Not all tokens are needed(NAT): token efficient reinforcement learning

Large language models increasingly rely on long chains of thought to improve accuracy, yet such gains come with substantial inference-time costs. We revisit token-efficient post-training and argue that existing sequence-level reward-shaping methods offer limited control over how reasoning effort is allocated across tokens. To bridge the gap, we propose IAPO, an information-theoretic post-training framework that assigns token-wise advantages based on each token's conditional mutual information (MI) with the final answer. This yields an explicit, principled mechanism for identifying informative reasoning steps and suppressing low-utility exploration. We provide a theoretical analysis showing that our IAPO can induce monotonic reductions in reasoning verbosity without harming correctness. Empirically, IAPO consistently improves reasoning accuracy while reducing reasoning length by up to 36%, outperforming existing token-efficient RL methods across various reasoning datasets. Extensive empirical evaluations demonstrate that information-aware advantage shaping is a powerful and general direction for token-efficient post-training. The code is available at https://github.com/YinhanHe123/IAPO.

Tokenization is a hardcoded compression step which remains in the training pipeline of Large Language Models (LLMs), despite a general trend towards architectures becoming increasingly end-to-end. Prior work has shown promising results at scale in bringing this compression step inside the LLMs' architecture with heuristics to draw token boundaries, and also attempts to learn these token boundaries with straight-through estimates, which treat the problem of drawing discrete token boundaries as a continuous one. We show that these token boundaries can instead be learned using score function estimates, which have tighter theoretical guarantees due to directly optimizing the problem of drawing discrete token boundaries to minimize loss. We observe that techniques from reinforcement learning, such as time discounting, are necessary to reduce the variance of this score function sufficiently to make it practicable. We demonstrate that the resultant method outperforms prior proposed straight-through estimates, both qualitatively and quantitatively at the $100$ million parameter scale.

In this paper, we propose an extremely efficient, training-free method to extract token-level reward signals directly from an existing deep reward model. Our core idea is to attribute the overall process reward to individual tokens by estimating each token's influence. This influence is defined as the change in the final macroscopic reward (e.g., the process reward) when a token is replaced with a semantically null token. Naively calculating this influence is computationally infeasible, requiring N forward passes through the PRM for an N-token sequence. We overcome this bottleneck by proposing a highly efficient gradient-based estimator. Specifically, we use a first-order Taylor approximation, which simplifies the influence calculation to the inner product of the difference between the token embedding and the null token embedding, and the gradient of the reward with respect to the token embedding. This requires only a single forward and backward pass. The resulting token-level rewards enable standard RL algorithms to perform precise credit assignment without requiring additional reward model training. Experiments on challenging reasoning benchmarks demonstrate that our method substantially improves policy optimization efficiency and enhances the generalization of LLM reasoning capabilities. Our P2T outperforms the outcome reward by +4.9% on MathVista for Qwen2.5-VL-7B-Instruct, and +11.5% on AIME24 for Qwen2.5-Math-7B. The code will be released via https://github.com/stonewst/P2T.