# H-SIREN: Improving implicit neural representations with hyperbolic periodic functions

arXiv: https://arxiv.org/abs/2410.04716 · HTML: https://mlsanity.com/paper/2410.04716/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 44 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 30 of 34)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Learning Spatial-Temporal Implicit Neural Representations for Event-Guided Video Super-Resolution](https://mlsanity.com/paper/2303.13767/) (2023)
- [INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddings](https://mlsanity.com/paper/2310.18846/) (2023)
- [DINER: Disorder-Invariant Implicit Neural Representation](https://mlsanity.com/paper/2211.07871/) (2022)
- [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)
- [A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations](https://mlsanity.com/paper/2212.14545/) (2022)
- [FlowIBR: Leveraging Pre-Training for Efficient Neural Image-Based Rendering of Dynamic Scenes](https://mlsanity.com/paper/2309.05418/) (2023)
- [NeuralGrasps: Learning Implicit Representations for Grasps of Multiple Robotic Hands](https://mlsanity.com/paper/2207.02959/) (2022)
- [Learning Spatially Collaged Fourier Bases for Implicit Neural Representation](https://mlsanity.com/paper/2312.17018/) (2023)

## Built on by (most cited first, 5 of 5)

- [ARC: Anchored Representation Clouds for High-Resolution INR Classification](https://mlsanity.com/paper/2503.15156/) (2025)
- [Enhancing Transformers Through Conditioned Embedded Tokens](https://mlsanity.com/paper/2505.12789/) (2025)
- [I-INR: Iterative Implicit Neural Representations](https://mlsanity.com/paper/2504.17364/) (2025)
- [Squeeze3D: Extreme Neural Compression with Latent Space Bridging](https://mlsanity.com/paper/2506.07932/) (2025)
- [The Inlet Rank Collapse in Implicit Neural Representations: Diagnosis and Unified Remedy](https://mlsanity.com/paper/2602.01526/) (2026)

## Abstract (arXiv)

Implicit neural representations (INR) have been recently adopted in various applications ranging from computer vision tasks to physics simulations by solving partial differential equations. Among existing INR-based works, multi-layer perceptrons with sinusoidal activation functions find widespread applications and are also frequently treated as a baseline for the development of better activation functions for INR applications. Recent investigations claim that the use of sinusoidal activation functions could be sub-optimal due to their limited supported frequency set as well as their tendency to generate over-smoothed solutions. We provide a simple solution to mitigate such an issue by changing the activation function at the first layer from sin(x) to sin(sinh(2x)). We demonstrate H-SIREN in various computer vision and fluid flow problems, where it surpasses the performance of several state-of-the-art INRs.