相关论文: Non-monotonicity of closed convexity in neural cod…

Motivated by applications to the theory of rank-metric codes, we study the problem of estimating the number of common complements of a family of subspaces over a finite field in terms of the cardinality of the family and its intersection…

Recently, code language models have achieved notable advancements in addressing a diverse array of essential code comprehension and generation tasks. Yet, the field lacks a comprehensive deep dive and understanding of the code embeddings of…

Deep Learning is mostly responsible for the surge of interest in Artificial Intelligence in the last decade. So far, deep learning researchers have been particularly successful in the domain of image processing, where Convolutional Neural…

Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…

Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code $C$ can be represented by its neural ideal $J_C$. In turn, the polynomials in $J_C$ can be used to…

In coding theory, a common question is to understand the threshold rates of various local properties of codes, such as their list decodability and list recoverability. A recent work Levi, Mosheiff, and Shagrithaya (FOCS 2025) gave a novel…

This paper examines the maximum code rate achievable by a data-driven communication system over some unknown discrete memoryless channel in the finite blocklength regime. A class of channel codes, called learning-based channel codes, is…

Small neural networks (NNs) used for error correction were shown to improve on classic channel codes and to address channel model changes. We extend the code dimension of any such structure by using the same NN under one-hot encoding…

Neural collapse (NC) describes the structured geometry that emerges in the features and weights of trained classifiers. Recent theory suggests NC can be suboptimal in deep architectures, attributing this to an explicit low-rank bias from L2…

We study shallow and deep neural networks whose inputs range over a general topological space. The model is built from a prescribed family of continuous feature maps and reduces to multilayer feedforward networks in the Euclidean case. We…

The integration of optimization problems within neural network architectures represents a fundamental shift from traditional approaches to handling constraints in deep learning. While it is long known that neural networks can incorporate…

New families of unit memory as well as multi-memory convolutional codes are constructed algebraically in this paper. These convolutional codes are derived from the class of group character codes. The proposed codes have basic generator…

Recent studies have revealed that neural networks learn interpretable algorithms for many simple problems. However, little is known about how these algorithms emerge during training. In this article, I study the training dynamics of a small…

Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

The backpropagation of error algorithm used to train deep neural networks has been fundamental to the successes of deep learning. However, it requires sequential backward updates and non-local computations, which make it challenging to…

Noncatastrophic encoders are an important class of polynomial generator matrices of convolutional codes. When these polynomials have coefficients in a finite field, these encoders have been characterized are being polynomial left prime…

We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…

Learning and inferring features that generate sensory input is a task continuously performed by cortex. In recent years, novel algorithms and learning rules have been proposed that allow neural network models to learn such features from…

MDS convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper we introduce a class of MDS convolutional codes whose column distances reach the generalized…