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Insights from Gradient Dynamics: Gradient Autoscaled Normalization

Created by
  • Haebom

Author

Vincent-Daniel Yun

Outline

This paper provides an empirical analysis of gradient dynamics, which plays a pivotal role in determining the stability and generalization ability of deep neural networks. We analyze the evolution of the variance and standard deviation of gradients in convolutional neural networks, which exhibit consistent changes at both layer-by-layer and global scales. Based on these observations, we propose a hyperparameter-free gradient regularization method that aligns gradient scaling with the natural evolutionary process. This method prevents unintended amplification, stabilizes optimization, and maintains convergence guarantees. Experiments on the challenging CIFAR-100 benchmark using ResNet-20, ResNet-56, and VGG-16-BN demonstrate that the method maintains or improves test accuracy even under strong generalization. In addition to demonstrating substantial performance improvements, this study highlights the importance of directly tracking gradient dynamics to bridge the gap between theoretical expectations and empirical behavior and to provide insights for future optimization research.

Takeaways, Limitations

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Takeaways:
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By analyzing the evolution of the variance and standard deviation of the slope, we provide new insights that can improve slope regularization methods.
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We propose a hyperparameter-free gradient regularization method and show that it can stabilize the optimization process and improve generalization performance.
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We highlight the importance of direct tracking of gradient dynamics to bridge the gap between theoretical expectations and empirical behavior.
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We verify the effectiveness of the proposed method through experiments using ResNet and VGG networks on the CIFAR-100 benchmark.
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Limitations:
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The effectiveness of the proposed method may be limited to specific network structures and datasets. Additional experiments with a wider variety of networks and datasets are needed.
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Since the analysis of slope dynamics is based on empirical observations, there is a need to further strengthen the theoretical basis.
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Analysis of the computational cost of the proposed method is lacking. Computational efficiency should be considered to increase practical applicability.
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