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Rényi Divergence Deep Mutual Learning

Weipeng Huang, Junjie Tao, Changbo Deng, Ming Fan, Wenqiang Wan, Qi Xiong, Guangyuan Piao

Abstract

This paper revisits Deep Mutual Learning (DML), a simple yet effective computing paradigm. We propose using Rényi divergence instead of the KL divergence, which is more flexible and tunable, to improve vanilla DML. This modification is able to consistently improve performance over vanilla DML with limited additional complexity. The convergence properties of the proposed paradigm are analyzed theoretically, and Stochastic Gradient Descent with a constant learning rate is shown to converge with $\mathcal{O}(1)$-bias in the worst case scenario for nonconvex optimization tasks. That is, learning will reach nearby local optima but continue searching within a bounded scope, which may help mitigate overfitting. Finally, our extensive empirical results demonstrate the advantage of combining DML and Rényi divergence, leading to further improvement in model generalization.

Rényi Divergence Deep Mutual Learning

Abstract

This paper revisits Deep Mutual Learning (DML), a simple yet effective computing paradigm. We propose using Rényi divergence instead of the KL divergence, which is more flexible and tunable, to improve vanilla DML. This modification is able to consistently improve performance over vanilla DML with limited additional complexity. The convergence properties of the proposed paradigm are analyzed theoretically, and Stochastic Gradient Descent with a constant learning rate is shown to converge with -bias in the worst case scenario for nonconvex optimization tasks. That is, learning will reach nearby local optima but continue searching within a bounded scope, which may help mitigate overfitting. Finally, our extensive empirical results demonstrate the advantage of combining DML and Rényi divergence, leading to further improvement in model generalization.
Paper Structure (17 sections, 4 theorems, 8 equations, 6 figures, 3 tables, 1 algorithm)

This paper contains 17 sections, 4 theorems, 8 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Deep Mutual Learning
  3. Rényi Divergence Deep Mutual Learning
  4. Rényi Divergence
  5. Properties of RDML
  6. Convergence Guarantee
  7. Computational Complexity of RDML
  8. Empirical Study
  9. Experimental Setup
  10. Convergence Trace Analysis
  11. Evaluation Results
  12. Image Classification.
  13. Text Classification.
  14. Summary.
  15. Generalization Results
  16. ...and 2 more sections

Key Result

proposition thmcounterproposition

For any student $k$ at any time $t$, the expected gradient for $\mathop{\mathrm{\mathcal{L}}}\nolimits_k$ is an unbiased estimator of the gradient, such that $\mathop{\mathrm{\mathbb{E}}}\nolimits [\nabla \mathop{\mathrm{\mathcal{L}}}\nolimits_k(d, j, \bm{\theta}_{k, t})] = \nabla \mathop{\mathrm{\m

Figures (6)

  • Figure 1: Example plots of Rényi divergence for distributions containing two events. The orange dashed line represents the KL divergence in both plots. The first plot fixes distribution $\mathbb{Q}$ to $(0.4, 0.6)$ and shows the divergence change over $p$ and $1-p$. The second plot fixes $\mathbb{P}= (0.4, 0.6)$ and shows the divergence change over $q$ and $1-q$. Note that when $q=0$ or $q=1$, the divergence value is $\infty$ for any $\alpha \in [0, 1) \cup (1, \infty)$. As infinity is not graphable, the x-axis in the second plot ranges from $0.001$ to $0.999$.
  • Figure 2: Plot of training loss for selected configurations, starting from the 50th epoch. The base loss and divergence loss are shown separately, with values presented for every third epoch.
  • Figure 3: Heatmap depicting the optimal $\alpha$ values obtained from $18$ experiments, each corresponding to a distinct pairing of a model M and a dataset D. The figure highlights the variability in $\alpha$ requirements for achieving superior performance when using different datasets with the same method (and vice versa).
  • Figure 4: Test loss of RDML for various $\alpha$ on the CIFAR100 dataset.
  • Figure 5: Test accuracy of RDML for various $\alpha$ on the CIFAR100 dataset.
  • ...and 1 more figures

Theorems & Definitions (6)

  • remark thmcounterremark
  • remark thmcounterremark
  • proposition thmcounterproposition
  • theorem thmcountertheorem
  • lemma thmcounterlemma
  • theorem thmcountertheorem