Jui-Hui Chung

Jui-Hui Chung, Ziyang Cai, Zihao Li et al.

We introduce Goedel-Architect, an agentic framework for formal theorem proving in Lean 4 centered on blueprint generation and refinement. A blueprint is a dependency graph of definitions and lemmas that builds up to the main theorem. First, Goedel-Architect generates a blueprint of formally stated definitions and lemmas, along with declared dependencies. This blueprint is optionally guided by a natural language proof. Then, a tool-equipped Lean prover component closes each open lemma node in parallel using relevant dependencies. Failed lemmas in turn drive refinement of the global blueprint. This strategy contrasts with other mainstream approaches which use recursive lemma decomposition, and can inefficiently loop on dead-end strategies. Using the open-weight DeepSeek-V4-Flash (284B-A13B) as the backbone, Goedel-Architect attains 99.2% pass@1 on MiniF2F-test and 75.6% pass@1 on PutnamBench. With an optional natural-language proof seeding the initial blueprint on the harder problems, we additionally close the remaining two MiniF2F-test problems (reaching 100%), lift PutnamBench to 88.8% (597/672), and solve 4/6 on IMO 2025, 11/12 on Putnam 2025, and 3/6 on USAMO 2026. This represents state-of-the-art performance for an open-source pipeline at a price point up to 500x less than comparable open-source pipelines.

Alireza Salemi, Chang Zeng, Atharva Nijasure et al.

Large Language Model (LLM) search agents have shown strong promise for knowledge-intensive language tasks through multiple rounds of reasoning and information retrieval. Most existing systems access information using a retriever that takes a keyword or natural language query and returns a ranked list of documents using an index of pre-computed document representations. In this work, we explore a complementary perspective in which the search agent treats the corpus itself as the search environment and finds evidence by issuing executable shell commands. We introduce GrepSeek, an optimized direct corpus interaction (DCI) search agent that trains a compact search agent to find, filter, and compose evidence from large text corpora. To address the instability of learning behavior directly with reinforcement learning on large corpora, we propose a two-stage training pipeline. First, we construct a cold-start dataset using an answer-aware Tutor and answer-blind Planner to generate verified, causally grounded search trajectories. Second, we refine the initialized policy with Group Relative Policy Optimization (GRPO), allowing the agent to improve its task-oriented search behavior through direct interaction with the corpus. To make DCI practical at scale, we further use a semantics-preserving sharded-parallel execution engine that accelerates shell-based retrieval by up to $7.6\times$ while preserving byte-exact equivalence with sequential execution of the shell command. Experiments across seven open-domain question answering benchmarks show that GrepSeek achieves the strongest overall token-level $F_1$ and Exact Match. Our analysis also highlights the limitations of purely lexical interaction on queries with substantial surface-form variation, suggesting DCI as a practical and competitive method for search agents that can complement existing retrieval paradigms in the real world.

Yong Lin, Shange Tang, Bohan Lyu et al. · uw

We introduce Goedel-Prover-V2, a series of open-source language models that set a new state-of-the-art in automated theorem proving. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) Scaffolded data synthesis: We generate synthetic tasks of increasing difficulty to train the model to master increasingly complex theorems; (2) Verifier-guided self-correction: We enable the model to iteratively revise its proofs by leveraging feedback from the Lean compiler; (3) Model averaging: We merge model checkpoints to mitigate the decrease in model output diversity in later stages of training. Our small model, Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing the first place among open-source models on the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by pass@1024 with a significantly smaller model size and compute budget. At the time of its release (July-August 2025), Goedel-Prover-V2 achieves the strongest overall performance among all open-source theorem provers. It also ranks among the top-performing models--including closed-source systems with publicly reported performance--under a constrained test-time compute budget. Our models, code, and data are released at https://github.com/Goedel-LM/Goedel-Prover-V2.

Jui-Hui Chung, Hongzhou Lin, Lai Jiang et al.

Heavy supervised fine-tuning on a target domain can strongly suppress capabilities that were present in the base model. We study this phenomenon in formal mathematics using Goedel-Prover-V2, an open-source model heavily trained on 1.8 million formal-math examples. After domain specialization, the model almost completely loses its ability to produce valid tool calls, even when explicitly instructed to use tools, dropping from 89.4% function-calling accuracy in the base model to nearly 0%. We ask whether this agentic collapse is permanent or instead reversible. To answer this question, we fine-tune the specialized model on a small amount of Lean-specific tool-use data. Remarkably, as few as 100 agentic traces are sufficient to restore strong tool-calling behavior. Importantly, this recovery is not the result of reward hacking or benchmark-specific optimization: the recovery data is entirely drawn from the Lean setting, where the model uses natural-language queries to search the Mathlib library for relevant theorems and lemmas, yet the regained capability transfers well beyond that domain. In particular, these same 100 Lean-specific traces improve performance on the Berkeley Function Calling Leaderboard from near zero to 83.8%, approaching the base model's 89.4% despite the mismatch in task distribution and protocol. The recovered capability is also practically useful in-domain. On ProofNet, pass@32 improves from 21.51% to 25.81%. Together, these results show that heavy domain supervised fine-tuning can suppress general tool-use ability without permanently erasing it, and that a small amount of domain-specific agentic data can awaken dormant tool-use capabilities.