While data curation is widely credited with improving large language model training, a basic question remains unresolved: does curation expand what a model can ultimately learn, or merely reach the same solution faster? In this paper, we formalize this distinction between advancement (improving the attainable performance) and acceleration (reaching the same performance with less data). Through an analytic characterization and real-world LLM experiments, we show that advancement requires a correctable train-target gap. When the baseline training and target objectives coincide, no curation policy improves the endpoint, although curation may still accelerate training. This reframes advancement as a property of the curation task rather than the curation method. Under a common gap-centric view of data mixture and selection, we operationalize this condition as the $Δ$-test, an observable discrepancy between the uncurated baseline's training and target losses that is computable prior to expensive curation. Across extensive experiments, an appreciably nonzero $Δ$ predicts persistent gains, whereas gains near $Δ=0$ tend to diminish as the training budget grows. Beyond individual methods, our findings recenter data curation on the task itself and point to target-set construction as a promising direction for shaping what curation can achieve.
Junxing Hu, Zicheng Zhang, Zhiqian Zhang, Ai Han, Yifeng Zhang, Pengzhang Liu, Ling Li
Reasoning models trained with Group Relative Policy Optimization (GRPO) now produce chains of thought thousands of tokens long, and recent studies reveal that such training is prone to policy collapse. Entropy regularization is the standard remedy, but it works by pushing probability mass away from the few tokens that carry it and toward the vast low-probability tail of the vocabulary, and it applies this force once for every token of the reasoning trace. This puts the bonus in direct conflict with the entropy decay that convergence requires, and makes its coefficient difficult to set in the long-trace regime. To resolve this tension, we propose Info-GRPO, an information-theoretic framework that cultivates correlation between the policy and a latent prior. Rather than raising entropy everywhere, Info-GRPO builds on the mutual information between a latent variable and the trajectory it induces: augmenting prompts with latent seeds during training lets the model explore diverse policies correlated with the prior, while the seed-conditioned entropy is guided toward convergence. Diversity is therefore carried across whole reasoning traces rather than by per-token randomness, and exploration no longer fights entropy reduction. Experiments show that Info-GRPO outperforms vanilla GRPO and entropy-regularized GRPO across diverse reasoning benchmarks. On AIME24, it improves $Avg@8$ over GRPO by 3.75%, 1.66%, 4.16%, and 4.17% on four backbones, and it reaches the same majority-vote accuracy with $8\times$ fewer samples. Code and models will be publicly released.