Related papers: The Linear Algebra Mapping Problem. Current state …
Context: Due to the demand for strong algorithmic reasoning, complex logic implementation, and strict adherence to input/output formats and resource constraints, competitive programming generation by large language models (LLMs) is…
Optimization modeling translates real decision-making problems into mathematical optimization models and solver-executable implementations. Although language models are increasingly used to generate optimization formulations and solver…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
This paper presents an in-depth analysis of the performance of seven different Large Language Models (LLMs) in solving a diverse set of math advanced calculus problems. The study aims to evaluate these models' accuracy, reliability, and…
This document describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities with symbolic computation in exact…
The objective of this research is to construct parallel implementations of the Jacobi algorithm used for the solution of linear algebraic systems, to measure their speedup with respect to the serial case and to compare each other, regarding…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
Effective math tutoring requires not only solving problems but also diagnosing students' difficulties and guiding them step by step. While multimodal large language models (MLLMs) show promise, existing benchmarks largely overlook these…
The pursuit of leaderboard rankings in Large Language Models (LLMs) has created a fundamental paradox: models excel at standardized tests while failing to demonstrate genuine language understanding and adaptability. Our systematic analysis…
Machine learning (ML) now pervades the field of Automated Program Repair (APR). Algorithms deploy neural machine translation and large language models (LLMs) to generate software patches, among other tasks. But, there are important…
Large Language Models (LLMs) are demonstrating rapid improvements on complex reasoning benchmarks, particularly when allowed to utilize intermediate reasoning steps before converging on a final solution. However, current literature often…
Manifold optimization appears in a wide variety of computational problems in the applied sciences. In recent statistical methodologies such as sufficient dimension reduction and regression envelopes, estimation relies on the optimization of…
We assess the situation of our elementary Linear Algebra classes in the US holistically and through personal history recollections. Possible remedies for our elementary Linear Algebra's teaching problems are discussed and a change from…
Recent frontier-level LLMs have saturated many previously difficult benchmarks, leaving little room for further differentiation. This progress highlights the need for challenging benchmarks that provide objective verification. In this…
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users…
Tropical algebra, including max-plus, min-plus, and related idempotent semirings, provides a unifying framework in which many optimization problems that are nonlinear in classical algebra become linear. This property makes tropical methods…
Large language models (LLMs) demonstrate impressive capabilities in mathematical reasoning. However, despite these achievements, current evaluations are mostly limited to specific mathematical topics, and it remains unclear whether LLMs are…
Important tasks such as reasoning and planning are fundamentally algorithmic, meaning that solving them robustly requires acquiring true reasoning or planning algorithms, rather than shortcuts. Large Language Models lack true algorithmic…
The ecosystem of Lean and Mathlib has become the de facto standard for large language model (LLM) assisted formal reasoning with remarkable successes in recent years. Those successes, however, only consume Mathlib as an essential dependency…
Large language models (LLMs) are used in software development to assist in various tasks, e.g., code generation and code completion, but empirical evaluations of the quality of the results produced by these models focus on correctness and…