Related papers: ML4PG in Computer Algebra verification
We describe a recently developed algebraic framework for proving first-order statements about linear operators by computations with noncommutative polynomials. Furthermore, we present our new SageMath package operator_gb, which offers…
Written answers to open-ended questions can have a higher long-term effect on learning than multiple-choice questions. However, it is critical that teachers immediately review the answers, and ask to redo those that are incoherent. This can…
The rapid adoption of Artificial Intelligence (AI) is increasingly realised through Machine Learning (ML) pipelines that integrate data preprocessing, model training, evaluation scripts, and configuration-heavy experimentation code. In…
Ensuring correctness is a pivotal aspect of software engineering. Among the various strategies available, software verification offers a definitive assurance of correctness. Nevertheless, writing verification proofs is resource-intensive…
In real world, large language models (LLMs) can serve as the assistant to help users accomplish their jobs, and also support the development of advanced applications. For the wide application of LLMs, the inference efficiency is an…
One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning…
This paper reports on the "Learning Computational Grammars" (LCG) project, a postdoc network devoted to studying the application of machine learning techniques to grammars suitable for computational use. We were interested in a more…
Large language models (LLMs) have demonstrated remarkable capability to generate fluent responses to a wide variety of user queries. However, this has also raised concerns about the potential misuse of such texts in journalism, education,…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…
We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our ML takes form of supervised learning using neural networks (multilayer perceptrons). When they achieve good results in classification, we…
Machine Learning (ML) is used in critical highly regulated and high-stakes fields such as finance, medicine, and transportation. The correctness of these ML applications is important for human safety and economic benefit. Progress has been…
We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to…
Formal verification using proof assistants, such as Coq, enables the creation of high-quality software. However, the verification process requires significant expertise and manual effort to write proofs. Recent work has explored automating…
Motivated by cryptographic applications, we investigate two machine learning approaches to modular multiplication: namely circular regression and a sequence-to-sequence transformer model. The limited success of both methods demonstrated in…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
The synergy between deep learning models and traditional automation tools, such as built-in tactics of the proof assistant and off-the-shelf automated theorem provers, plays a crucial role in developing robust and efficient neural theorem…
We introduce PineAPPL, a library that produces fast-interpolation grids of physical cross sections, computed with a general-purpose Monte Carlo generator, accurate to fixed order in the strong, electroweak, and combined strong-electroweak…
We introduce Logic Guided Machine Learning (LGML), a novel approach that symbiotically combines machine learning (ML) and logic solvers with the goal of learning mathematical functions from data. LGML consists of two phases, namely a…
This paper focuses on the biderivations of 4-dimensional nilpotent complex Leibniz algebras. Using the existing classification of these algebras, we develop algorithms to compute derivations, antiderivations, and biderivations as pairs of…
Partial Multi-label Learning (PML) is a type of weakly supervised learning where each training instance corresponds to a set of candidate labels, among which only some are true. In this paper, we introduce \our{}, a novel probabilistic…