Related papers: Binary perceptron: efficient algorithms can find s…

The geometrical features of the (non-convex) loss landscape of neural network models are crucial in ensuring successful optimization and, most importantly, the capability to generalize well. While minimizers' flatness consistently…

We study the binary perceptron, a random constraint satisfaction problem that asks to find a Boolean vector in the intersection of independently chosen random halfspaces. A striking feature of this model is that at every positive constraint…

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 show that discrete synaptic weights can be efficiently used for learning in large scale neural systems, and lead to unanticipated computational performance. We focus on the representative case of learning random patterns with binary…

We show that two related classes of algorithms, stable algorithms and Boolean circuits with bounded depth, cannot produce an approximate sample from the uniform measure over the set of solutions to the symmetric binary perceptron model at…

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,…

Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving…

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…

The statistical picture of the solution space for a binary perceptron is studied. The binary perceptron learns a random classification of input random patterns by a set of binary synaptic weights. The learning of this network is difficult…

We study the binary and continuous negative-margin perceptrons as simple non-convex neural network models learning random rules and associations. We analyze the geometry of the landscape of solutions in both models and find important…

Supervised learning in a binary perceptron is able to classify an extensive number of random patterns by a proper assignment of binary synaptic weights. However, to find such assignments in practice, is quite a nontrivial task. The relation…

In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…

Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters $K$ is known, this ambiguity often still exists, particularly when there is variation…

Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…

We study the critical window of the symmetric binary perceptron, or equivalently, combinatorial discrepancy. Consider the problem of finding a binary vector $\sigma$ satisfying $\|A\sigma\|_\infty \le K$, where $A$ is an $\alpha n \times n$…

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…

We prove, under an assumption on the critical points of a real-valued function, that the symmetric Ising perceptron exhibits the `frozen 1-RSB' structure conjectured by Krauth and Mezard in the physics literature; that is, typical solutions…

We study statistical and computational limits of clustering when the means of the centres are sparse and their dimension is possibly much larger than the sample size. Our theoretical analysis focuses on the model $X_i = z_i \theta +…

Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights…

We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…