Related papers: Breaking the Mold: Nonlinear Ranking Function Synt…
This is part of an ongoing project to find a general algebraic framework for semiring theory. The structure theory of semirings is quite challenging, largely because of the lack of negation, and such basic properties such as unique…
Let R be a finite principal left ideal ring. Via a total ordering of the ring elements and an ordered basis a lexicographic ordering of the module R^n is produced. This is used to set up a greedy algorithm that selects vectors for which all…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
Evaluating LLM-generated text has become a key challenge, especially in domain-specific contexts like the medical field. This work introduces a novel evaluation methodology for LLM-generated medical explanatory arguments, relying on Proxy…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…
Transformer networks, particularly those achieving performance comparable to GPT models, are well known for their robust feature extraction abilities. However, the nature of these extracted features and their alignment with human-engineered…
The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The…
The rank of a finite algebraic structure with a single binary operation is the minimum number of elements needed to express every other element under the closure of the operation. In the case of groups, the previous best algorithm for…
Satisfiability Modulo the Theory of Nonlinear Real Arithmetic, SMT(NRA) for short, concerns the satisfiability of polynomial formulas, which are quantifier-free Boolean combinations of polynomial equations and inequalities with integer…
We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in…
Lexicographic Ranking SuperMartingale (LexRSM) is a probabilistic extension of Lexicographic Ranking Function (LexRF), which is a widely accepted technique for verifying program termination. In this paper, we are the first to propose sound…
Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the…
It is open whether equivalence ( f = g ) is decidable for string-to-string polyregular functions. We consider their higher-order extension based on the {\lambda}-calculus definition of polyregular functions from Boja\'nczyk (2018). In this…
This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as…
We show that finding rank-$R$ decompositions of a 3D tensor, for $R\le 4$, over a fixed finite field can be done in polynomial time. However, if some cells in the tensor are allowed to have arbitrary values, then rank-2 is NP-hard over the…
This paper is about certain string-to-string functions, called the polyregular functions. These are like the regular string-to-string functions, except that they can have polynomial (and not just linear) growth. The class has four…
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…
Textual explanations, generated with large language models (LLMs), are increasingly used to justify recommendations. Yet, evaluating these explanations remains a critical challenge. We advocate a shift in objective: rank, don't generate. We…
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…