SCOUT: Teaching Pre-trained Language Models to Enhance Reasoning via Flow Chain-of-Thought

Chain-of-Thought (CoT) prompting improves the reasoning performance of large language models (LLMs) by encouraging step-by-step thinking. However, CoTbased methods depend on intermediate reasoning steps, which limits scalability and generalization. Recent work explores recursive reasoning, where LLMs reuse internal layers across iterations to refine latent representations without explicit CoT supervision. While promising, these approaches often require costly pretraining and lack a principled framework for how reasoning should evolve across iterations. We address this gap by introducing Flow Chain-of-Thought (Flow CoT), a reasoning paradigm that models recursive inference as a progressive trajectory of latent cognitive states. Flow CoT frames each iteration as a distinct cognitive stage-deepening reasoning across iterations without relying on manual supervision. To realize this, we propose SCOUT (Stepwise Cognitive Optimization Using Teachers), a lightweight fine-tuning framework that enables Flow CoT-style reasoning without the need for pretraining. SCOUT uses progressive distillation to align each iteration with a teacher of appropriate capacity, and a cross-attention-based retrospective module that integrates outputs from previous iterations while preserving the model's original computation flow. Experiments across eight reasoning benchmarks show that SCOUT consistently improves both accuracy and explanation quality, achieving up to 1.8% gains under fine-tuning. Qualitative analyses further reveal that SCOUT enables progressively deeper reasoning across iterations-refining both belief formation and explanation granularity. These results not only validate the effectiveness of SCOUT, but also demonstrate the practical viability of Flow CoT as a scalable framework for enhancing reasoning in LLMs.