Neural Networks Trained by Weight Permutation are Universal Approximators
This provides a theoretical foundation for an incremental permutation training method, addressing researchers interested in alternative neural network training techniques.
The paper tackles the problem of theoretically guaranteeing a novel permutation-based training method for neural networks, proving that ReLU networks trained by weight permutation can approximate one-dimensional continuous functions, with numerical results validating its efficiency in regression tasks.
The universal approximation property is fundamental to the success of neural networks, and has traditionally been achieved by training networks without any constraints on their parameters. However, recent experimental research proposed a novel permutation-based training method, which exhibited a desired classification performance without modifying the exact weight values. In this paper, we provide a theoretical guarantee of this permutation training method by proving its ability to guide a ReLU network to approximate one-dimensional continuous functions. Our numerical results further validate this method's efficiency in regression tasks with various initializations. The notable observations during weight permutation suggest that permutation training can provide an innovative tool for describing network learning behavior.