Simple initialization and parametrization of sinusoidal networks via their kernel bandwidth
This work addresses the problem of empirical design choices in sinusoidal networks for researchers and practitioners, offering a more principled approach, though it is incremental as it builds on existing sinusoidal network frameworks.
The authors tackled the challenge of understanding and improving sinusoidal neural networks by proposing a simplified version and analyzing it through the neural tangent kernel perspective, showing that its kernel approximates a low-pass filter with adjustable bandwidth, which they used to optimize initialization and achieve better performance on tasks like learning implicit models and solving differential equations.
Neural networks with sinusoidal activations have been proposed as an alternative to networks with traditional activation functions. Despite their promise, particularly for learning implicit models, their training behavior is not yet fully understood, leading to a number of empirical design choices that are not well justified. In this work, we first propose a simplified version of such sinusoidal neural networks, which allows both for easier practical implementation and simpler theoretical analysis. We then analyze the behavior of these networks from the neural tangent kernel perspective and demonstrate that their kernel approximates a low-pass filter with an adjustable bandwidth. Finally, we utilize these insights to inform the sinusoidal network initialization, optimizing their performance for each of a series of tasks, including learning implicit models and solving differential equations.