Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks

TL;DR

This paper provides a theoretical framework for sinusoidal neural networks, introducing TUNER, a method that enhances training stability and reconstruction quality by controlling spectral properties during initialization and training.

Contribution

It offers a novel amplitude-phase expansion analysis of sinusoidal networks and introduces TUNER, a robust training method with spectral control for better performance.

Findings

Improved training stability and convergence with TUNER.

Enhanced reconstruction detail and quality.

Prevention of overfitting during training.

Abstract

Sinusoidal neural networks have been shown effective as implicit neural representations (INRs) of low-dimensional signals, due to their smoothness and high representation capacity. However, initializing and training them remain empirical tasks which lack on deeper understanding to guide the learning process. To fill this gap, our work introduces a theoretical framework that explains the capacity property of sinusoidal networks and offers robust control mechanisms for initialization and training. Our analysis is based on a novel amplitude-phase expansion of the sinusoidal multilayer perceptron, showing how its layer compositions produce a large number of new frequencies expressed as integer combinations of the input frequencies. This relationship can be directly used to initialize the input neurons, as a form of spectral sampling, and to bound the network's spectrum while training. Our method, referred to as TUNER (TUNing sinusoidal nEtwoRks), greatly improves the stability and convergence of sinusoidal INR training, leading to detailed reconstructions, while preventing overfitting.