Learning to Reason with Mixture of Tokens
Reinforcement learning with verifiable rewards (RLVR) has become a leading approach for improving large language model (LLM) reasoning capabilities. Most current methods follow variants of Group Relative Policy Optimization, which samples multiple reasoning completions, scores them relative to each other, and adjusts the policy accordingly. However, these approaches invariably sample discrete tokens at each reasoning step, discarding the rich distributional information in the model's probability distribution over candidate tokens. While preserving and utilizing this distributional information has proven beneficial in non-RL settings, current RLVR methods seem to be unnecessarily constraining the reasoning search space by not using this information. To address this limitation, we investigate mixture-of-token generation (MoT-G) in RLVR. We present a unified framework that generalizes existing MoT-G approaches, including existing training-free methods that construct mixture embeddings as weighted sums over token embeddings, and extend RLVR to operate directly in this continuous mixture space for generating chain-of-thought. Evaluating two MoT-G variants on Reasoning-Gym, a suite of reasoning-intensive language tasks, we find that MoT--G methods achieve substantial improvements (5--35 \% gains on 7 out of 10 tasks) compared to standard decoding with the Qwen2.5-1.5B model, while reaching comparable accuracy with half the number of trajectories, suggesting improved training efficiency. Through comprehensive hidden-state and token-level analyses, we provide evidence that MoT--G's benefits may stem from its ability to maintain higher hidden-state entropy throughout the reasoning process and promote exploration in token space.