Chi Jin

Large language models (LLMs) can generate plausible code but offer limited guarantees of correctness. Formally verifying that implementations satisfy specifications requires constructing machine-checkable proofs, a task that remains beyond current automation. We propose a hierarchical proof search framework for automated code verification in Lean~4 that decomposes complex verification goals into structurally simpler subgoals before attempting tactic-level proving. Central to our approach is a principled decomposition score that combines constructive justification with structural effectiveness. The same score serves as both the training reward and the inference-time ranking criterion, aligning optimization and deployment. We train *Goedel Code Prover*, a single unified policy for both decomposition and completion, through supervised initialization followed by hybrid reinforcement learning, where a continuous decomposition reward supports planning exploration while supervised replay stabilizes proof generation. On three Lean-based code verification benchmarks comprising 427 tasks, our 8B-parameter model achieves a 62.0\% prove success rate, a 2.6$\times$ improvement over the strongest baseline under the reported inference settings. We further observe consistent inference-time scaling: success rates improve monotonically with search iterations and sampling budget, while whole-proof baselines plateau within the evaluated budgets.

Given the rapidly growing capabilities of vision-language models (VLMs), extending them to interactive decision-making tasks such as video games has emerged as a promising frontier. However, existing approaches either rely on large-scale supervised fine-tuning (SFT) on human trajectories or apply reinforcement learning (RL) only in relatively short-horizon settings (typically around 20--30 environment turns). In this work, we study RL-based training of VLMs for long-horizon decision-making in Super Mario Land, a visually grounded environment requiring 100+ turns of interaction with coordinated perception, reasoning, and action. We begin with a systematic investigation of key algorithmic components and propose an adapted variant of PPO with a lightweight turn-level critic, which substantially improves training stability and sample efficiency over critic-free methods such as GRPO and Reinforce++. We further show that pretrained VLMs provide strong action priors, significantly improving sample efficiency during RL training and reducing the need for manual design choices such as action engineering, compared to classical deep RL trained from scratch. Building on these insights, we introduce Odysseus, an open training framework for VLM agents, achieving substantial gains across multiple levels of the game and at least $3\times$ average game progresses than frontier models. Moreover, the trained models exhibit consistent improvements under both in-game and cross-game generalization settings, while maintaining general-domain capabilities. Overall, our results identify key ingredients for making RL stable and effective in long-horizon, multi-modal settings, and provide practical guidance for developing VLMs as embodied agents.

Translating complex reinforcement learning (RL) environments into high-performance implementations has traditionally required months of specialized engineering. We present a closed-loop methodology that produces equivalent high-performance environments for minimal compute cost. Our method uses a generic prompt template, hierarchical verification (property, interaction, and rollout tests), iterative repair, and cross-backend policy transfer to verify no sim-to-sim gap. We demonstrate three distinct workflows across five environments: (1) Direct translation (no prior performance implementation exists) from Game Boy emulator PyBoy to our EmuRust (via Rust IPC) and from Pokemon Showdown to our PokeJAX (via JAX); (2) Translation verified against existing performance implementations via throughput parity with Puffer Pong, MJX and Brax at matched GPU batch sizes; and (3) New environment creation: TCGJax, the first Pokemon TCG Pocket environment, created from a web-extracted specification. At 200M parameters, the environment overhead drops below 4\% of training time. Our closed-loop methodology confirms equivalence for all five environments. TCGJax, synthesized from a private reference absent from public repositories, serves as a contamination control for agent pretraining data concerns.

The deployment of Large Language Models (LLMs) as autonomous economic agents introduces systemic risks that extend beyond individual capability failures. As agents transition to directly interacting with marketplaces, their collective behavior can amplify volatility and mask deception at scale. We introduce the Agent Bazaar, a multi-agent simulation framework for evaluating Economic Alignment, the capacity of agentic systems to preserve market stability and integrity. We identify two failure modes: (1) Algorithmic Instability in a B2C market (“The Crash”), where firms amplify price volatility until the market collapses, and (2) Sybil Deception in a C2C market (“The Lemon Market”), where a single deceptive agent controlling multiple coordinated seller identities floods the market with fraudulent listings, eroding trust and consumer welfare. We evaluate frontier and open-weight models across both scenarios and find that models largely fail to self-regulate, with failure severity varying by model rather than by size. We propose economically aligned harnesses, Stabilizing Firms and Skeptical Guardians, that improve outcomes but remain fragile under harder market conditions. To close this gap, we train agents with REINFORCE++ using an adaptive curriculum, producing a 9B model that outperforms all evaluated frontier and open-weight models. We propose the Economic Alignment Score (EAS), a 4-component scalar metric aggregating stability, integrity, welfare, and profitability, enabling direct cross-model comparison. Our results show that economic alignment is orthogonal to general capability and can be directly trained with targeted RL.

Heavy supervised fine-tuning (SFT) 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 1.8M 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, and 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. This recovery is not benchmark-specific optimization: the recovery dataset is entirely drawn from the Lean setting, where the model uses natural-language queries to search the Mathlib library, yet these same 100 traces improve the Berkeley Function Calling Leaderboard (BFCL) 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: ProofNet pass@32 improves from 21.51% to 25.81%. Controlled comparisons show that recovery depends strongly on trace structure and diversity, and a code-specialized 7B replication establishes the pattern beyond formal mathematics. Together, these results show that heavy domain SFT 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.