# HOSC: A Periodic Activation Function for Preserving Sharp Features in Implicit Neural Representations

arXiv: https://arxiv.org/abs/2401.10967 · HTML: https://mlsanity.com/paper/2401.10967/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 20 Jan 2024.

## Builds on (most cited first, 26 of 26)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [State of the Art on Neural Rendering](https://mlsanity.com/paper/2004.03805/) (2020)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [A survey on modern trainable activation functions](https://mlsanity.com/paper/2005.00817/) (2020)
- [Factor Fields: A Unified Framework for Neural Fields and Beyond](https://mlsanity.com/paper/2302.01226/) (2023)
- [Deep Learning with S-shaped Rectified Linear Activation Units](https://mlsanity.com/paper/1512.07030/) (2015)
- [A Survey on Deep Geometry Learning: From a Representation Perspective](https://mlsanity.com/paper/2002.07995/) (2020)
- [Siamese SIREN: Audio Compression with Implicit Neural Representations](https://mlsanity.com/paper/2306.12957/) (2023)
- [Improving Deep Neural Network with Multiple Parametric Exponential Linear Units](https://mlsanity.com/paper/1606.00305/) (2016)

## Built on by (most cited first, 14 of 14)

- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Superpixel-informed Implicit Neural Representation for Multi-Dimensional Data](https://mlsanity.com/paper/2411.11356/) (2024)
- [Optimizing 3D Geometry Reconstruction from Implicit Neural Representations](https://mlsanity.com/paper/2410.12725/) (2024)
- [Spectral Bottleneck in Sinusoidal Representation Networks: Noise is All You Need](https://mlsanity.com/paper/2509.09719/) (2025)
- [COSMO-INR: Complex Sinusoidal Modulation for Implicit Neural Representations](https://mlsanity.com/paper/2505.11640/) (2025)
- [TabINR: An Implicit Neural Representation Framework for Tabular Data Imputation](https://mlsanity.com/paper/2510.01136/) (2025)
- [Content-Aware Frequency Encoding for Implicit Neural Representations with Fourier-Chebyshev Features](https://mlsanity.com/paper/2603.01028/) (2026)
- [Implicit Neural Representations: A Signal Processing Perspective](https://mlsanity.com/paper/2604.15047/) (2026)
- [Zorro: A Flexible and Differentiable Parametric Family of Activation Functions That Extends ReLU and GELU](https://mlsanity.com/paper/2409.19239/) (2024)
- [FLAIR: Frequency- and Locality-Aware Implicit Neural Representations](https://mlsanity.com/paper/2508.13544/) (2025)
- [Multi-resolution Enhancement for Full Spectrum Neural Representations](https://mlsanity.com/paper/2509.15494/) (2025)
- [Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations](https://mlsanity.com/paper/2604.02846/) (2026)
- [Adaptive Oscillatory Inductive Bias for Modeling Sharp Prosodic Dynamics in Diffusion-Based TTS](https://mlsanity.com/paper/2606.25424/) (2026)
- [ScaLe-INR: Scale and Learn Implicit Neural Representations](https://mlsanity.com/paper/2606.27862/) (2026)

## Abstract (arXiv)

Recently proposed methods for implicitly representing signals such as images, scenes, or geometries using coordinate-based neural network architectures often do not leverage the choice of activation functions, or do so only to a limited extent. In this paper, we introduce the Hyperbolic Oscillation function (HOSC), a novel activation function with a controllable sharpness parameter. Unlike any previous activations, HOSC has been specifically designed to better capture sudden changes in the input signal, and hence sharp or acute features of the underlying data, as well as smooth low-frequency transitions. Due to its simplicity and modularity, HOSC offers a plug-and-play functionality that can be easily incorporated into any existing method employing a neural network as a way of implicitly representing a signal. We benchmark HOSC against other popular activations in an array of general tasks, empirically showing an improvement in the quality of obtained representations, provide the mathematical motivation behind the efficacy of HOSC, and discuss its limitations.