kumar M.V. Marathe S. Thite S. Thulasidasan Virginia Bio-Informatics Institute and Department of Computer Science Virginia Polytechnic Institute and State University USA Basic and Applied Simulation Science (CCS-5) Los Alamos National Laboratory USA Department of Math & Computer Science Technische Universiteit Eindhoven Netherlands

We give efficient sequential and distributed approximation algorithms for strong edge coloring graphs modeling wireless networks. Strong edge coloring is equivalent to computing a conflict-free assignment of channels ... 详细信息

关键词： Intelligent networks Radio networks Transceivers Interference Radio network Approximation algorithms Frequency computer science Media Access Protocol Computational modeling

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