Abductive reasoning, often characterized as inference to the best explanation, is central to explanation under uncertainty, from everyday sense-making and investigation to scientific discovery. Yet LLM research has mostly studied abduction through narrow, task-specific benchmarks, making it unclear whether observed gains transfer beyond the benchmark family used for training or evaluation. We ask whether RL post-training can improve abduction as a transferable reasoning capability. We introduce CEDAR-GRPO, a process-aware framework that combines final-answer correctness with abductive rewards for evidence coverage and evidence-to-explanation directionality. Four open-weight LLMs are post-trained on a controlled, domain-neutral mixture of abductive hypothesis-generation and hypothesis-selection tasks. We evaluate them on 11 unseen tasks spanning hypothesis selection, missing-fact generation, defeasible inference, long-context investigation, clinical reasoning, code debugging, and non-abductive controls. CEDAR- GRPO improves every model on every held-out task over both base models and correctness-only GRPO, with average gains of 7.4 and 2.7 points, respectively, and a maximum gain of 30.8 points. Ablations confirm that RL, abductive reward design, and task diversity each contribute to transfer. Process-level metrics further show stronger abductive behavior, including exploration of alternatives, elimination of rivals, backtracking, and uncertainty marking.
Reinforcement learning holds significant potential for training large language models (LLMs) to handle multi-turn interactive tasks. However, in long-horizon, multi-turn tasks characterized by sparse outcome rewards, directly training with outcome rewards often results in slow convergence due to the sparsity of signals and the lack of fine-grained feedback. Furthermore, the model may fail to learn successful trajectories that are not sampled during training, thereby limiting its performance. Conversely, while employing customized dense process rewards provides richer signals and accelerates convergence, these surrogate rewards may exhibit potential misalignment with the ground-truth outcome rewards. This inconsistency can bias the training direction and ultimately degrade the model's final performance. In this work, we propose Reward-Swap Policy Optimization (RSPO), a method designed to leverage the rich information from dense process rewards to facilitate training with outcome rewards. By utilizing a reward-swap mechanism, RSPO ensures the diversity of sampled trajectories while guaranteeing consistency between the optimization objective and the true outcome rewards, thereby elevating the performance ceiling of the model. We conduct extensive experiments on two challenging agent benchmarks, WebShop and ALFWorld. By applying our method to various reinforcement learning algorithms, including GRPO, PPO, and GiGPO, we demonstrate that RSPO achieves consistent performance improvements across different baselines and benchmarks.
Pooling, substituting, or reusing evaluator-derived step rewards assumes that their direction survives a change of evaluation channel. The same frozen transition can violate that assumption. Process rewards vary agent states, while evaluator audits vary scoring configurations; neither first difference isolates their interaction. We define Agent Step Value (ASV) as a channel-indexed target-margin gain and identify the state-by-channel interaction on complete matched faces. Across frozen PubMed question-answering transitions, direct scoring yields a positive mean ASV, while the generated-view channel yields a negative mean. Two matched replay waves reproduce this reversal, and cross-channel sign disagreement exceeds same-channel retry disagreement by 48.0 percentage points. Matched retrieval faces localize the reversal to the generated-view coordinate and trace its direction across a readout-and-stack bridge. A source-only generation contract restores the positive mean direction on artifact-bearing retrievals and removes parser-detected substantive support claims from artifact-free before-state views. ASV turns channel sensitivity into an identified measurement problem that can be localized and tested by intervention before step rewards are reused.
Recent multimodal large language models have shown great promise in clinical image reasoning, but existing post-training pipelines remain predominantly outcome-centric, relying on final answer correctness or sequence-level preferences. This suffers from sparse credit assignment, making it difficult to optimize the reasoning process essential for clinical applications. Our analysis reveals that cascading errors from early-stage reasoning failures are a leading cause of incorrect predictions in medical visual question answering (VQA) benchmarks. Motivated by this, we propose Medical Reasoning-aware Policy Optimization (MRPO), an RL algorithm that incorporates step-wise process rewards. When the final answer is incorrect, MRPO assigns exponentially larger penalties to tokens in earlier invalid reasoning steps, breaking failure cascades without compromising successful paths. Across three multimodal LLM backbones, MRPO consistently outperforms standard GRPO and a recent RL baseline, and on Qwen3-VL-8B-Instruct even surpasses substantially larger medical MLLMs such as HuatuoGPT-Vision-34B by 2.79 points. Moreover, MRPO reduces early-stage reasoning failures from 64.0% to 13.0%, showing that targeted mitigation of cascading failures improves both reasoning quality and final answer accuracy. Our code is available at https://github.com/dmis-lab/MRPO
While reinforcement learning from verifiable rewards (RLVR) typically has relied on a single binary verification signal, symbolic proof assistants in formal reasoning offer rich, fine-grained structured feedback. This gap between structured processes and unstructured rewards highlights the importance of feedback that is both dense and sound. In this work, we demonstrate that the Lean proof assistant itself can serve as a symbolic process oracle, supplying both outcome-level and fine-grained tactic-level verified feedback during training. Proof attempts are parsed into tactic sequences, and Lean's elaboration marks both locally sound steps and the earliest failing step, yielding dense, verifier-grounded credit signals rooted in type theory. We incorporate these structured rewards into a GRPO-style reinforcement learning objective with first-error propagation and first-token credit methods that balances outcome- and process-level advantages. Experiments with STP-Lean and DeepSeek-Prover-V1.5 show that tactic-level supervision outperforms outcome-only baselines in most settings, delivering improvements on benchmarks such as MiniF2F and ProofNet. Beyond empirical gains, our study highlights a broader perspective: symbolic proof assistants are not only verifiers at evaluation time, but can also act as process-level reward oracles during training. This opens a path toward reinforcement learning frameworks that combine the scalability of language models with the reliability of symbolic verification for formal reasoning.
Reinforcement learning (RL) holds immense promise for enhancing the reasoning capabilities of diffusion large language models (dLLMs). However, progress is fundamentally constrained by a dual misalignment between authentic generation trajectory and the gradient update process: (i) Process-reward misalignment. Sparse, terminal rewards are indiscriminately assigned to all intermediate steps of the generation process, failing to provide discriminative credit assignment. (ii) State-trajectory misalignment. Policy updates are often diverted toward artificial, out-of-trajectory states, squandering gradients on less informative samples. To address these limitations, we introduce Process Aligned Policy Optimization (PAPO), a novel framework that holistically aligns the RL update with the dLLM's generative trajectory via Step-Aware Process Rewards (SPR) that transform sparse terminal rewards into dense, step-wise credit, and Entropy-Guided Historical Re-enactment (EHR) that replays authentic trajectories at high-uncertainty steps. Extensive experiments on four benchmarks demonstrate that PAPO significantly outperforms baselines, achieving gains of up to 4.5% on GSM8K, 4.8% on MATH500, 42.2% on Countdown and 16.1% on Sudoku.