Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.34960

ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization

Feiming Wang·Daibo Li·Kun Yuan
View original source ↗Read source document ↗Export metadata ↓

Abstract

Formalizing research-level stochastic optimization in Lean requires both an algorithm model and domain theory connecting foundational libraries to convergence proofs. Revising a model to restore provability can change the mathematical claim. We introduce ProofLoom, a fully automated LLM-agent system for Proof-Obligation-Driven Theory Construction. Given a published algorithm, target theorem, and source proof, ProofLoom autonomously constructs the Lean model and supporting theory. Open proof obligations drive the development of definitions, interfaces, lemmas, and proof plans. Signature contracts record evidence and obligations for model revisions; an independent Judge rejects unsupported assumptions and weakened conclusions. Planner expands the published argument into intermediate claims, and Audit checks whether the Lean proof follows it. Across tasks, SOptLib accumulates verified mathematics and construction experience: reusable results are extracted, generalized, and verified, while modeling decisions and failed proof routes are recorded. Later tasks retrieve these results and records and contribute new developments, forming a cycle of construction, accumulation, and reuse. On fifteen textbook and research-paper tasks, ProofLoom obtains mean human ratings of 6.3/7 and 6.4/7, compared with 4.9/7 and 5.0/7 for the strongest of six baselines. Across 33 developments, it produces 490,693 lines of algorithm-local Lean code with no sorry. The formalizations also expose 28 incorrect formulas, proof gaps, and algorithm-analysis mismatches in published sources across 22 developments, each with checked evidence.

Explore related subjects

cs.AImath.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Feiming Wang, Daibo Li, Kun Yuan. 2026-09-28. ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization. https://arxiv.org/abs/2609.34960

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

KEEP EXPLORING

Related papers

arXiv2026

FlexQuant: Elastic Quantization Framework for Locally Hosted LLM on Edge Devices

Deploying LLMs on edge devices presents serious technical challenges. Memory elasticity is crucial for edge devices with unified memory, where memory is shared and fluctuates dynamically. Existing solutions suffer from either poor transition granularity or high storage costs. We propose FlexQuant, a novel elasticity framework that generates an ensemble of quantized models, providing an elastic hosting solution with 31x more deployment options, 15x granularity improvement, and 10x storage reduction compared to SoTA methods. FlexQuant works with most quantization methods and creates a family of trade-off options under various storage limits through our pruning method. It brings great performance and flexibility to the edge deployment of LLMs.

cs.AI↗
arXiv2026

Rethinking Prospect Theory for LLMs: Revealing the Instability of Decision-Making under Epistemic Uncertainty

Real-world decision-making often involves uncertainty expressed in linguistic rather than numerical terms, and Prospect Theory (PT) provides a classic framework for modeling human behavior under such uncertainty. Although recent studies have developed frameworks to estimate PT parameters for Large Language Models (LLMs), few have examined whether PT itself adequately describes LLM decision-making behavior. To address these gaps, we develop a streamlined workflow grounded in a classic behavioral economics experimental paradigm. First, we estimate PT parameters and evaluate how well the resulting model captures LLM decision-making behavior. We then derive probability mappings for epistemic markers in the same context and inject them into prompts to examine the stability of PT parameters under linguistic uncertainty. Our findings suggest that PT does not consistently provide a reliable account of LLM decision-making across models, and that its application to LLMs is likely sensitive to epistemic uncertainty. The findings caution against the deployment of PT-based frameworks in real-world applications where epistemic ambiguity is prevalent, giving valuable insights in behaviour interpretation and future alignment direction for LLM decision-making.

cs.AI↗
arXiv2026

Enabling Regulatory Multi-Agent Collaboration: Architecture, Challenges, and Solutions

Large language models (LLMs)-empowered autonomous agents are transforming both digital and physical environments by enabling adaptive, multi-agent collaboration. While these agents offer significant opportunities across domains such as finance, healthcare, and smart manufacturing, their unpredictable behaviors and heterogeneous capabilities pose substantial governance and accountability challenges. In this paper, we propose a blockchain-enabled layered architecture for regulatory agent collaboration, comprising an agent layer, an off-chain computation layer, and an on-chain anchoring layer. Within this framework, we design three key modules: (i) an agent behavior tracing and arbitration module for automated accountability, (ii) a dynamic reputation evaluation module for trust assessment in collaborative scenarios, and (iii) a malicious behavior forecasting module for early detection of adversarial activities. Our approach establishes a systematic foundation for trustworthy, resilient, and scalable regulatory mechanisms in large-scale agent ecosystems. Finally, we discuss the future research directions for blockchain-enabled regulatory frameworks in multi-agent systems.

cs.AI↗