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Knowledge Distillation Under Ideal Joint Classifier Assumption

Huayu Li, Xiwen Chen, Gregory Ditzler, Janet Roveda, Ao Li

TL;DR

This work introduces IJCKD, a theory-guided framework for knowledge distillation that leverages an Ideal Joint Classifier assumption to bound the student’s error in terms of the teacher’s performance and representation alignment. By unifying SRRL and SimKD under a domain adaptation–inspired bound, IJCKD justifies using the teacher classifier as supervision while also aligning student features, and it formalizes two complementary loss terms (cross-entropy with hard labels and logits/feature matching). Empirically, IJCKD consistently improves over SRRL and SRL-based baselines on CIFAR-100 and ImageNet, with robust performance across connector architectures and notable gains on mobile/compact backbones. The results support the central claim that aligning teacher–student representations through the Ideal Joint Classifier framework facilitates more effective knowledge transfer and generalizes across model pairs and datasets. The paper thus offers a principled, adaptable approach to distillation with potential for broad applicability and future theoretical tightening.

Abstract

Knowledge distillation constitutes a potent methodology for condensing substantial neural networks into more compact and efficient counterparts. Within this context, softmax regression representation learning serves as a widely embraced approach, leveraging a pre-established teacher network to guide the learning process of a diminutive student network. Notably, despite the extensive inquiry into the efficacy of softmax regression representation learning, the intricate underpinnings governing the knowledge transfer mechanism remain inadequately elucidated. This study introduces the 'Ideal Joint Classifier Knowledge Distillation' (IJCKD) framework, an overarching paradigm that not only furnishes a lucid and exhaustive comprehension of prevailing knowledge distillation techniques but also establishes a theoretical underpinning for prospective investigations. Employing mathematical methodologies derived from domain adaptation theory, this investigation conducts a comprehensive examination of the error boundary of the student network contingent upon the teacher network. Consequently, our framework facilitates efficient knowledge transference between teacher and student networks, thereby accommodating a diverse spectrum of applications.

Knowledge Distillation Under Ideal Joint Classifier Assumption

TL;DR

This work introduces IJCKD, a theory-guided framework for knowledge distillation that leverages an Ideal Joint Classifier assumption to bound the student’s error in terms of the teacher’s performance and representation alignment. By unifying SRRL and SimKD under a domain adaptation–inspired bound, IJCKD justifies using the teacher classifier as supervision while also aligning student features, and it formalizes two complementary loss terms (cross-entropy with hard labels and logits/feature matching). Empirically, IJCKD consistently improves over SRRL and SRL-based baselines on CIFAR-100 and ImageNet, with robust performance across connector architectures and notable gains on mobile/compact backbones. The results support the central claim that aligning teacher–student representations through the Ideal Joint Classifier framework facilitates more effective knowledge transfer and generalizes across model pairs and datasets. The paper thus offers a principled, adaptable approach to distillation with potential for broad applicability and future theoretical tightening.

Abstract

Knowledge distillation constitutes a potent methodology for condensing substantial neural networks into more compact and efficient counterparts. Within this context, softmax regression representation learning serves as a widely embraced approach, leveraging a pre-established teacher network to guide the learning process of a diminutive student network. Notably, despite the extensive inquiry into the efficacy of softmax regression representation learning, the intricate underpinnings governing the knowledge transfer mechanism remain inadequately elucidated. This study introduces the 'Ideal Joint Classifier Knowledge Distillation' (IJCKD) framework, an overarching paradigm that not only furnishes a lucid and exhaustive comprehension of prevailing knowledge distillation techniques but also establishes a theoretical underpinning for prospective investigations. Employing mathematical methodologies derived from domain adaptation theory, this investigation conducts a comprehensive examination of the error boundary of the student network contingent upon the teacher network. Consequently, our framework facilitates efficient knowledge transference between teacher and student networks, thereby accommodating a diverse spectrum of applications.
Paper Structure (18 sections, 1 theorem, 10 equations, 4 figures, 6 tables, 4 algorithms)

This paper contains 18 sections, 1 theorem, 10 equations, 4 figures, 6 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related works
  3. Knowledge Distillation Under Ideal Joint Classifier Assumption
  4. Experiments
  5. Results on CIFAR-100
  6. Compare with SimKD
  7. Ablation Study
  8. Results on ImageNet
  9. Validation of the Ideal Joint Classifier Assumption
  10. Can teacher classifier be the ideal joint classifier?
  11. Evolution of Classifier Alignment During SRRL Training
  12. Alternative Implementations of IJCKD
  13. Discussion
  14. Scope
  15. Understanding the 'Ideal Joint Classifier Assumption'
  16. ...and 3 more sections

Key Result

Theorem 1

For a teacher network $f_t=g_t\circ\Phi_t$, a student network $f_s=g_s\circ\Phi_s$, the student error can be bounded as:

Figures (4)

  • Figure 1: An illustration to show the differences between the SRRL, SimKD, and IJCKD frameworks.
  • Figure 2: Top-1 accuracy curves for different $\alpha_{ce}$.
  • Figure 3: Top-1 accuracy curves for different loss combination.
  • Figure 4: Frobenius Norm of the difference of the weight of teacher's classifier ($W^{tc}$) and student's classifier ($W^{sc}$) during SRRL training.

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • Definition 1