aiqbench analysis
This research demonstrates that self-distillation using privileged information fails as a standalone training objective for complex tasks, causing models to optimize token-level loss rather than actual reasoning accuracy. The study identifies "PI bias" as the root cause, where students learn to mimic specific reference trajectories instead of generalizing toward correctness, ultimately degrading performance on difficult problems in math, coding, and agentic workflows.
Privileged, but Biased: How PI-Conditioned Teachers Break Self-Distillation
arXiv:2608.04794v1 Announce Type: cross Abstract: 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.
Abstract: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.
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2608.04794 [cs.AI]
(or arXiv:2608.04794v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2608.04794 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 365 words
Related coverage
Projection sampling preserves capabilities but diminishes gains from alignment fine-tuning
LessWrong · Oct 16, 2026
Self-Distillation with Verbal Regularization
arXiv · Oct 14, 2026
One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation
arXiv · Aug 27, 2026
Beyond Absolute Imitation: Anchored Residual Guidance for Privileged On-Policy Distillation
arXiv · Jun 10, 2026