Towards the Fundamental Limits of Knowledge Transfer over Finite Domains

Published: 16 Jan 2024, Last Modified: 05 Mar 2024ICLR 2024 posterEveryoneRevisionsBibTeX
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: knowledge transfer, classification, minimax optimality, density estimation, knowledge distillation
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
TL;DR: We settle the sample complexity of knowledge transfer at various levels of privileged information in the tabular setting.
Abstract: We characterize the statistical efficiency of knowledge transfer through $n$ samples from a teacher to a probabilistic student classifier with input space $\mathcal{S}$ over labels $\mathcal{A}$. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate $\sqrt{{|\mathcal{S}||\mathcal{A}|}/{n}}$. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to ${{|\mathcal{S}||\mathcal{A}|}/{n}}$. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on $\mathcal{A}$ given every sampled input, thereby provably enables the student to enjoy a rate ${|\mathcal{S}|}/{n}$ free of $|\mathcal{A}|$. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
Supplementary Material: pdf
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Primary Area: learning theory
Submission Number: 1228
Loading