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Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning (2012.09816v3)

Published 17 Dec 2020 in cs.LG, cs.NE, math.OC, and stat.ML

Abstract: We formally study how ensemble of deep learning models can improve test accuracy, and how the superior performance of ensemble can be distilled into a single model using knowledge distillation. We consider the challenging case where the ensemble is simply an average of the outputs of a few independently trained neural networks with the SAME architecture, trained using the SAME algorithm on the SAME data set, and they only differ by the random seeds used in the initialization. We show that ensemble/knowledge distillation in Deep Learning works very differently from traditional learning theory (such as boosting or NTKs, neural tangent kernels). To properly understand them, we develop a theory showing that when data has a structure we refer to as multi-view'', then ensemble of independently trained neural networks can provably improve test accuracy, and such superior test accuracy can also be provably distilled into a single model by training a single model to match the output of the ensemble instead of the true label. Our result sheds light on how ensemble works in deep learning in a way that is completely different from traditional theorems, and how thedark knowledge'' is hidden in the outputs of the ensemble and can be used in distillation. In the end, we prove that self-distillation can also be viewed as implicitly combining ensemble and knowledge distillation to improve test accuracy.

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Authors (2)
  1. Zeyuan Allen-Zhu (53 papers)
  2. Yuanzhi Li (119 papers)
Citations (332)

Summary

Understanding Ensemble, Knowledge Distillation, and Self-Distillation in Deep Learning

The paper provides a formal exploration of how ensemble methods and knowledge distillation improve test accuracy in deep learning models. It focuses on scenarios where data has a structural property termed as "multi-view", which is integral to the proposed theoretical framework. This paper applies primarily to standard neural networks, highlighting the distinct nature of ensemble learning in deep learning compared to traditional perspectives like boosting or neural tangent kernels (NTKs).

Key Insights and Theoretical Contributions

  1. Ensemble Learning in Neural Networks: The paper demonstrates that ensemble techniques, particularly those involving simple averaging of independently trained models, significantly enhance testing accuracy. This is explicitly validated under the premise of multi-view data structures where data instances can be correctly classified using different sets of features. Each neural network in the ensemble may learn partial feature sets, but collectively, they cover the entire feature spectrum needed for accurate classification.
  2. Knowledge Distillation: The paper evidences that the improved performance of an ensemble model can be distilled into a single network by training it to mimic the ensemble outputs instead of the true labels. This process, based on matching the ensemble’s soft labels, forces the single model to learn a broader range of features—hypothetically, the "dark knowledge" captured by the ensemble.
  3. Self-Distillation: The research offers insights into self-distillation, where a single model is refined by further training it to match its own outputs. This is seen as performing implicit ensemble and knowledge distillation in a single step, leading to improved generalization.

Practical Implications

This paper has multiple practical implications. It suggests methodologies for constructing more robust single models by leveraging ensemble outputs, providing a pathway to efficient use of compute resources without sacrificing performance. The multi-view perspective offers an analytical justification for deep learning's success in domains where different segments or features in data representations (like images) can provide equivalent information regarding the target class.

Theoretical and Empirical Framework

Empirically, the research sheds light on why ensemble techniques do not benefit linear methods over random feature mappings like NTKs, stressing the significance of neural networks' ability to learn feature representations rather than simply select them. Notably, experiments on Gaussian-like data reveal that ensemble methods don't always improve performance, pointing towards the importance of inherent data structures for ensemble efficacy.

Future Directions

The paper opens several avenues for future exploration, such as extending the theoretical framework to deeper or more complex network architectures, examining other data structures where ensemble techniques may be exploited effectively, and refining self-distillation methods further. Additionally, integrating multi-view considerations into network design could indirectly lead to models that inherently leverage ensemble-based learning strategies.

Conclusion

Thus, the paper provides critical insights into optimizing neural networks through ensemble strategies and distillation processes, aligning closely with the practical successes observed in deep learning applications. This work establishes a firm theoretical foundation to explain and potentially enhance the widespread practice of ensemble learning in AI.