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Towards Theoretical Analysis of Transformation Complexity of ReLU DNNs
Jie Ren · Mingjie Li · Meng Zhou · Shih-Han Chan · Quanshi Zhang

Wed Jul 20 07:40 AM -- 07:45 AM (PDT) @ Room 318 - 320

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. The code is released at https://github.com/sjtu-XAI-lab/transformation-complexity.

Author Information

Jie Ren (Shanghai Jiao Tong University)
Mingjie Li (Shanghai Jiao Tong University)
Meng Zhou (Carnegie Mellon University)
Shih-Han Chan (University of California San Diego)
Quanshi Zhang (Shanghai Jiao Tong University)

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