Related papers: Constrained Linear Representability of Polymatroid…
In this paper, we investigate the verification of quantized Graph Neural Networks (GNNs), where some fixed-width arithmetic is used to represent numbers. We introduce the linear-constrained validity (LVP) problem for verifying GNNs…
In this work we study approximation algorithms for the \textit{Bounded Color Matching} problem (a.k.a. Restricted Matching problem) which is defined as follows: given a graph in which each edge $e$ has a color $c_e$ and a profit $p_e \in…
Efficient deterministic algorithms to construct representations of lattice path matroids over finite fields are presented. They are built on known constructions of hierarchical secret sharing schemes, a recent characterization 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…
The problem of finding network codes for general connections is inherently difficult in capacity constrained networks. Resource minimization for general connections with network coding is further complicated. Existing methods for…
We consider the problem of learning discriminative representations for data in a high-dimensional space with distribution supported on or around multiple low-dimensional linear subspaces. That is, we wish to compute a linear injective map…
Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…
Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network is NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are…
We consider the following \textit{network computation problem}. In an acyclic network, there are multiple source nodes, each generating multiple messages, and there are multiple sink nodes, each demanding a function of the source messages.…
Determining information ratios of access structures is an important problem in secret sharing. Information inequalities and linear rank inequalities play an important role for proving bounds. Characteristic-dependent linear rank…
The decomposition theory of matroids initiated by Paul Seymour in the 1980's has had an enormous impact on research in matroid theory. This theory, when applied to matrices over the binary field, yields a powerful decomposition theory for…
Forwarding table verification consists in checking the distributed data-structure resulting from the forwarding tables of a network. A classical concern is the detection of loops. We study this problem in the context of software-defined…
Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
In this paper we give a necessary and sufficient criterion for representability of a matroid over an algebraic closed field. This leads to an algorithm, based on an extension of Groebner Bases, in order to decide if a given matroid is…
We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real…
It is well known that linear rank-metric codes give rise to q-polymatroids. Analogously to matroid theory one may ask whether a given q-polymatroid is representable by a rank-metric code. We provide an answer by presenting an example of a…
Skew-representable matroids form a fundamental class in matroid theory, bridging combinatorics and linear algebra. They play an important role in areas such as coding theory, optimization, and combinatorial geometry, where linear structure…
We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…