# HOSC: A Periodic Activation with Saturation Control for High-Fidelity Implicit Neural Representations

arXiv: https://arxiv.org/abs/2601.07870 · HTML: https://mlsanity.com/paper/2601.07870/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 32 references that are in the map.
- First posted on arXiv 10 Jan 2026.

## Builds on (most cited first, 25 of 25)

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- [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)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [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)
- [Towards Understanding the Spectral Bias of Deep Learning](https://mlsanity.com/paper/1912.01198/) (2019)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [GARF: Gaussian Activated Radiance Fields for High Fidelity Reconstruction and Pose Estimation](https://mlsanity.com/paper/2204.05735/) (2022)
- [Neural Point Catacaustics for Novel-View Synthesis of Reflections](https://mlsanity.com/paper/2301.01087/) (2023)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Residual Multiplicative Filter Networks for Multiscale Reconstruction](https://mlsanity.com/paper/2206.00746/) (2022)
- [A Sampling Theory Perspective on Activations for Implicit Neural Representations](https://mlsanity.com/paper/2402.05427/) (2024)
- [Anti-Aliased Neural Implicit Surfaces with Encoding Level of Detail](https://mlsanity.com/paper/2309.10336/) (2023)
- [Periodic Activation Functions Induce Stationarity](https://mlsanity.com/paper/2110.13572/) (2021)
- [FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representation](https://mlsanity.com/paper/2407.19434/) (2024)
- [Neural Gaussian Scale-Space Fields](https://mlsanity.com/paper/2405.20980/) (2024)
- [INR-Bench: A Unified Benchmark for Implicit Neural Representations in Multi-Domain Regression and Reconstruction](https://mlsanity.com/paper/2510.10188/) (2025)

## Abstract (arXiv)

Periodic activations such as sine preserve high-frequency information in implicit neural representations (INRs) through their oscillatory structure, but often suffer from gradient instability and limited control over multi-scale behavior. We introduce the Hyperbolic Oscillator with Saturation Control (HOSC) activation, HOSC(x) = tanhbigl(β sin(ω0 x)bigr), which exposes an explicit parameter β that controls the Lipschitz bound of the activation by β ω0. This provides a direct mechanism to tune gradient magnitudes while retaining a periodic carrier. We provide a mathematical analysis and conduct a comprehensive empirical study across images, audio, video, NeRFs, and SDFs using standardized training protocols. Comparative analysis against SIREN, FINER, and related methods shows where HOSC provides substantial benefits and where it achieves competitive parity. Results establish HOSC as a practical periodic activation for INR applications, with domain-specific guidance on hyperparameter selection. For code visit the project page https://hosc-nn.github.io/ .