Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks

• URL: http://arxiv.org/abs/2309.15244v3
• Date: Sun, 06 Oct 2024 03:12:12 GMT
• Title: Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks
• Authors: Yahong Yang, Qipin Chen, Wenrui Hao,
• Abstract summary: We present a novel training approach called the Homotopy Relaxation Training Algorithm (HRTA) Our algorithm incorporates two key mechanisms: one involves building a homotopy activation function that seamlessly connects the linear activation function with the ReLU activation function. We have conducted an in-depth analysis of this novel method within the context of the neural tangent kernel (NTK)
• Score: 1.8434042562191815
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• Abstract: In this paper, we present a novel training approach called the Homotopy Relaxation Training Algorithm (HRTA), aimed at accelerating the training process in contrast to traditional methods. Our algorithm incorporates two key mechanisms: one involves building a homotopy activation function that seamlessly connects the linear activation function with the ReLU activation function; the other technique entails relaxing the homotopy parameter to enhance the training refinement process. We have conducted an in-depth analysis of this novel method within the context of the neural tangent kernel (NTK), revealing significantly improved convergence rates. Our experimental results, especially when considering networks with larger widths, validate the theoretical conclusions. This proposed HRTA exhibits the potential for other activation functions and deep neural networks.

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