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The problem of devising learning strategies for discrete losses (e.g., multilabeling, ranking) is currently addressed with methods and theoretical analyses ad-hoc for each loss. In this paper we study a least-squares framework to…

Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…

Given an edge-weighted undirected graph and a list of k source-sink pairs of vertices, the well-known minimum multicut problem consists in selecting a minimum-weight set of edges whose removal leaves no path between every source and its…

We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions and on interpolation, which has received little attention in…

A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…

We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also useful in computational topology and computer graphics. We…

We consider the median procedure (Barthelemy and Monjardet, 1981) that aggregates a sequence n of binary relations from some input class into a single binary relation from some (possibly different) output class, minimizing the number of…

We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.

Modern retrieval problems are characterised by training sets with potentially billions of labels, and heterogeneous data distributions across subpopulations (e.g., users of a retrieval system may be from different countries), each of which…

We consider the distributed weight balancing problem in networks of nodes that are interconnected via directed edges, each of which is able to admit a positive integer weight within a certain interval, captured by individual lower and upper…

We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…

We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…

The discrete logarithm problem in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have time complexity of $\mathcal{O}(\sqrt{N}\log N)$, and a space complexity of…

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…

In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…

Weight binarization has emerged as a promising strategy to reduce the complexity of large language models (LLMs). Existing approaches fall into post-training binarization, which is simple but causes severe performance loss, and…

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been…

We construct cryptographic trilinear maps that involve simple, non-ordinary abelian varieties over finite fields. In addition to the discrete logarithm problems on the abelian varieties, the cryptographic strength of the trilinear maps is…

The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of…

In this research, we examine the minsum flow problem in dynamic path networks where flows are represented as discrete and weighted sets. The minsum flow problem has been widely studied for its relevance in finding evacuation routes during…