English
Related papers

Related papers: Binary perceptron computational gap -- a parametri…

200 papers

We develop an Accelerated Back Pressure (ABP) algorithm using Accelerated Dual Descent (ADD), a distributed approximate Newton-like algorithm that only uses local information. Our construction is based on writing the backpressure algorithm…

Optimization and Control · Mathematics 2013-02-07 Michael Zargham , Alejandro Ribeiro , Ali Jadbabaie

Attributions aim to identify input pixels that are relevant to the decision-making process. A popular approach involves using modified backpropagation (BP) rules to reverse decisions, which improves interpretability compared to the original…

Machine Learning · Computer Science 2025-03-17 Guanhua Zheng , Jitao Sang , Changsheng Xu

The Fredrickson-Andersen 2-spin facilitated model on $\mathbb{Z}^d$ (FA-2f) is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring dynamical facilitation, an important mechanism in condensed matter physics.…

Probability · Mathematics 2024-01-31 Ivailo Hartarsky , Fabio Martinelli , Cristina Toninelli

We consider restricted Boltzmann machines with a binary visible layer and a Gaussian hidden layer trained by an unlabelled dataset composed of noisy realizations of a single ground pattern. We develop a statistical mechanics framework to…

Disordered Systems and Neural Networks · Physics 2024-06-17 Alberto Fachechi , Elena Agliari , Miriam Aquaro , Anthony Coolen , Menno Mulder

We extend the Rate-Distortion-Perception (RDP) framework to the R\'enyi information-theoretic regime, utilizing Sibson's $\alpha$-mutual information to characterize the fundamental limits under distortion and perception constraints. For…

Information Theory · Computer Science 2026-05-12 Jiahui Wei , Marios Kountouris

The symmetric binary perceptron ($\mathrm{SBP}_{\kappa}$) problem with parameter $\kappa : \mathbb{R}_{\geq1} \to [0,1]$ is an average-case search problem defined as follows: given a random Gaussian matrix $\mathbf{A} \sim…

Statistics Theory · Mathematics 2025-07-29 Neekon Vafa , Vinod Vaikuntanathan

Arbitrary Pattern Formation (APF) is a fundamental coordination problem in swarm robotics. It requires a set of autonomous robots (mobile computing units) to form an arbitrary pattern (given as input) starting from any initial pattern. This…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-03-28 Avisek Sharma , Satakshi Ghosh , Pritam Goswami , Buddhadeb Sau

Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density…

Computational Physics · Physics 2024-03-01 He Li , Zechen Tang , Jingheng Fu , Wen-Han Dong , Nianlong Zou , Xiaoxun Gong , Wenhui Duan , Yong Xu

Deep learning has redefined the field of artificial intelligence (AI) thanks to the rise of artificial neural networks, which are architectures inspired by their neurological counterpart in the brain. Through the years, this dualism between…

Machine Learning · Computer Science 2023-02-21 Tommaso Salvatori , Yuhang Song , Thomas Lukasiewicz , Rafal Bogacz , Zhenghua Xu

Square Wave Perceptrons (SWPs) form a class of neural network models with oscillating activation function that exhibit intriguing ``hardness'' properties in the high-dimensional limit at a fixed constraint density $\alpha = O(1)$. In this…

In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…

Probability · Mathematics 2025-10-30 Laurent Massoulié

We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit. This…

Statistics Theory · Mathematics 2018-06-18 Ahmed El Alaoui , Michael I. Jordan

Stochastic gradient descent with backpropagation is the workhorse of artificial neural networks. It has long been recognized that backpropagation fails to be a biologically plausible algorithm. Fundamentally, it is a non-local procedure --…

Machine Learning · Statistics 2021-12-24 Ganlin Song , Ruitu Xu , John Lafferty

This paper examines the role of threshold logic in understanding generative artificial intelligence. Threshold functions, originally studied in the 1960s in digital circuit synthesis, provide a structurally transparent model of neural…

Artificial Intelligence · Computer Science 2026-04-06 Ilya Levin

This paper introduces the Adaptive Base Representation (ABR) Theorem and proposes a novel number system that offers a structured alternative to the binary number system for digital computers. The ABR number system enables each decimal…

Information Theory · Computer Science 2025-10-20 Ravin Kumar

Wasserstein distributionally robust control (DRC) recently emerges as a principled paradigm for handling uncertainty in stochastic dynamical systems. However, it constructs data-driven ambiguity sets via uniform distribution shifts before…

Optimization and Control · Mathematics 2025-10-14 Jingyi Wu , Chao Ning , Yang Shi

We study the stationary states of an over-damped active Brownian particle (ABP) in a harmonic trap in two dimensions, via mathematical calculations and numerical simulations. In addition to translational diffusion, the ABP self-propels with…

Statistical Mechanics · Physics 2023-07-27 Urvashi Nakul , Manoj Gopalakrishnan

Limited precision of synaptic weights is a key aspect of both biological and hardware implementation of neural networks. To assign low-precise weights during learning is a non-trivial task, but may benefit from representing to-be-learned…

Disordered Systems and Neural Networks · Physics 2020-07-13 Zedong Bi , Changsong Zhou

We study a generic class of \emph{random optimization problems} (rops) and their typical behavior. The foundational aspects of the random duality theory (RDT), associated with rops, were discussed in \cite{StojnicRegRndDlt10}, where it was…

Probability · Mathematics 2023-12-04 Mihailo Stojnic

This thesis develops a general theoretical and numerical framework for achieving high-contrast atom interferometry based on double Bragg diffraction (DBD). While DBD offers intrinsic symmetry, reduced sensitivity to internal-state…

Quantum Physics · Physics 2026-03-25 Rui Li