相关论文: On the similarities between generalized rank and H…

Generalized pair weights of linear codes are generalizations of minimum symbol-pair weights, which were introduced by Liu and Pan \cite{LP} recently. Generalized pair weights can be used to characterize the ability of protecting information…

Binary codes have been widely used in vision problems as a compact feature representation to achieve both space and time advantages. Various methods have been proposed to learn data-dependent hash functions which map a feature vector to a…

We show that the network coding and index coding problems are equivalent. This equivalence holds in the general setting which includes linear and non-linear codes. Specifically, we present an efficient reduction that maps a network coding…

In this work, we explore the relationship between free resolution of some monomial ideals and Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure smaller than the set of codewords of minimal support…

This paper investigates general properties of codes with the rank metric. We first investigate asymptotic packing properties of rank metric codes. Then, we study sphere covering properties of rank metric codes, derive bounds on their…

In this paper, we develop a geometric framework for matrix rank-metric codes based on generator tensors and their slice spaces. To every nondegenerate matrix rank-metric code, we associate two systems, which translate metric properties of…

The code equivalence problem is central in coding theory and cryptography. While classical invariants are effective for Hamming and rank metrics, the sum-rank metric, which unifies both, introduces new challenges. This paper introduces new…

Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…

The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of K\"otter and Kschischang. A large class of constant-dimension subspace codes is…

We extend the notion of locality from the Hamming metric to the rank and subspace metrics. Our main contribution is to construct a class of array codes with locality constraints in the rank metric. Our motivation for constructing such codes…

Evaluation of generative models is mostly based on the comparison between the estimated distribution and the ground truth distribution in a certain feature space. To embed samples into informative features, previous works often use…

We show that the influence of a subset of the training samples can be removed -- or "forgotten" -- from the weights of a network trained on large-scale image classification tasks, and we provide strong computable bounds on the amount of…

We consider a class of linear codes associated to projective algebraic varieties defined by the vanishing of minors of a fixed size of a generic matrix. It is seen that the resulting code has only a small number of distinct weights. The…

Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes. In those works the focus is on full privacy and full…

In the training of large deep neural networks, there is a need for vast amounts of training data. To meet this need, data is collected from multiple domains, such as Wikipedia and GitHub. These domains are heterogeneous in both data quality…

In recent years, network embedding methods have garnered increasing attention because of their effectiveness in various information retrieval tasks. The goal is to learn low-dimensional representations of vertexes in an information network…

Link prediction is a fundamental problem in network science, aiming to infer potential or missing links based on observed network structures. With the increasing adoption of parameterized models, the rigor of evaluation protocols has become…

We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight matrices. Our bound is tighter than existing norm-based…

Understanding how feature learning affects generalization is among the foremost goals of modern deep learning theory. Here, we study how the ability to learn representations affects the generalization performance of a simple class of…

Recent literature generalization in deep learning has examined the relationship between the curvature of the loss function at minima and generalization, mainly in the context of overparameterized neural networks. A key observation is that…