Related papers: The Network Structure of Mathlib
The Lean mathematical library mathlib features extensive use of the typeclass pattern for organising mathematical structures, based on Lean's mechanism of instance parameters. Related mechanisms for typeclasses are available in other…
Large language models have achieved striking results in interactive theorem proving, particularly in Lean. However, most benchmarks for LLM-based proof automation are drawn from mathematics in the Mathlib ecosystem, whereas proofs in…
Datasets of real-world applications are characterized by entities of different types, which are defined by multiple features and connected via varied types of relationships. A critical challenge for these datasets is developing models and…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
Mathematical reasoning remains challenging for LLMs due to complex logic and the need for precise computation. Existing methods enhance LLM reasoning by synthesizing datasets through problem rephrasing, but face issues with generation…
Lean 4 autoformalization has become increasingly popular in recent years, with frontier language models and open-weight autoformalizers now producing valid formalizations of mathematical theorems. However, these evaluations often rely on…
Automated theorem proving systems built on Lean 4 increasingly rely on parallel tactic search over partially specified proofs, such as those generated by Draft-Sketch-Prove (DSP) pipelines. In current systems, each search branch…
We introduce CSLib, an open-source framework for proving computer-science-related theorems and writing formally verified code in the Lean proof assistant. CSLib aims to be for computer science what Lean's Mathlib is for mathematics. Mathlib…
The interactive theorem prover Lean enables the verification of formal mathematical proofs and is backed by an expanding community. Central to this ecosystem is its mathematical library, mathlib4, which lays the groundwork for the…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific…
Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on…
Premise selection is a key bottleneck for scaling theorem proving in large formal libraries. Yet existing language-based methods often treat premises in isolation, ignoring the web of dependencies that connects them. We present a…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
AI-driven autoformalization of mathematics is advancing rapidly. However, the type checker of a proof assistant guarantees only the logical correctness of proofs; it does not verify whether propositions and definitions faithfully capture…
This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…
Despite the remarkable success of large large-scale neural networks, we still lack unified notation for thinking about and describing their representational spaces. We lack methods to reliably describe how their representations are…
Mathematical knowledge exists in many forms, ranging from informal textbooks and lecture notes to large formal proof libraries, yet moving between these representations remains difficult. Informal texts hide dependencies, while formal…
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 natural language…