We present Reap, an open framework for learning and analyzing formal proof search in Lean4. Reap implements policy-value-guided Monte Carlo Tree Search directly in Lean, sharing proof-state transitions, AND-OR search, and replay verification between inference and training rollouts. Structured action logs expose how neural predictions and tactic execution interact during search. Using this framework, we train Reaper-1, a 1.7B-parameter policy-value model, through continued pre-training, supervised tactic learning, and iterative search-based reinforcement learning. Using a separate premise selector, the final system solves 79.9% of miniF2F-test at pass@32, establishing state-of-the-art performance among open provers of comparable size while remaining competitive with substantially larger models. Beyond improved solve rates, our results suggest that RL strengthens the prover's ability to organize proofs around useful intermediate results, favoring substantial advances over repeated local adjustments. This more directed proof construction is accompanied by increasingly elaborate tactic programs: fewer explicit search decisions are needed, while more work is performed within each decision. The resulting trade-off between search effort and tactic execution cost provides insight into how learning changes the prover's problem-solving strategy.
Siyuan Li Peng Cheng Laboratory and Harbin Institute of Technology, Shenzhen, Yunjia Wu, Yiyong Xiao Fudan University, Pingyang Huang, Peize Li, Ruitong Liu, Yan Wen, Te Sun
Temporal knowledge graph (TKG) forecasting requires predicting future facts by jointly modeling structural dependencies within each snapshot and temporal evolution across snapshots. However, most existing methods are stateless: they recompute entity representations at each timestamp from a limited query window, leading to episodic amnesia and rapid decay of long-term dependencies. To address this limitation, we propose Entity State Tuning (EST), an encoder-agnostic framework that endows TKG forecasters with persistent and continuously evolving entity states. EST maintains a global state buffer and progressively aligns structural evidence with sequential signals via a closed-loop design. Specifically, a topology-aware state perceiver first injects entity-state priors into structural encoding. Then, a unified temporal context module aggregates the state-enhanced events with a pluggable sequence backbone. Subsequently, a dual-track evolution mechanism writes the updated context back to the global entity state memory, balancing plasticity against stability. Experiments on multiple benchmarks show that EST consistently improves diverse backbones and achieves state-of-the-art performance, highlighting the importance of state persistence for long-horizon TKG forecasting.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表