# FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representation

arXiv: https://arxiv.org/abs/2407.19434 · HTML: https://mlsanity.com/paper/2407.19434/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 51 references that are in the map.
- First posted on arXiv 28 Jul 2024.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [ObjectFolder 2.0: A Multisensory Object Dataset for Sim2Real Transfer](https://mlsanity.com/paper/2204.02389/) (2022)
- [Seeing Implicit Neural Representations as Fourier Series](https://mlsanity.com/paper/2109.00249/) (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)
- [ParticleNeRF: A Particle-Based Encoding for Online Neural Radiance Fields](https://mlsanity.com/paper/2211.04041/) (2022)
- [Disorder-invariant Implicit Neural Representation](https://mlsanity.com/paper/2304.00837/) (2023)

## Built on by (most cited first, 11 of 11)

- [Inductive Gradient Adjustment For Spectral Bias In Implicit Neural Representations](https://mlsanity.com/paper/2410.13271/) (2024)
- [F-INR: Functional Tensor Decomposition for Implicit Neural Representations](https://mlsanity.com/paper/2503.21507/) (2025)
- [Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential](https://mlsanity.com/paper/2502.18959/) (2025)
- [WIPES: Wavelet-based Visual Primitives](https://mlsanity.com/paper/2508.12615/) (2025)
- [Spectral Bottleneck in Sinusoidal Representation Networks: Noise is All You Need](https://mlsanity.com/paper/2509.09719/) (2025)
- [Improving Accuracy and Efficiency of Implicit Neural Representations: Making SIREN a WINNER](https://mlsanity.com/paper/2509.12980/) (2025)
- [Blockwise Stabilized Adaptive Cubic Regularization with Subsolvers via Recurrence](https://mlsanity.com/paper/2608.22129/) (2026)
- [HOSC: A Periodic Activation with Saturation Control for High-Fidelity Implicit Neural Representations](https://mlsanity.com/paper/2601.07870/) (2026)
- [ASTRA: Asynchronous Spatio-Temporal Reconstruction via Trajectory Alignment](https://mlsanity.com/paper/2608.02006/) (2026)
- [Learning Spatial-Spectral Refinement and Calibrating Complementary Observations for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2609.05303/) (2026)
- [Learnable Spectral Activations](https://mlsanity.com/paper/2610.07419/) (2026)

## 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 the "frequency"-specified spectral bias and capacity-convergence gap, resulting in imperfect performance when representing complex signals with multiple "frequencies". We have identified that both of these two characteristics could be handled by increasing the utilization of definition domain in current activation functions, for which we propose the FINER++ framework by extending existing periodic/non-periodic activation functions to variable-periodic ones. By initializing the bias of the neural network with different ranges, sub-functions with various frequencies in the variable-periodic function are selected for activation. Consequently, the supported frequency set can be flexibly tuned, leading to improved performance in signal representation. We demonstrate the generalization and capabilities of FINER++ with different activation function backbones (Sine, Gauss. and Wavelet) and various tasks (2D image fitting, 3D signed distance field representation, 5D neural radiance fields optimization and streamable INR transmission), and we show that it improves existing INRs. Project page: {https://liuzhen0212.github.io/finerpp/}