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This research introduces $\Delta$-MOPD, a novel distillation technique that isolates post-training logit shifts from inherited base model preferences to improve multi-teacher training efficiency. By re-anchoring these shifts at the student's frozen initialization, the method significantly reduces performance gaps in complex routing scenarios and enhances mathematical reasoning capabilities. This work advances the theoretical understanding of policy transfer mechanisms, offering a more robust framework for combining specialist models without contaminating student learning with outdated base priors.
Composing What Each Teacher Learned: Multi-Teacher On-Policy Distillation through Teacher-Relative Shifts
arXiv:2610.10460v1 Announce Type: new Abstract: Multi-teacher on-policy distillation (MOPD) is used in two settings. In common-domain composition, several teachers score each student rollout from one prompt domain and their signals form a single target; in routed-domain distillation, prompts from different domains are assigned to the corresponding specialist. Both settings usually transfer each teacher's endpoint policy, which mixes what post-training changed with preferences inherited from the teacher's base. We introduce $\Delta$-MOPD, which transfers each teacher's teacher-minus-base logit shift re-anchored at the student's frozen initialization, and compare it with endpoint supervision in both settings while holding teacher selection fixed. We first expose the mechanism that impedes endpoint transfer: inherited base pull can exceed the post-training shift. Removing it reduces the teacher-term norm ratio and target--student KL. Across our experiments, the results suggest that shift targets are particularly useful when teacher signals are combined at a state. With three composed teachers, $\Delta$-MOPD exceeds endpoint composition by $4.11$ Math and $1.95$ five-benchmark points; with two, it matches endpoint accuracy. Under phased routing, it achieves higher mean performance in both phase orders and reduces the observed order gap from $10.50$ to $6.42$ points. Under interleaved routing, where each update involves one teacher, the two targets perform comparably. The phased results provide supporting evidence that the benefit may extend to signals accumulated across training phases. Target construction is thus an independent design axis in MOPD, complementary to teacher selection.
Abstract:Multi-teacher on-policy distillation (MOPD) is used in two settings. In common-domain composition, several teachers score each student rollout from one prompt domain and their signals form a single target; in routed-domain distillation, prompts from different domains are assigned to the corresponding specialist. Both settings usually transfer each teacher's endpoint policy, which mixes what post-training changed with preferences inherited from the teacher's base. We introduce $\Delta$-MOPD, which transfers each teacher's teacher-minus-base logit shift re-anchored at the student's frozen initialization, and compare it with endpoint supervision in both settings while holding teacher selection fixed. We first expose the mechanism that impedes endpoint transfer: inherited base pull can exceed the post-training shift. Removing it reduces the teacher-term norm ratio and target--student KL. Across our experiments, the results suggest that shift targets are particularly useful when teacher signals are combined at a state. With three composed teachers, $\Delta$-MOPD exceeds endpoint composition by $4.11$ Math and $1.95$ five-benchmark points; with two, it matches endpoint accuracy. Under phased routing, it achieves higher mean performance in both phase orders and reduces the observed order gap from $10.50$ to $6.42$ points. Under interleaved routing, where each update involves one teacher, the two targets perform comparably. The phased results provide supporting evidence that the benefit may extend to signals accumulated across training phases. Target construction is thus an independent design axis in MOPD, complementary to teacher selection.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.10460 [cs.LG]
(or arXiv:2610.10460v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.10460 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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