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Chen Wang

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Preprint Aug 2026

Divergent-Convergent Reasoning: Scaling Test-Time Compute through Structured Solution Synthesis

Test-time compute can substantially improve Large Language Model (LLM) reasoning performance, yet how and when additional compute helps remains poorly understood. We study Divergent-Convergent Reasoning (DCR), a simple two-phase primitive consisting of an exploration phase that generates multiple candidate solutions followed by a convergent reconciliation phase. We present three core results. First, we show that even a single reconciliation step can reliably amplify correct minority reports: across datasets, DCR often recovers the correct answer when correct exploration outputs are in the minority, a regime where majority voting fails. Second, we introduce recursive DCR, an autoregressive reconciliation system that iteratively analyzes disagreements and allocates additional test-time compute. Recursive DCR achieves higher accuracy than fixed-compute baselines-reaching 93.3% on AIME 2024 and 92.0% on AIME 2025-while using roughly 27% less compute on average, demonstrating that attentive resource allocation is superior to uniform scaling. Third, we analyze disagreement among exploration outputs via a simple, training-free dispersion metric. Dispersion reveals a structured relationship between disagreement and test-time gains: in regimes where DCR is effective, higher disagreement among exploration outputs is associated with larger accuracy improvements from reconciliation. Together, these results show that disagreement, often viewed as noise, can be systematically exploited to improve test-time reasoning and reveal emerging scaling laws for agentic LLM systems.

Bo Wen, Yuhao Chen, E. Bilal et al. · 0 citations

Preprint Jul 2026

Distilled Reinforcement Learning for LLM Post-training

Large language model (LLM) post-training is essential for improving reasoning, adaptation, and alignment. Existing methods mainly follow two paradigms: reinforcement learning (RL) and on-policy distillation (OPD). However, RL relies on coarse-grained outcome supervision, resulting in difficult credit assignment and limited capability to acquire new knowledge. OPD, meanwhile, unconditionally matches teacher logits through KL divergence, which creates a dilemma: similar teachers provide little new knowledge, while substantially different teachers often yield ineffective guidance, largely restricting OPD to within-family distillation. We propose Distilled Reinforcement Learning (Distilled RL), which integrates teacher supervision into the RL objective to provide fine-grained guidance, selectively transfer new knowledge and avoid unconditional imitation. Distilled RL contains three components: reverse importance sampling with clipping, negative sample reset, and sequence-level geometric normalization. Through a concise and interpretable case study, we demonstrate that Distilled RL can effectively transfer previously unavailable knowledge from a teacher model to a student model. Extensive experiments across both within-family and cross-family distillation settings show that Distilled RL substantially outperforms standard RL and OPD in terms of both pass@1 and pass@k. Our code is available at https://github.com/597358816/Distilled-RL.

Chen Wang, Zhaochun Li, Jionghao Bai et al. · 2 citations