Towards Theoretical Analysis of Transformation Complexity of ReLU DNNs
This work addresses the need for theoretical tools to understand and optimize DNN behavior, offering incremental advancements in metrics for transformation complexity.
This paper tackles the problem of theoretically analyzing the complexity of feature transformations in ReLU-based deep neural networks (DNNs) by proposing information-theoretic metrics, discovering a correlation with disentanglement, and using these metrics to analyze training phenomena and control over-fitting, adversarial robustness, and knowledge consistency.
This paper aims to theoretically analyze the complexity of feature transformations encoded in piecewise linear DNNs with ReLU layers. We propose metrics to measure three types of complexities of transformations based on the information theory. We further discover and prove the strong correlation between the complexity and the disentanglement of transformations. Based on the proposed metrics, we analyze two typical phenomena of the change of the transformation complexity during the training process, and explore the ceiling of a DNN's complexity. The proposed metrics can also be used as a loss to learn a DNN with the minimum complexity, which also controls the over-fitting level of the DNN and influences adversarial robustness, adversarial transferability, and knowledge consistency. Comprehensive comparative studies have provided new perspectives to understand the DNN.