# A new initialisation to Control Gradients in Sinusoidal Neural network

arXiv: https://arxiv.org/abs/2512.06427 · HTML: https://mlsanity.com/paper/2512.06427/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 23 of 23)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [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)
- [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)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Deep Information Propagation](https://mlsanity.com/paper/1611.01232/) (2016)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice](https://mlsanity.com/paper/1711.04735/) (2017)
- [On the Impact of the Activation Function on Deep Neural Networks Training](https://mlsanity.com/paper/1902.06853/) (2019)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2306.08827/) (2023)
- [Mean Field Residual Networks: On the Edge of Chaos](https://mlsanity.com/paper/1712.08969/) (2017)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domains](https://mlsanity.com/paper/2305.02657/) (2023)
- [Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initialization](https://mlsanity.com/paper/2202.00553/) (2022)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [Simple initialization and parametrization of sinusoidal networks via their kernel bandwidth](https://mlsanity.com/paper/2211.14503/) (2022)
- [Robustifying Fourier Features Embeddings for Implicit Neural Representations](https://mlsanity.com/paper/2502.05482/) (2025)

## Built on by (most cited first, 1 of 1)

- [Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers](https://mlsanity.com/paper/2609.20641/) (2026)

## Abstract (arXiv)

Proper initialisation strategy is of primary importance to mitigate gradient explosion or vanishing when training neural networks. Yet, the impact of initialisation parameters still lacks a precise theoretical understanding for several well-established architectures. Here, we propose a new initialisation for networks with sinusoidal activation functions such as textttSIREN, focusing on gradients control, their scaling with network depth, their impact on training and on generalization. To achieve this, we identify a closed-form expression for the initialisation of the parameters, differing from the original textttSIREN scheme. This expression is derived from fixed points obtained through the convergence of pre-activation distribution and the variance of Jacobian sequences. Controlling both gradients and targeting vanishing pre-activation helps preventing the emergence of inappropriate frequencies during estimation, thereby improving generalization. We further show that this initialisation strongly influences training dynamics through the Neural Tangent Kernel framework (NTK). Finally, we benchmark textttSIREN with the proposed initialisation against the original scheme and other baselines on function fitting and image reconstruction. The new initialisation consistently outperforms state-of-the-art methods across a wide range of reconstruction tasks, including those involving physics-informed neural networks.