Related papers: Parametric RDT approach to computational gap of sy…
Recent studies suggest that asymmetric binary perceptron (ABP) likely exhibits the so-called statistical-computational gap characterized with the appearance of two phase transitioning constraint density thresholds: \textbf{\emph{(i)}} the…
In [97,99,100], an fl-RDT framework is introduced to characterize \emph{statistical computational gaps} (SCGs). Studying \emph{symmetric binary perceptrons} (SBPs), [100] obtained an \emph{algorithmic} threshold estimate $\alpha_a\approx…
We study classical asymmetric binary perceptron (ABP) and associated \emph{local entropy} (LE) as potential source of its algorithmic hardness. Isolation of \emph{typical} ABP solutions in SAT phase seemingly suggests a universal…
We study the statistical capacity of the classical binary perceptrons with general thresholds $\kappa$. After recognizing the connection between the capacity and the bilinearly indexed (bli) random processes, we utilize a recent progress in…
The symmetric binary perceptron ($\texttt{SBP}$) exhibits a dramatic statistical-to-computational gap: the densities at which known efficient algorithms find solutions are far below the threshold for the existence of solutions. Furthermore,…
Recent advances in Rate-Distortion-Perception (RDP) theory highlight the importance of balancing compression level, reconstruction quality, and perceptual fidelity. While previous work has explored numerical approaches to approximate the…
Raptor codes are rateless codes that achieve the capacity on the binary erasure channels. However the maximum degree of optimal output degree distribution is unbounded. This leads to a computational complexity problem both at encoders and…
We study the random binary symmetric perceptron problem, focusing on the behavior of rare high-margin solutions. While most solutions are isolated, we demonstrate that these rare solutions are part of clusters of extensive entropy,…
We consider the injectivity property of the ReLU networks layers. Determining the ReLU injectivity capacity (ratio of the number of layer's inputs and outputs) is established as isomorphic to determining the capacity of the so-called…
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…
We consider the distributed compression of Soft Random Geometric Graphs (SRGGs) above the connectivity threshold. We establish the Slepian-Wolf rate region for the SRGG in the setting where there are a finite number of encoders compressing…
A sequential quadratic programming (SQP) algorithm is designed for nonsmooth optimization problems with upper-C^2 objective functions. Upper-C^2 functions are locally equivalent to difference-of-convex (DC) functions with smooth convex…
We consider the spherical perceptron with Gaussian disorder. This is the set $S$ of points $\sigma \in \mathbb{R}^N$ on the sphere of radius $\sqrt{N}$ satisfying $\langle g_a , \sigma \rangle \ge \kappa\sqrt{N}\,$ for all $1 \le a \le M$,…
We consider the symmetric binary perceptron model, a simple model of neural networks that has gathered significant attention in the statistical physics, information theory and probability theory communities, with recent connections made to…
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…
The binary perceptron problem asks us to find a sign vector in the intersection of independently chosen random halfspaces with intercept $-\kappa$. We analyze the performance of the canonical discrepancy minimization algorithms of…
The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the…
Sequential change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. When the post-change parameters are unknown, we consider a set of detection procedures based on…
We compare analytic predictions for real and Fourier space two-point statistics for biased tracers from a variety of Lagrangian Perturbation Theory approaches against those from state of the art N-body simulations in $f(R)$ Hu-Sawicki and…
We analyze the problem of storing random pattern-label associations using two classes of continuous non-convex weights models, namely the perceptron with negative margin and an infinite-width two-layer neural network with non-overlapping…