automated reasoning software teams

Abstract: Reinforcement learning with verifiable rewards (RLVR) can enable generalizable improvement for large language model (LLM) reasoning. This paper studies how to incentivize such generalization via reasoning strategies. We study this question with a controllable equation-solving framework: finding multiple inputs x for equations f(x)=y, where f is a non-bijective string function. This setting makes reasoning strategies observable while supporting a clear definition of easy-to-hard out-of-distribution (OOD) shifts, e.g., more solutions, longer y, etc. We uncover a subtle RLVR failure: it teaches the model to solve in-distribution tasks with high accuracy and structured step-by-step derivation, yet under OOD shifts, the same model abandons derivation and collapses to ineffective brute-force enumeration, causing sharp accuracy drops. This observation reveals the deeper challenges of RLVR generalization as it is neither incapable base model nor reward hacking, since the model succeeds in-distribution with the correct reasoning strategy. The key to mitigating this failure is an indirect intervention that surprisingly helps: co-training with bijective inversion tasks. Although these bijective tasks are actually not uniformly harder and even further from the non-bijective OOD evaluation, they make derivation more certain and substantially restore the correct strategy and accuracy under OOD shifts. This effect further motivates our theoretical analysis: outcome-only RLVR can shape reasoning processes through implicitly crediting the effective reasoning strategies more, even without process supervision. To conclude, our analysis framework and findings systematically reveal the crucial role and incentivization of reasoning strategies in RLVR generalization under OOD shifts. Code is available at https://github.com/ziqipang/rl_meta_thinking.

Abstract: On-policy self-distillation provides dense supervision for reasoning models via a privileged self-teacher. However, this supervision reflects local token preferences rather than the expected return of an unguided student continuation. Recent methods combine this signal with GRPO. They use GRPO for update directions and the teacher for signal scaling. However, we demonstrate a more effective integration within PPO. Specifically, we identify complementary positional dynamics: privileged information enhances a critic's value-prediction accuracy toward the response's end, whereas self-teacher guidance is strong initially, drops mid-generation, and rebounds finally. These insights motivate Value-Augmented Self-Distillation Policy Optimization (VASPO), wherein a self-teacher and critic evaluate identical privileged information at student-generated prefixes. The critic computes token-level PPO advantages from predicted continuation returns, while the self-teacher modulates selected positive advantages via bounded probability ratios. Across six mathematical reasoning benchmarks, VASPO improves mean accuracy over PPO by 2.59 and 1.81 percentage points on Qwen3-4B and OLMo3-7B variants, respectively, and achieves the highest mean accuracy among evaluated methods on Knights and Knaves. Our code is available at https://github.com/cii030/VASPO.

Abstract: Adaptive rollout methods for group-relative reinforcement learning typically allocate a fixed per-update budget across prompts. We instead study how to coordinate a finite rollout budget over the entire training horizon. We formulate this problem using a concave surrogate utility of cumulative prompt exposure and introduce CERO, an online primal dual scheduler for prompt admission and budget pacing. In our experiments, each admitted prompt receives a fixed-size response group. CERO instead adapts which prompts are selected, how often they are revisited across rounds, and how many groups are generated in each round. A compact Fenchel representation linearizes the dependence on cumulative exposure, while projected online gradient descent updates prompt-specific supporting slopes and a shared budget price using reward-variation feedback and budget deviations. We establish pathwise guarantees for the surrogate allocation objective against fixed-rate and same-path time-varying benchmarks, with explicit terms for proxy discrepancy and rate variation. Under matched training-response budgets, CERO attains the highest avg@16 macro-average on each of three backbones across five mathematical reasoning benchmarks. Mechanistic analyses link CERO's prompt choices to within-group reward contrast, while multi-seed ablations show gains from adaptive pacing over both uniform and preset spending schedules.