Related papers: Quantified Linear and Polynomial Arithmetic Satisf…

Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step in checking for possible errors in LTL assertions. Extant LTL satisfiability checkers use a variety of different search procedures. With the sole exception of LTL…

Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5…

The Satisfiability (SAT) problem is a core challenge with significant applications in software engineering, including automated testing, configuration management, and program verification. This paper presents SolSearch, a novel framework…

Large Language Models (LLMs) have demonstrated impressive performance across various domains. However, the enormous number of model parameters makes fine-tuning challenging, significantly limiting their application and deployment. Existing…

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical…

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and…

Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…

We introduce notions of simulation between semiring-weighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo---hence soundness against language…

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…

Large pre-trained models, such as large language models (LLMs), present significant resource challenges for fine-tuning due to their extensive parameter sizes, especially for applications in mobile systems. To address this, Low-Rank…

This report showcases the role of, and future directions for, the field of Randomized Numerical Linear Algebra (RNLA) in a selection of scientific applications. These applications span the domains of imaging, genomics and dynamical systems,…

Generative AI agents are often expected to respond to complex user requests that have No One Right Answer (NORA), e.g., "design a vegetarian meal plan below 1800 calories". Such requests may entail a set of constraints that the agent should…

Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…

Low rank approximation of a matrix (hereafter LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA at sublinear cost -- by using much fewer memory cells and…

In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to…

For large language models (LLMs), post-training quantization (PTQ) can significantly reduce memory footprint and computational overhead. Model quantization is rapidly evolving. Though many papers report breakthrough results, they are often…

We present a method for solving nonlinear eigenvalue problems using rational approximation. The method uses the AAA method by Nakatsukasa, S\`{e}te, and Trefethen to approximate the nonlinear eigenvalue problem by a rational eigenvalue…

Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…

Despite impressive results on curated benchmarks, the practical impact of large language models (LLMs) on research-level neural theorem proving and proof autoformalization is still limited. We introduce RLMEval, an evaluation suite for…

This study combines simulated annealing with delta evaluation to solve the joint stratification and sample allocation problem. In this problem, atomic strata are partitioned into mutually exclusive and collectively exhaustive strata. Each…