Related papers: Dimension Expanders via Rank Condensers

The subspace design property for additive codes is a higher-dimensional generalization of the minimum distance property. As shown recently by Brakensiek, Chen, Dhar and Zhang, it implies that the code has similar performance as random…

In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity…

We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…

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…

We introduce a novel concept of rank for subsets of finite metric spaces E^n_q (the set of all n-dimensional vectors over an alphabet of size q) equipped with the Hamming distance, where the rank R(A) of a subset A is defined as the number…

A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…

Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…

Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random network coding. In this paper, we show that constant-rank codes are closely related to constant-dimension codes and…

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…

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…

In this paper we develop a method for investigating semi-device-independent randomness expansion protocols that was introduced in [Li et al., Phys. Rev. A $\mathbf{87}$, 020302(R) (2013)]. This method allows to lower-bound, with…

In this paper we investigate connections between linear sets and subspaces of linear maps. We give a geometric interpretation of the results of [18, Section 5] on linear sets on a projective line. We extend this to linear sets in arbitrary…

In this work we describe an explicit, simple, construction of large subsets of F^n, where F is a finite field, that have small intersection with every k-dimensional affine subspace. Interest in the explicit construction of such sets, termed…

As network data has become ubiquitous in the sciences, there has been growing interest in network models whose structure is driven by latent node-level variables in a (typically low-dimensional) latent geometric space. These "latent…

We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

Low-dimensional embeddings, from classical spectral embeddings to modern neural-net-inspired methods, are a cornerstone in the modeling and analysis of complex networks. Recent work by Seshadhri et al. (PNAS 2020) suggests that such…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

Due to the success of residual networks (resnets) and related architectures, shortcut connections have quickly become standard tools for building convolutional neural networks. The explanations in the literature for the apparent…

For a growing number of applications such as cellular, peer-to-peer, and sensor networks, efficient error-free transmission of data through a network is essential. Toward this end, K\"{o}tter and Kschischang propose the use of subspace…