Neural Characteristic Activation Analysis and Geometric Parameterization for ReLU Networks

• URL: http://arxiv.org/abs/2305.15912v5
• Date: Sun, 13 Oct 2024 13:24:22 GMT
• Title: Neural Characteristic Activation Analysis and Geometric Parameterization for ReLU Networks
• Authors: Wenlin Chen, Hong Ge,
• Abstract summary: We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during convergence optimization, which impedes fast convergence and hurts performance.
• Score: 2.2713084727838115
• License:
• Abstract: We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's advantages of optimization stability, convergence speed and generalization performance.

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