# FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions

arXiv: https://arxiv.org/abs/2312.02434 · HTML: https://mlsanity.com/paper/2312.02434/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 5 Dec 2023.

## Builds on (most cited first, 28 of 28)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [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)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Layered Neural Atlases for Consistent Video Editing](https://mlsanity.com/paper/2109.11418/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [HDR-NeRF: High Dynamic Range Neural Radiance Fields](https://mlsanity.com/paper/2111.14451/) (2021)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [GARF: Gaussian Activated Radiance Fields for High Fidelity Reconstruction and Pose Estimation](https://mlsanity.com/paper/2204.05735/) (2022)
- [ObjectFolder 2.0: A Multisensory Object Dataset for Sim2Real Transfer](https://mlsanity.com/paper/2204.02389/) (2022)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [DINER: Disorder-Invariant Implicit Neural Representation](https://mlsanity.com/paper/2211.07871/) (2022)
- [Neural Fourier Filter Bank](https://mlsanity.com/paper/2212.01735/) (2022)
- [Polynomial Implicit Neural Representations For Large Diverse Datasets](https://mlsanity.com/paper/2303.11424/) (2023)
- [Inverting the Imaging Process by Learning an Implicit Camera Model](https://mlsanity.com/paper/2304.12748/) (2023)
- [Neural Free-Viewpoint Relighting for Glossy Indirect Illumination](https://mlsanity.com/paper/2307.06335/) (2023)

## Built on by (most cited first, 30 of 78)

- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [FreSh: Frequency Shifting for Accelerated Neural Representation Learning](https://mlsanity.com/paper/2410.05050/) (2024)
- [MiraGe: Editable 2D Images using Gaussian Splatting](https://mlsanity.com/paper/2410.01521/) (2024)
- [FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representation](https://mlsanity.com/paper/2407.19434/) (2024)
- [Fast Training of Sinusoidal Neural Fields via Scaling Initialization](https://mlsanity.com/paper/2410.04779/) (2024)
- [Neural Experts: Mixture of Experts for Implicit Neural Representations](https://mlsanity.com/paper/2410.21643/) (2024)
- [EVOS: Efficient Implicit Neural Training via EVOlutionary Selector](https://mlsanity.com/paper/2412.10153/) (2024)
- [F-INR: Functional Tensor Decomposition for Implicit Neural Representations](https://mlsanity.com/paper/2503.21507/) (2025)
- [Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.09323/) (2024)
- [H-SIREN: Improving implicit neural representations with hyperbolic periodic functions](https://mlsanity.com/paper/2410.04716/) (2024)
- [Towards Lossless Implicit Neural Representation via Bit Plane Decomposition](https://mlsanity.com/paper/2502.21001/) (2025)
- [A Unified Theory of Sinusoidal Activation Families for Implicit Neural Representations](https://mlsanity.com/paper/2502.00869/) (2025)
- [Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential](https://mlsanity.com/paper/2502.18959/) (2025)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Implicit Inversion turns CLIP into a Decoder](https://mlsanity.com/paper/2505.23161/) (2025)
- [HOIN: High-Order Implicit Neural Representations](https://mlsanity.com/paper/2404.14674/) (2024)
- [Neural Video Representation for Redundancy Reduction and Consistency Preservation](https://mlsanity.com/paper/2409.18497/) (2024)
- [SASNet: Spatially-Adaptive Sinusoidal Networks for INRs](https://mlsanity.com/paper/2503.09750/) (2025)
- [Cross-Frequency Implicit Neural Representation with Self-Evolving Parameters](https://mlsanity.com/paper/2504.10929/) (2025)
- [Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Data](https://mlsanity.com/paper/2606.26763/) (2026)
- [Towards the Spectral bias Alleviation by Normalizations in Coordinate Networks](https://mlsanity.com/paper/2407.17834/) (2024)
- [MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representation](https://mlsanity.com/paper/2503.10000/) (2025)
- [LIFT: Latent Implicit Functions for Task- and Data-Agnostic Encoding](https://mlsanity.com/paper/2503.15420/) (2025)
- [Exploring Kernel Transformations for Implicit Neural Representations](https://mlsanity.com/paper/2504.04728/) (2025)
- [V2V3D: View-to-View Denoised 3D Reconstruction for Light-Field Microscopy](https://mlsanity.com/paper/2504.07853/) (2025)
- [Tree-NeRV: A Tree-Structured Neural Representation for Efficient Non-Uniform Video Encoding](https://mlsanity.com/paper/2504.12899/) (2025)
- [SR-NeRV: Improving Embedding Efficiency of Neural Video Representation via Super-Resolution](https://mlsanity.com/paper/2505.00046/) (2025)
- [VidFuncta: Towards Generalizable Neural Representations for Ultrasound Videos](https://mlsanity.com/paper/2507.21863/) (2025)
- [WIPES: Wavelet-based Visual Primitives](https://mlsanity.com/paper/2508.12615/) (2025)

## Abstract (arXiv)

Implicit Neural Representation (INR), which utilizes a neural network to map coordinate inputs to corresponding attributes, is causing a revolution in the field of signal processing. However, current INR techniques suffer from a restricted capability to tune their supported frequency set, resulting in imperfect performance when representing complex signals with multiple frequencies. We have identified that this frequency-related problem can be greatly alleviated by introducing variable-periodic activation functions, for which we propose FINER. By initializing the bias of the neural network within different ranges, sub-functions with various frequencies in the variable-periodic function are selected for activation. Consequently, the supported frequency set of FINER can be flexibly tuned, leading to improved performance in signal representation. We demonstrate the capabilities of FINER in the contexts of 2D image fitting, 3D signed distance field representation, and 5D neural radiance fields optimization, and we show that it outperforms existing INRs.