Training Large Reasoning Models Efficiently via Progressive Thought Encoding

Large reasoning models (LRMs) excel on complex problems but face a critical barrier to efficiency: reinforcement learning (RL) training requires long rollouts for outcome-based rewards, where autoregressive decoding dominates time and memory usage. While sliding-window cache strategies can bound memory, they disrupt long-context reasoning and degrade performance. We introduce Progressive Thought Encoding, a parameter-efficient fine-tuning method that enables LRMs to reason effectively under fixed-size caches. By progressively encoding intermediate reasoning into compact representations, our approach eliminates the need to backpropagate through full-cache rollouts, thereby reducing training-time memory usage, while maintaining constant memory during inference. Experiments on three models, including Qwen2.5-3B-Instruct, Qwen2.5-7B-Instruct, and DeepSeek-R1-Distill-Llama-8B, across six widely used challenging mathematical benchmarks show consistent gains: our method achieves +19.3\% improvement over LoRA and +29.9\% over the baseline on average, with up to +23.4 absolute gains on AIME2024/2025 under tight cache budgets. These results demonstrate that Progressive Thought Encoding not only improves reasoning accuracy but also makes RL training of LRMs substantially more efficient and scalable under real-world memory constraints.