Reinforcement Learning with Verifiable Rewards (RLVR) is widely used to improve reasoning across domains, but outcome-only scalar rewards are often sparse and uninformative, especially for failed samples, where they indicate only failure without explaining why the reasoning breaks down. In this paper, we leverage richer verbal feedback to guide RLVR on failed samples and convert feedback-induced progress into trainable learning signals. We propose MulFeRL (Multi-turn Feedback-guided Reinforcement Learning), a multi-turn, event-triggered RLVR framework that combines progress induction for feedback-guided regeneration of failed samples, progress credit assignment for learning from verifier-confirmed progress, and structured feedback injection for integrating feedback into the model’s reasoning process. Trained on sampled OpenR1-Math, MulFeRL outperforms supervised, self-distillation-based, and RLVR baselines in-domain and shows strong out-of-domain generalization. [We release our code at <https://anonymous.4open.science/r/MulFeRL>.]

Large language models (LLMs) are largely static and often redo reasoning or repeat mistakes. Prior experience reuse typically relies on external retrieval, which is similarity-based, can introduce noise, and adds latency. We introduce SEAM (Structured Experience Adapter Module), a lightweight, executor-specific plug-in that stores experience in its parameters and generates a structured, instance-tailored experience entry in a single forward pass to guide a frozen LLM executor. SEAM is trained for utility via executor rollouts and GRPO while keeping the executor frozen, and can be further improved with logged-success SFT after deployment. Experiments on mathematical reasoning benchmarks show consistent accuracy gains across executors with low overhead. Extensive ablation and analysis further elucidate the mechanisms underlying SEAM’s effectiveness and robustness.