Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks
This work addresses training efficiency for neural networks, particularly in the infinite-width regime, but appears incremental as it builds on existing neural tangent kernel theory.
The paper tackles the problem of slow training for infinite-width two-layer ReLU neural networks by introducing the Homotopy Relaxation Training Algorithm (HRTA), which uses a homotopy activation function and parameter relaxation to achieve significantly improved convergence rates, as validated by experiments with larger widths.
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.