On-policy self-distillation (OPSD) trains a student on its own responses using token-level supervision from the same model conditioned on privileged reference information. We investigate whether performance gains from OPSD show that the student learned the information in the reference or instead reflect recovery of reasoning behavior already present in the base model. We perform OPSD experiments on science and mathematics datasets using Qwen3 models ranging from 1.7B to 8B. Our analysis framework separates the supervision induced by the reference from the supervision provided by the teacher without the reference and measures how each aligns with changes in the student's predictions. The correct reference does not provide a consistent performance benefit across teacher generation modes, model sizes, and training datasets. Students can improve without the correct reference, and a solution from another problem can outperform the correct solution on several mathematical reasoning benchmarks. The student's predictions align more strongly with the base model's thinking behavior than with the supervision induced by the reference, but controls constructed from other problems reproduce much of both alignments. Moreover, stronger alignment attributable to the correct reference does not reliably coincide with a greater performance benefit from the reference. Performance gains and distributional alignment alone therefore cannot determine how privileged reference information contributes to student learning in OPSD.
Self-distillation (SD) has emerged as a compute-efficient alternative to reinforcement learning with verifiable rewards: a self-teacher, conditioned on privileged information (PI) about the answer such as a reference solution, supplies dense per-token supervision to a student that never sees it. Reported gains, however, come almost exclusively from narrow, low-difficulty settings, leaving open a basic question: as a lone objective, with no reward term, does SD teach anything? We reproduce SDPO's reported gains in its easy setting, then apply the identical setup to difficult tasks and find that it does not. Across question answering, mathematics, coding, and multi-turn agentic tool use, across reasoning modes, model sizes, and forms of PI, and under both the SDPO and OPSD recipes, the per-token loss falls steadily while validation accuracy does not improve and typically degrades. We explain this failure through a single causal chain from the loss to the model it produces. The chain begins with PI bias: having seen one particular reference solution, the teacher's per-token target is pulled toward that trajectory rather than toward correctness in general, an effect we quantify with a PI Bias Score. Trained to match this target everywhere, the student's objective becomes nearly blind to whether a rollout is correct, and the loss it assigns falls mostly on low-information tokens like stopwords, punctuation, uncertainty markers, rather than those that determine the answer; within correct rollouts the exploratory tokens incur the highest divergence, so it penalizes the hesitation that reasoning requires. The result is a flatter, less decisive student that is no better at reasoning: as a lone objective, SD optimizes a signal decoupled from task success.
Large language models have demonstrated significant capabilities in generating diverse and context-aware responses for empathetic dialogue. However, their computational demands severely limit their deployment in resource-constrained environments. While knowledge distillation offers a promising compression solution, it often fails to transfer the nuanced understanding essential for empathy, as it overlooks the implicit contextual cues that guide human connection. To bridge this gap, we propose a \textbf{pr}ivileged \textbf{i}nformation-enhanced knowledge \textbf{d}istillation method for \textbf{e}mpathetic dialogue generation (PRIDE). Our method leverages privileged information, such as expert psychological annotations or future event summaries, which is available exclusively during training but unavailable at inference time. This allows us to transfer the teacher model's empathetic reasoning to smaller models without relying on extra inputs during deployment. Specifically, PRIDE has three key components: (1) An empathy-reasoning prompt that guides the teacher to explicitly decompose the empathetic process into understanding feelings and analyzing situations step-by-step; (2) A multi-source attention mechanism that directs the student to effectively integrate privileged information; (3) A dual-alignment loss that combines reversed Kullback-Leibler divergence and maximum mean discrepancy to ensure robust knowledge transfer at both logit and feature levels. Experiments on multi-modal and text-only datasets demonstrate that our method achieves competitive performance, and in some cases matches or even surpasses larger teacher models in terms of accuracy and semantic relevance.