Understanding deep learning requires rethinking generalization (1611.03530v2)

Abstract: Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the model family, or to the regularization techniques used during training. Through extensive systematic experiments, we show how these traditional approaches fail to explain why large neural networks generalize well in practice. Specifically, our experiments establish that state-of-the-art convolutional networks for image classification trained with stochastic gradient methods easily fit a random labeling of the training data. This phenomenon is qualitatively unaffected by explicit regularization, and occurs even if we replace the true images by completely unstructured random noise. We corroborate these experimental findings with a theoretical construction showing that simple depth two neural networks already have perfect finite sample expressivity as soon as the number of parameters exceeds the number of data points as it usually does in practice. We interpret our experimental findings by comparison with traditional models.

• The paper demonstrates that over-parameterized deep networks can perfectly fit training data yet maintain strong generalization performance.
• It employs empirical evaluations on datasets like CIFAR-10 and ImageNet to reveal discrepancies between classical theory and modern deep learning behavior.
• The findings imply that traditional risk minimization frameworks must be rethought to account for implicit regularization and the effects of over-parameterization.

Understanding Deep Learning Requires Rethinking Generalization

Overview

The paper "Understanding Deep Learning Requires Rethinking Generalization" by Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals provides a comprehensive analysis of the generalization properties of deep learning models. It challenges conventional wisdom regarding the relationship between model complexity, training data, and generalization performance in deep learning.

Main Contributions

The authors investigate several phenomena that traditional statistical learning theory cannot adequately explain. They observe that deep neural networks (DNNs) generalize well despite being over-parameterized to the extent that they could potentially memorize training data.

Key Experiments and Findings:

1. Capacity to Memorize: The paper demonstrates that deep learning models have significant capacity. For instance, standard architectures can perfectly fit random labels on datasets such as CIFAR-10 and ImageNet.
2. Comparison with Classical Models: The fact that DNNs generalize well in practice, despite their potential for high capacity, stands in stark contrast to classical models. These traditional approaches usually avoid overfitting by limiting capacity.
3. Empirical Study on Robustness: The performance of DNNs is robust to changes in the number of parameters and various training conditions. By altering hyperparameters and architectures, the authors show that out-of-sample error remains low even as in-sample error approaches zero.

Theoretical and Practical Implications

The evident discrepancy between traditional learning theory and the observed behavior of DNNs necessitates a re-evaluation of generalization theory. Specifically, the risk minimization framework needs to be adapted to account for:

• Over-parameterization: The success of extremely large models warrants a rethink of its theoretical foundation.
• Implicit regularization: The mechanisms by which training algorithms like SGD implicitly regularize models need deeper exploration.

Future Directions

The insights from this paper pave the way for numerous future research avenues:

• Novel Regularization Techniques: Developing new regularization methods tailored to the unique properties of DNNs.
• Generalization Bounds: Formulating generalization bounds that are more suitable for over-parameterized models.
• Training Dynamics: Further analyses into the dynamics of optimization algorithms to understand implicit regularization effects.

Conclusion

This paper offers a critical perspective by challenging the prevailing understanding of generalization in deep learning. The empirical evidence presented demands a thorough re-examination of classic theories and encourages the development of new theoretical frameworks. The results are pivotal for both the ongoing refinement of deep learning models and the broader discourse on machine learning theory.