Papers Abstract Algebra
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Lean-GAP: A Dataset of Formalized Graduate Algebra Problems
We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pipeline consisting of PDF-to-LaTeX prepro…
Abstract AlgebraAlgebraic Structure Discovery for Real World Combinatorial Optimisation Problems: A General Framework from Abstract Algebra to Quotient Space Learning
Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identi…
Abstract AlgebraDo Transformers Have the Ability for Periodicity Generalization?
Large language models (LLMs) based on the Transformer have demonstrated strong performance across diverse tasks. However, current models still exhibit substantial limitations in out-of-distribution (OOD) generalization c…
Abstract AlgebraAx-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics
We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve…
Automated Theorem ProvingAbstract AlgebraNeural Low-Discrepancy Sequences
Low-discrepancy points are designed to efficiently fill the space in a uniform manner. This uniformity is highly advantageous in many problems in science and engineering, including in numerical integration, computer visi…
Abstract AlgebraMotion PlanningGen AI in Proof-based Math Courses: A Pilot Study
With the rapid rise of generative AI in higher education, understanding how students use AI is increasingly important. This exploratory study examines student use and perceptions of generative AI across three proof-based…
Abstract AlgebraMachine Learning meets Algebraic Combinatorics: A Suite of Datasets Capturing Research-level Conjecturing Ability in Pure Mathematics
With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources ca…
Abstract AlgebraProgram SynthesisEffectiveness of Zero-shot-CoT in Japanese Prompts
We compare the effectiveness of zero-shot Chain-of-Thought (CoT) prompting in Japanese and English using ChatGPT-3.5 and 4o-mini. The technique of zero-shot CoT, which involves appending a phrase such as "Let's think ste…
Abstract AlgebraCollege MathematicsMMLUMulti-task Language UnderstandingAlgebraic Machine Learning: Learning as computing an algebraic decomposition of a task
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach,…
Abstract AlgebraLeanAgent: Lifelong Learning for Formal Theorem Proving
Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-t…
Abstract AlgebraAutomated Theorem ProvingLifelong learningMathematical ReasoningMathematical Formalized Problem Solving and Theorem Proving in Different Fields in Lean 4
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reason…
Abstract AlgebraAutomated Theorem ProvingMathMathematical Proofs+1Automated Planning Techniques for Elementary Proofs in Abstract Algebra
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematica…
Abstract AlgebraAutomated Theorem ProvingMathematical ProofsData valuation: The partial ordinal Shapley value for machine learning
Data valuation using Shapley value has emerged as a prevalent research domain in machine learning applications. However, it is a challenge to address the role of order in data cooperation as most research lacks such disc…
Abstract AlgebraData ValuationMinimizing Fuzzy Interpretations in Fuzzy Description Logics by Using Crisp Bisimulations
The problem of minimizing finite fuzzy interpretations in fuzzy description logics (FDLs) is worth studying. For example, the structure of a fuzzy/weighted social network can be treated as a fuzzy interpretation in FDLs,…
Abstract AlgebraProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics
We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a…
Abstract AlgebraAutomated Theorem ProvingIn-Context LearningRetrievalKnowledgebra: An Algebraic Learning Framework for Knowledge Graph
Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings traine…
Abstract AlgebraGeneral KnowledgeKnowledge GraphsLink Prediction+1Graph Neural Networks are Dynamic Programmers
Recent advances in neural algorithmic reasoning with graph neural networks (GNNs) are propped up by the notion of algorithmic alignment. Broadly, a neural network will be better at learning to execute a reasoning task (i…
Abstract AlgebraLearning to ExecuteAlgebraic Learning: Towards Interpretable Information Modeling
Along with the proliferation of digital data collected using sensor technologies and a boost of computing power, Deep Learning (DL) based approaches have drawn enormous attention in the past decade due to their impressiv…
Abstract AlgebraScaling Language Models: Methods, Analysis & Insights from Training Gopher
Language modelling provides a step towards intelligent communication systems by harnessing large repositories of written human knowledge to better predict and understand the world. In this paper, we present an analysis o…
Abstract AlgebraAnachronismsAnalogical SimilarityAnalytic Entailment+143Artificial Cognitively-inspired Generation of the Notion of Topological Group in the Context of Artificial Mathematical Intelligence
The new computational paradigm of conceptual computation has been introduced in the research program of Artificial Mathematical Intelligence. We provide the explicit artificial generation (or conceptual computation) for …
Abstract Algebra