Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2302.12433

ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics

Zhangir Azerbayev·Bartosz Piotrowski·Hailey Schoelkopf·Edward W. Ayers·Dragomir Radev·Jeremy Avigad
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 theorem statement, and a natural language proof. The problems are primarily drawn from popular undergraduate pure mathematics textbooks and cover topics such as real and complex analysis, linear algebra, abstract algebra, and topology. We intend for ProofNet to be a challenging benchmark that will drive progress in autoformalization and automatic theorem proving. We report baseline results on statement autoformalization via in-context learning. Moreover, we introduce two novel statement autoformalization methods: prompt retrieval and distilled backtranslation.

Explore related subjects

cs.CLcs.AIcs.LO

Keep this discovery

BibTeXRIS

Zhangir Azerbayev, Bartosz Piotrowski, Hailey Schoelkopf, Edward W. Ayers, Dragomir Radev, Jeremy Avigad. 2023-02-24. ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics. https://arxiv.org/abs/2302.12433

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Auto-RecSys: Harnessing Autonomous Research Agents for Industry-Scale Recommender System

Auto-research agents have shown the potential to automate hypothesis generation, experiment execution, and iterative refinement. However, scaling this paradigm to industry-scale recommendation models introduces two challenges: (1) long feedback loops, where model training can take days, making serial iteration prohibitively slow and requiring parallel exploration across multiple research directions; and (2) system complexity, where large configurations, fragile infrastructure dependencies, and multi-day GPU jobs require robust and recoverable execution. We present Auto-RecSys, an autonomous research system for long-horizon experimentation on industry-scale recommendation models. Auto-RecSys addresses these challenges through three harness designs: (1) distributed asynchronous execution for running multiple experiments in parallel across servers, (2) centralized cross-server memory for persistent and recoverable execution across sessions and failures, and (3) cognitive-procedural separation, where natural-language skill files guide LLM reasoning while deterministic scripts enforce operational correctness. Auto-RecSys further employs a dual-loop self-evolving architecture: an Execution Evolution Loop in which model-specific playbooks accumulate operational knowledge by recording failed attempts and crystallizing successful pipelines, and an Idea Evolution Loop in which experimental outcomes inform subsequent ideation. Evaluated on recommendation models, Auto-RecSys significantly reduces the human time required per experiment cycle and improves execution reliability as its playbooks mature.

cs.CL↗
arXiv2026

Structurally Speaking: Motif-Oriented Graph Captioning through Bidirectional Graph-Text Translation

Graph captions should help readers understand graph structure, rather than simply translate adjacency matrices into long textual edge lists. A useful graph caption abstracts connectivity into recognizable motifs, such as hubs, paths, cycles, cliques, and bridges, because these motifs provide compact structural units that are easier to read, compare, and recover. In this paper, we study motif-oriented graph captioning as a bidirectional graph-text translation task, where captions must both preserve enough topology for graph recovery and express the graph through concise motif-level descriptions. We show that direct prompting of GPT-5.1 often produces graph-recoverable captions by enumerating node-to-node connections, but these captions are verbose and can contain inconsistent motif interpretations. To address this gap, we introduce Structurally Speaking, a lightweight structured prompting protocol that guides translation between explicit connectivity and motif-level abstraction. Experiments on a synthetic motif-based dataset show that structured prompting produces shorter and more motif-consistent captions while maintaining comparable graph recovery. These results suggest that explicit topology-to-motif reasoning guidance can make LLM-generated graph captions more interpretable without model fine-tuning.

cs.CL↗
arXiv2026

Using Semantic Uncertainty to Estimate Transition Relevance in Turn-taking

Turn-taking is a fundamental mechanism that governs when interlocutors speak and listen. Although Spoken Dialogue Systems (SDS) exploit a range of linguistic, acoustic, and non-verbal cues, they produce ill-timed responses in unscripted interaction. A central challenge is anticipating Transition Relevance Places (TRPs), or opportunities, not obligations, for a listener to take the floor. Human listeners do not wait for turn endings; as an utterance unfolds, they use expectations about its developing meaning to anticipate TRPs and decide whether to take the floor. We examine whether these evolving expectations can be modeled through semantic uncertainty -- an LLM-derived measure of how strongly a turn so far constrains what may plausibly come next. To do so, we sample possible continuations of an ongoing turn and use changes in semantic dispersion to identify TRPs within turns. We evaluate this account on a dataset with TRP labels derived from real-time listener responses, rather than retrospective annotation. Our approach substantially outperforms prompt-based and fine-tuned text-only baselines, providing empirical support for the view that evolving semantic constraints inform perceived turn-taking opportunities in unscripted interaction.

cs.CL↗