Reinforcement learning (RL) offers a principled way to enhance the reasoning capabilities of large language models, yet its effectiveness hinges on training signals that remain informative as models evolve. In practice, RL progress often slows when task difficulty becomes poorly aligned with model capability or when training is dominated by a narrow set of recurring problem patterns.To jointly address these issues, we propose SCALER (Synthetic sCalable Adaptive Learning Environment for Reasoning), a framework that sustains effective learning signals through adaptive environment design.SCALER introduces a scalable synthesis pipeline that converts real-world programming problems into verifiable reasoning environments with controllable difficulty and unbounded instance generation, enabling RL training beyond finite datasets while preserving strong correctness guarantees. Building on this, SCALER further employs an adaptive multi-environment RL strategy that dynamically adjusts instance difficulty and curates the active set of environments to track the model’s capability frontier and maintain distributional diversity. This co-adaptation prevents reward sparsity, mitigates overfitting to narrow task patterns, and supports sustained improvement throughout training. Extensive experiments show that SCALER consistently outperforms other RL baselines across diverse reasoning benchmarks and exhibits more stable, long-horizon training dynamics.

Translating natural language mathematical statements into formal, executable code is a fundamental challenge in automated theorem proving. While prior work has focused on generation and compilation success, little attention has been paid to the critic phase—the evaluation of whether generated formalizations truly capture the semantic intent of the original problem. In this paper, we introduce CriticLean, a novel critic-guided reinforcement learning framework that elevates the role of the critic from a passive validator to an active learning component. Specifically, first, we propose the CriticLeanGPT, trained via supervised fine-tuning and reinforcement learning, to rigorously assess the semantic fidelity of Lean 4 formalizations. Then, we introduce CriticLeanBench, a benchmark designed to measure models’ ability to distinguish semantically correct from incorrect formalizations, and demonstrate that our trained CriticLeanGPT models can significantly outperform strong open- and closed-source baselines. Building on the CriticLean framework, we construct FineLeanCorpus, a dataset comprising over 509K problems that exhibits rich domain diversity, broad difficulty coverage, and high correctness based on human evaluation.Overall, our findings highlight that optimizing the critic phase is essential for producing reliable formalizations and we hope our CriticLean will provide valuable insights for future advances in formal mathematical reasoning.