$T^5$: Twin-Critic Training for Token-Level Thoughts in Reinforcement Mid-Training

A commonly accepted explanation of critic-free RL for LLMs, based on sequence-level rewards, is that it reinforces successful rollouts with a positive advantage while penalizing failed ones. In contrast, we study critic-free RL from a token-level perspective, revealing the token-flipping phenomenon: positive and negative rollouts exhibit remarkably similar proportions of tokens whose probabilities are boosted or suppressed during RL training. To explain this phenomenon, we further show that a token's change in probability is not fully determined by its own advantage; coupled gradient interactions with other tokens also play a non-negligible role. Specifically, these token coupling effects occur primarily between identical tokens that are both predicted with low confidence. Building upon this analysis, we propose the cancellation hypothesis: as a result of coupling, opposing signals cancel out for tokens shared by positive and negative rollouts, while tokens more specific to successful rollouts receive stronger reinforcement, thereby inducing hidden token-level credit assignment from rollout-level rewards. We support this hypothesis with complementary empirical evidence. (1) Compared with training on only positive rollouts, critic-free RL shifts updates from template and formatting tokens toward reasoning tokens; (2) Tokens boosted by critic-free RL consistently demonstrate higher value than suppressed tokens, regardless of whether they originate from positive or negative rollouts. Guided by this view, we implement two batching interventions to encourage or preserve cancellation in critic-free RL training: query-preserved mini-batching and reward-balanced batching. Despite their simplicity, these interventions improve RLVR training across multiple model scales, supporting cancellation as both an explanatory principle and a practical design criterion for critic-free RL training.

Group-based reinforcement learning methods such as GRPO for large language models avoid training a critic by sampling multiple responses for each prompt. A reliable critic could instead estimate token-level advantages from one response, but standard critic-based training recipes are often unstable. We study this instability and develop Best Practice Critic Optimization (BPCO), a recipe that combines DPPO, value predictions bounded to the reward range, Monte Carlo value targets, unnormalized policy advantages, and length-adaptive generalized advantage estimation. Because the critic is used only during training, BPCO can also condition it on reward-defining information, such as a reference answer or grading rubric, that is hidden from the policy. Controlled experiments isolate the effect of each design choice. Across mathematical reasoning tasks with models ranging from 1.5B parameters to 30B-A3B mixtures of experts, BPCO improves a strong critic-based baseline consistently, and matches or exceeds a group-based baseline while sampling one response per prompt. The same recipe also improves learning with rubric-based rewards. These results show that a carefully designed critic provides a reliable alternative to group-relative advantage estimation. Code is available at https://github.com/QPHutu/golden_critic.

Agentic reinforcement learning trains large language models using multi-turn trajectories that interleave long reasoning traces with short environment-facing actions. Common policy-gradient methods, such as PPO and GRPO, treat each token in a trajectory equally, leading to uniform credit assignment. In this paper, we critically demonstrate that such uniform credit assignment largely misallocates token-level training signals. From an energy-based modeling perspective, we show that token-level training signals, quantified by their correlations with reward variance of different rollouts sampled from a given prompt, concentrate sharply on action tokens rather than reasoning tokens, even though action tokens account for only a small fraction of the trajectory. We refer to this phenomenon as the Action Bottleneck. Motivated by this observation, we propose an embarrassingly simple token reweighting approach, ActFocus, that downweights gradients on reasoning tokens, along with an additional energy-based redistribution mechanism that further increases the weights on action tokens with higher uncertainty. Across four environments and different model sizes, ActFocus consistently outperforms PPO and GRPO, yielding final-step gains of up to 65.2 and 63.7 percentage points, respectively, without any additional runtime or memory cost.