Related papers: The Equational Theories Project: Advancing Collabo…
Monte Carlo (MC) simulations are powerful computational tools for investigating thermodynamic behavior and validating analytical approaches in complex physical systems. Here we present ETHER (Efficient Tool for THermodynamics Exploration…
Educational technology innovations leveraging large language models (LLMs) have shown the potential to automate the laborious process of generating and analysing textual content. While various innovations have been developed to automate a…
LLM-empowered multi-agent systems offer new potential to accelerate scientific discovery by generating novel research ideas. However, existing methods typically coordinate agents through temporary texts, such as drafts or chat logs; it is…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…
Plagiarism is a pressing concern, even more so with the availability of large language models. Existing plagiarism detection systems reliably find copied and moderately reworded text but fail for idea plagiarism, especially in mathematical…
Graph data management and querying has many practical applications. When graphs are very heterogeneous and/or users are unfamiliar with their structure, they may need to find how two or more groups of nodes are connected in a graph, even…
We present the Mathematica group theory package GTPack providing about 200 additional modules to the standard Mathematica language. The content ranges from basic group theory and representation theory to more applied methods like crystal…
Background: As traditional coding tasks in education become increasingly vulnerable to the use of Generative AI, there is a critical need for authentic, project-based assessments that evaluate students' scientific inquiry. To address this…
The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…
Large Language Models (LLMs) often do not perform well on queries that require the aggregation of information across texts. To better evaluate this setting and facilitate modeling efforts, we introduce TACT - Text And Calculations through…
Recent efforts have aimed to improve AI machines in legal case matching by integrating legal domain knowledge. However, successful legal case matching requires the tacit knowledge of legal practitioners, which is difficult to verbalize and…
Large language models (LLMs) have shown remarkable progress in mathematical problem-solving, but evaluation has largely focused on problems that have exact analytical solutions or involve formal proofs, often overlooking approximation-based…
Traditionally, theory and practice of Cognitive Control are linked via literature reviews by human domain experts. This approach, however, is inadequate to track the ever-growing literature. It may also be biased, and yield redundancies and…
We address the task of explaining relationships between two scientific documents using natural language text. This task requires modeling the complex content of long technical documents, deducing a relationship between these documents, and…
Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
Current evaluations of mathematical reasoning in large language models (LLMs) are dominated by static benchmarks, either derived from competition-style problems or curated through costly expert effort, resulting in limited coverage of…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…