Related papers: Representation Gap of the Motzkin Monoid

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…

Transformer models underpin many recent advances in practical machine learning applications, yet understanding their internal behavior continues to elude researchers. Given the size and complexity of these models, forming a comprehensive…

Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…

We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the…

Vector quantization is a technique in machine learning that discretizes continuous representations into a set of discrete vectors. It is widely employed in tokenizing data representations for large language models, diffusion models, and…

By introducing a subsampling strategy, we propose a randomized block Kaczmarz-Motzkin method for solving linear systems. Such strategy not only determines the block size, but also combines and extends two famous strategies, i.e., randomness…

Neural networks have been shown vulnerable to a variety of adversarial algorithms. A crucial step to understanding the rationale for this lack of robustness is to assess the potential of the neural networks' representation to encode the…

Motivated by recent advances in solution methods for mixed-integer convex optimization (MICP), we study the fundamental and open question of which sets can be represented exactly as feasible regions of MICP problems. We establish several…

We present a performant and rigorous algorithm for certifying that a matrix is close to being a projection onto an irreducible subspace of a given group representation. This addresses a problem arising when one seeks solutions to…

Foundation machine learning interatomic potentials (MLIPs) are trained on overlapping chemical spaces, yet their latent representations remain model-specific. Here, we show that independently developed MLIPs exhibit statistically consistent…

This article is a survey of matroid theory aimed at algebraic geometers. Matroids are combinatorial abstractions of linear subspaces and hyperplane arrangements. Not all matroids come from linear subspaces; those that do are said to be…

This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…

We introduce an algorithm to decompose orthogonal matrix representations of the symmetric group over the reals into irreducible representations, which as a by-product also computes the multiplicities of the irreducible representations. The…

An `obfuscation' for encrypted computing is quantified exactly here, leading to an argument that security against polynomial-time attacks has been achieved for user data via the deliberately `chaotic' compilation required for security…

Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…

In contrast to human vision, common recognition algorithms often fail on partially occluded images. We propose characterizing, empirically, the algorithmic limits by finding a minimal recognizable patch (MRP) that is by itself sufficient to…

Complex networks representing social interactions, brain activities, molecular structures have been studied widely to be able to understand and predict their characteristics as graphs. Models and algorithms for these networks are used in…

The performance of graph representation learning is affected by the quality of graph input. While existing research usually pursues a globally smoothed graph embedding, we believe the rarely observed anomalies are as well harmful to an…

There is some theoretical evidence that deep neural networks with multiple hidden layers have a potential for more efficient representation of multidimensional mappings than shallow networks with a single hidden layer. The question is…