MoL-RL: Distilling Multi-Step Environmental Feedback into LLMs for Feedback-Independent Reasoning

Large language models (LLMs) face significant challenges in effectively leveraging sequential environmental feedback (EF) signals, such as natural language evaluations, for feedback-independent chain-of-thought (CoT) reasoning. Existing approaches either convert EF into scalar rewards, losing rich contextual information, or employ refinement datasets, failing to exploit the multi-step and discrete nature of EF interactions. To address these limitations, we propose MoL-RL, a novel training paradigm that integrates multi-step EF signals into LLMs through a dual-objective optimization framework. Our method combines MoL (Mixture-of-Losses) continual training, which decouples domain-specific EF signals (optimized via cross-entropy loss) and general language capabilities (preserved via Kullback-Leibler divergence), with GRPO-based post-training to distill sequential EF interactions into single-step inferences. This synergy enables robust feedback-independent reasoning without relying on external feedback loops. Experimental results on mathematical reasoning (MATH-500, AIME24/AIME25) and code generation (CodeAgent-Test) benchmarks demonstrate that MoL-RL achieves state-of-the-art performance with the Qwen3-8B model, while maintaining strong generalization across model scales (Qwen3-4B). This work provides a promising approach for leveraging multi-step textual feedback to enhance LLMs' reasoning capabilities in diverse domains.

MoL for LLMs: Dual-Loss Optimization to Enhance Domain Expertise While Preserving General Capabilities

Although LLMs perform well in general tasks, domain-specific applications suffer from hallucinations and accuracy limitations. CPT approaches encounter two key issues: (1) domain-biased data degrades general language skills, and (2) improper corpus-mixture ratios limit effective adaptation. To address these, we propose a novel framework, Mixture of Losses (MoL), which decouples optimization objectives for domain-specific and general corpora. Specifically, cross-entropy (CE) loss is applied to domain data to ensure knowledge acquisition, while Kullback-Leibler (KL) divergence aligns general-corpus training with the base model's foundational capabilities. This dual-loss architecture preserves universal skills while enhancing domain expertise, avoiding catastrophic forgetting. Empirically, we validate that a 1:1 domain-to-general corpus ratio optimally balances training and overfitting without the need for extensive tuning or resource-intensive experiments. Furthermore, our experiments demonstrate significant performance gains compared to traditional CPT approaches, which often suffer from degradation in general language capabilities; our model achieves 27.9% higher accuracy on the Math-500 benchmark in the non-think reasoning mode, and an impressive 83.3% improvement on the challenging AIME25 subset in the think mode, underscoring the effectiveness of our approach.