Abstract Algebra
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Benchmarks
BIG-bench
Most implemented
Scaling Language Models: Methods, Analysis & Insights from Training Gopher
Algebraic Machine Learning: Learning as computing an algebraic decomposition of a task
LeanAgent: Lifelong Learning for Formal Theorem Proving
Mathematical Formalized Problem Solving and Theorem Proving in Different Fields in Lean 4
Data valuation: The partial ordinal Shapley value for machine learning
Papers
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 Algebra