Related papers: Characteristic-Dependent Linear Rank Inequalities …
Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An…
The problem of all-relevant feature selection is concerned with finding a relevant feature set with preserved redundancies. There exist several approximations to solve this problem but only one could give a distinction between strong and…
We consider the conformal properties of geometries described by higher-rank line elements. A crucial role is played by the conformal Killing equation (CKE). We introduce the concept of null-flat spaces in which the line element can be…
In rank-metric cryptography, a vector from a finite dimensional linear space over a finite field is viewed as the linear space spanned by its entries. The rank decoding problem which is the analogue of the problem of decoding a random…
Learning a particular task from a dataset, samples in which originate from diverse contexts, is challenging, and usually addressed by deepening or widening standard neural networks. As opposed to conventional network widening, multi-path…
Networks offer a powerful approach to modeling complex systems by representing the underlying set of pairwise interactions. Link prediction is the task that predicts links of a network that are not directly visible, with profound…
In this paper we study a homological version of the higher-dimensional divergence invariants defined by Brady and Farb. We show that they are quasi-isometry invariants in the class of proper cocompact Hadamard spaces in the sense of…
Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this…
Choosing a deep neural network architecture is a fundamental problem in applications that require balancing performance and parameter efficiency. Standard approaches rely on ad-hoc engineering or computationally expensive validation on a…
The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional)…
Object ranking is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects, which are typically represented as feature vectors, the goal is to learn a ranking…
Rank-based linkage is a new tool for summarizing a collection $S$ of objects according to their relationships. These objects are not mapped to vectors, and ``similarity'' between objects need be neither numerical nor symmetrical. All an…
We give new explicit constructions of several fundamental objects in linear-algebraic pseudorandomness and combinatorics, including lossless rank extractors, weak subspace designs, and strong $s$-blocking sets over finite fields. Our focus…
Methods are described for the solution of linear inference problems subject to deterministic constraints. The approach builds on work by Backus (1970a,b,c) and Parker (1977), but a range useful advances are suggested to address both…
We study the maximal rank in affine subspaces of symmetric or alternating matrices, in terms of the matching numbers of certain associated graphs. Applications include simple proofs of upper bounds on the dimension of such subspaces in…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
Spatial self-attention layers, in the form of Non-Local blocks, introduce long-range dependencies in Convolutional Neural Networks by computing pairwise similarities among all possible positions. Such pairwise functions underpin the…
Diffusion models have become the de facto standard for modern visual generation, including well-established frameworks such as latent diffusion and flow matching. Recently, modeling high-order dynamics has emerged as a promising frontier in…
The standard definition of the dimension of a vector space or rank of a module states that dimension or rank is equal to the cardinality of any basis, which requires an understanding of the concepts of basis, generating set, and linear…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…