Related papers: Polarized Rewriting and Tableaux in B Set Theory
In classification, it is usual to observe that models trained on a given set of classes can generalize to previously unseen ones, suggesting the ability to learn beyond the initial task. This ability is often leveraged in the context of…
We carry out some of Galois's work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite…
We demonstrate that the checkable/synthesisable split in bidirectional typechecking coincides with existing dualities in polarised System L, also known as polarised $\mu\tilde{\mu}$-calculus. Specifically, positive terms and negative…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
We introduce a notion of a (V,T)-module over a vertex algebra V for an arbitrary positive integer T, which is a generalization of a twisted V-module. Under some conditions on V, we construct an associative algebra A^{T}_{m}(V) for…
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…
Rearranging the rows or columns of a sparse matrix using an appropriate ordering can significantly reduce fill-ins, i.e., new nonzeros introduced during matrix factorization, decreasing memory usage and runtime. However, finding an ordering…
Pre-trained language models have been successful on text classification tasks, but are prone to learning spurious correlations from biased datasets, and are thus vulnerable when making inferences in a new domain. Prior work reveals such…
Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
In this paper, we present the Inter-Battery Topic Model (IBTM). Our approach extends traditional topic models by learning a factorized latent variable representation. The structured representation leads to a model that marries benefits…
We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a…
Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning…
Despite success in many domains, neural models struggle in settings where train and test examples are drawn from different distributions. In particular, in contrast to humans, conventional sequence-to-sequence (seq2seq) models fail to…
One introduces a class of projective parameterizations that resemble generalized de Jonqui\`eres maps. Any such parametrization defines a birational map $\mathfrak{F}$ of $\pp^n$ onto a hypersurface $V(F)\subset \pp^{n+1}$ with a strong…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring…
This text, Chapter 23 in the "AutoMathA" handbook, is devoted to the study of rational subsets of groups, with particular emphasis on the automata-theoretic approach to finitely generated subgroups of free groups. Indeed, Stallings'…
We study prime ideals, prime modules, and associated primes of graded modules over rings $S$ graded by a unique product monoid. We consider two situations in detail: (a) the case where $S$ is strongly group-graded and (b) the case where $S$…