Related papers: ML4PG in Computer Algebra verification

Model interpretability has become an important problem in machine learning (ML) due to the increased effect that algorithmic decisions have on humans. Counterfactual explanations can help users understand not only why ML models make certain…

This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…

We present a novel approach to tackle explainability of deep graph networks in the context of molecule property prediction tasks, named MEG (Molecular Explanation Generator). We generate informative counterfactual explanations for a…

Machine learning may enable the automated generation of test oracles. We have characterized emerging research in this area through a systematic literature review examining oracle types, researcher goals, the ML techniques applied, how the…

In this work we announce the Maple package conley to compute connection and C-connection matrices. conley is based on our abstract homological algebra package homalg. We emphasize that the notion of braids is irrelevant for the definition…

We study cohomology for classical Lie superalgebras $\mathfrak{g}$ (e.g. gl(m|n)) over the complex numbers. Using results from invariant theory, we show that there exist subsuperalgebras which detect the cohomology of $\mathfrak{g}.$…

Linear algebra routines are basic building blocks for the statistical software. In this paper we analyzed how can we can improve R performance for matrix computations. We benchmarked few matrix operations using the standard linear algebra…

This paper presents the first demonstration of a viable, ultra-fast, radiation-hard machine learning (ML) application on FPGAs, which could be used in future high-energy physics experiments. We present a three-fold contribution, with the…

We discuss the deal of imperfectness of atomic actions in reality with the background of process algebras. And we show the applications of the imperfect actions in verification of computational systems.

Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…

This paper introduces ProofCloud, a proof retrieval engine for verified proofs in higher order logic. It provides a fast proof searching service for mathematicians and computer scientists for the reuse of proofs and proof packages. In…

While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…

We introduce LinAlg-Bench, a diagnostic benchmark evaluating 10 frontier large language models on structured linear algebra computation across a strict dimensional gradient of 3x3, 4x4, and 5x5 matrices. Spanning 9 task types and 660…

Machine learning (ML) needs industry-standard performance benchmarks to support design and competitive evaluation of the many emerging software and hardware solutions for ML. But ML training presents three unique benchmarking challenges…

This paper is a note on new directions and methodologies for validation and explanation of Machine Learning (ML) models employed for retail credit scoring in finance. Our proposed framework draws motivation from the field of Artificial…

Common programming tools, like compilers, debuggers, and IDEs, crucially rely on the ability to analyse program code to reason about its behaviour and properties. There has been a great deal of work on verifying compilers and static…

Machine learning models have been progressively used for predicting materials properties. These models can be built using pre-existing data and are useful for rapidly screening the physicochemical space of a material, which is…

The software patterns provide building blocks to the design and implementation of a software system, and try to make the software engineering to progress from experience to science. The software patterns were made famous because of the…

We introduce PPL Bench, a new benchmark for evaluating Probabilistic Programming Languages (PPLs) on a variety of statistical models. The benchmark includes data generation and evaluation code for a number of models as well as…

Machine Learner for Automated Reasoning (MaLARea) is a learning and reasoning system for proving in large formal libraries where thousands of theorems are available when attacking a new conjecture, and a large number of related problems and…