Related papers: ML4PG in Computer Algebra verification
Craig interpolation is used in program verification for automating key tasks such as the inference of loop invariants and the computation of program abstractions. This chapter covers some of the most important techniques that have been…
Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as well as special models (e.g. Toeplitz, sparse, trees) that…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
Machine learning (ML) applications have automated numerous real-life tasks, improving both private and public life. However, the black-box nature of many state-of-the-art models poses the challenge of model verification; how can one be sure…
An integer program is called ideal if its continuous relaxation coincides with its convex hull allowing the problem to be solved as a continuous program and offering substantial computational advantages. Proving idealness analytically can…
Modern computing workloads commonly involve matrix-matrix multiplication (mmul) as a core computing pattern. Coarse-Grained Reconfigurable Arrays (CGRAs) can flexibly and efficiently support it, since they combine operation-level…
Machine learning applications are increasingly deployed not only to serve predictions using static models, but also as tightly-integrated components of feedback loops involving dynamic, real-time decision making. These applications pose a…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…
We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a…
With the announcement that the Aurora Supercomputer will be composed of general purpose Intel CPUs complemented by discrete high performance Intel GPUs, and the deployment of the oneAPI ecosystem, Intel has committed to enter the arena of…
This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary…
We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions.…
Many machine learning (ML) libraries are accessible online for ML practitioners. Typical ML pipelines are complex and consist of a series of steps, each of them invoking several ML libraries. In this demo paper, we present ExeKGLib, a…
Machine learning potentials (MLP) allow to perform large-scale molecular dynamics simulations with about the same accuracy as electronic structure calculations provided that the selected model is able to capture the relevant physics of the…
This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…
Program code as a data source is gaining popularity in the data science community. Possible applications for models trained on such assets range from classification for data dimensionality reduction to automatic code generation. However,…
Linear Genetic Programming (LGP) is a powerful technique that allows for a variety of problems to be solved using a linear representation of programs. However, there still exists some limitations to the technique, such as the need for…
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in…
This paper contains a discussion of a library of formalized mathematics for the proof assistant Coq which the author worked on in 2011-13.