Related papers: The Equational Theories Project: Advancing Collabo…
Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large…
Typed entailment graphs try to learn the entailment relations between predicates from text and model them as edges between predicate nodes. The construction of entailment graphs usually suffers from severe sparsity and unreliability of…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
In this work we describe a new learning-based proof guidance -- ENIGMAWatch -- for saturation-style first-order theorem provers. ENIGMAWatch combines two guiding approaches for the given-clause selection implemented for the E ATP system:…
We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization sets. We present a framework to combine Inductive Logic…
Current autoformalization benchmarks are largely focused on olympiad or undergraduate mathematics, while graduate and research-level mathematics remains underexplored. In this paper, we introduce MathAtlas, the first large-scale…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…
We present four open conjectures in graph theory generated by the automated conjecturing system \texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariants, and empirically validated across hundreds of graphs.…
Identifying academic plagiarism is a pressing task for educational and research institutions, publishers, and funding agencies. Current plagiarism detection systems reliably find instances of copied and moderately reworded text. However,…
Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…
Large Language Models (LLMs) often struggle with maintaining coherent multi-step reasoning traces, particularly in tasks that require a structured logical flow. This work introduces a quantum-inspired approach to address the challenge by…
We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and…
In this methodological article on experimental-yet-rigorous enumerative combinatorics, we use two instructive case studies, to show that often, just like Alexander the Great before us, the simple, "cheating" solution to a hard problem is…
We study classic scheduling problems on uniformly related machines. Efficient polynomial time approximation schemes (EPTAS's) are fast and practical approximation schemes. New methods and techniques are essential in developing such improved…
This paper extends prior work on the connections between logics from finite model theory and propositional/algebraic proof systems. We show that if all non-isomorphic graphs in a given graph class can be distinguished in the logic…
The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90% accuracy. However, their capabilities to solve more challenging math problems which require…
Aiming to support Retrieval Augmented Generation (RAG) in the design process, we present a method to identify explicit, engineering design facts - {head entity :: relationship :: tail entity} from patented artefact descriptions. Given a…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…
We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…