# Simple initialization and parametrization of sinusoidal networks via their kernel bandwidth

arXiv: https://arxiv.org/abs/2211.14503 · HTML: https://mlsanity.com/paper/2211.14503/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 26 Nov 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [The Convergence Rate of Neural Networks for Learned Functions of Different Frequencies](https://mlsanity.com/paper/1906.00425/) (2019)
- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions](https://mlsanity.com/paper/1905.06076/) (2019)
- [Solving Partial Differential Equations with Point Source Based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2111.01394/) (2021)

## Built on by (most cited first, 6 of 6)

- [Space and Time Continuous Physics Simulation From Partial Observations](https://mlsanity.com/paper/2401.09198/) (2024)
- [Physics-Informed Neural Networks: Minimizing Residual Loss with Wide Networks and Effective Activations](https://mlsanity.com/paper/2405.01680/) (2024)
- [A new initialisation to Control Gradients in Sinusoidal Neural network](https://mlsanity.com/paper/2512.06427/) (2025)
- [ParCo-SDF: Learning Prior-Free Partial-to-Complete Signed Distance Fields of Deformable Objects](https://mlsanity.com/paper/2605.29417/) (2026)
- [A Novel Fourier Feature Network for Solving Partial Differential Equations](https://mlsanity.com/paper/2608.14733/) (2026)
- [Stable initialization without the CLT](https://mlsanity.com/paper/2609.30633/) (2026)

## Abstract (arXiv)

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.