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Large Language Models (LLMs) exhibit persistent logical failures in complex reasoning due to the lack of an internal axiomatic framework. We propose Mathesis, a neuro-symbolic architecture that encodes mathematical states as higher-order…
Structural Health Monitoring (SHM) plays a crucial role in maintaining aging and critical infrastructure, supporting applications such as smart cities and digital twinning. These applications demand machine learning models capable of…
Diagrammatic reasoning (DR) is pervasive in human problem solving as a powerful adjunct to symbolic reasoning based on language-like representations. The research reported in this paper is a contribution to building a general purpose DR…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational…
Stochastic Computing (SC) is a computing paradigm that allows for the low-cost and low-power computation of various arithmetic operations using stochastic bit streams and digital logic. In contrast to conventional representation schemes…
Symbolic computation systems suffer from memory inefficiencies due to redundant storage of structurally identical subexpressions, commonly known as expression swell, which degrades performance in both classical computer algebra and emerging…
Geometric algebra (GA) is a mathematical tool for geometric computing, providing a framework that allows a unified and compact approach to geometric relations which in other mathematical systems are typically described using different more…
The experimental evaluation of algorithms results in a large set of data which generally do not follow a normal distribution or are not heteroscedastic. Besides, some of its entries may be missing, due to the inability of an algorithm to…
The computation of the $L_\infty $-norm is an important issue in $H_{\infty}$ control, particularly for analyzing system stability and robustness. This paper focuses on symbolic computation methods for determining the $L_{\infty} $-norm of…
This paper studies the large-scale subspace clustering (LSSC) problem with million data points. Many popular subspace clustering methods cannot directly handle the LSSC problem although they have been considered as state-of-the-art methods…
A semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities having real coefficients and is a union of finitely many maximally connected components. We consider the problem of deciding whether two…
The paper studies sequential reasoning over graph-structured data, which stands as a fundamental task in various trending fields like automated math problem solving and neural graph algorithm learning, attracting a lot of research interest.…
Recent advances in large language models have demonstrated impressive capabilities in mathematical formalization. However, existing benchmarks focus on logical verification of declarative propositions, often neglecting the task of…
Efficient omission of symmetric solution candidates is essential for combinatorial problem-solving. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for…
Despite outstanding performance in many tasks, language models are notoriously inclined to make factual errors in tasks requiring arithmetic computation. We address this deficiency by creating Calc-X, a collection of datasets that…
Many software engineering studies or tasks rely on categorizing software engineering artifacts. In practice, this is done either by defining simple but often imprecise heuristics, or by manual labelling of the artifacts. Unfortunately,…
Pointer arithmetic is widely used in low-level programs, e.g. memory allocators. The specification of such programs usually requires using pointer arithmetic inside inductive definitions to define the common data structures, e.g. heap lists…
Symbolic regression (SR) traditionally balances accuracy and complexity, implicitly assuming that simpler formulas are structurally more rational. We argue that this assumption is insufficient: existing algorithms often exploit this metric…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…