Recent reinforcement learning (RL) post-training approaches primarily optimize the final output policy using sparse outcome-level rewards, while largely overlooking predictive signals encoded in intermediate representations. In this paper, we introduce a new paradigm called on-policy internal self-distillation and propose the OISD framework, which improves reasoning by transferring on-policy predictive signals from the final layer to intermediate representations. During rollout and Group Relative Policy Optimization (GRPO) optimization, the final layer acts as both the policy and a detached internal teacher for selected intermediate layers, which are guided to align with it through two complementary mechanisms: logit alignment, which transfers high-level reasoning behaviors (how to think), and attention alignment, which enforces consistent attention patterns (where to look) from the final layer to the selected intermediate layer, both without requiring external privileged information. Our OISD, together with GRPO, employs signed advantage-weighted Jensen–Shannon alignment to distill informative intermediate representations while preserving policy consistency under a unified acting policy. Experimental results demonstrate the effectiveness of OISD, with substantial and consistent improvements over strong reasoning RL baselines across four mathematical reasoning tasks.

As a promising paradigm to collaboratively train models with decentralized data, Federated Learning (FL) can be exploited to fine-tune Large Language Models (LLMs). While LLMs correspond to huge size, the scale of the training data significantly increases, which leads to tremendous amounts of computation and communication costs. The training data is generally non-Independent and Identically Distributed (non-IID), which requires adaptive data processing within each device. Although Low-Rank Adaptation (LoRA) can significantly reduce the scale of parameters to update in the fine-tuning process, it still takes unaffordable time to transfer the low-rank parameters of all the layers in LLMs. In this paper, we propose a Fisher Information-based Efficient Curriculum Federated Learning framework (FibecFed) with two novel methods, i.e., adaptive federated curriculum learning and efficient sparse parameter update. First, we propose a fisher information-based method to adaptively sample data within each device to improve the effectiveness of the FL fine-tuning process. Second, we dynamically select the proper layers for global aggregation and sparse parameters for local update with LoRA so as to improve the efficiency of the FL fine-tuning process. Extensive experimental results based on 10 datasets demonstrate that FibecFed yields excellent performance (up to 45.35% in terms of accuracy) and superb fine-tuning speed (up to 98.61% faster) compared with 17 baseline approaches).