# Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations

arXiv: https://arxiv.org/abs/2604.02846 · HTML: https://mlsanity.com/paper/2604.02846/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 28 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 19 of 19)

- [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)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [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)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [ACORN: Adaptive Coordinate Networks for Neural Scene Representation](https://mlsanity.com/paper/2105.02788/) (2021)
- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [NeuLF: Efficient Novel View Synthesis with Neural 4D Light Field](https://mlsanity.com/paper/2105.07112/) (2021)
- [Neural Fourier Filter Bank](https://mlsanity.com/paper/2212.01735/) (2022)
- [Disorder-invariant Implicit Neural Representation](https://mlsanity.com/paper/2304.00837/) (2023)
- [A Sampling Theory Perspective on Activations for Implicit Neural Representations](https://mlsanity.com/paper/2402.05427/) (2024)
- [Polynomial Implicit Neural Representations For Large Diverse Datasets](https://mlsanity.com/paper/2303.11424/) (2023)
- [HOSC: A Periodic Activation Function for Preserving Sharp Features in Implicit Neural Representations](https://mlsanity.com/paper/2401.10967/) (2024)

## Abstract (arXiv)

Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial domain, making them poorly suited to signals with spatially varying local spectra and often leading to slow convergence of high-frequency details. To address this issue, we propose an adaptive local frequency filtering method for Fourier-encoded INRs. The proposed method introduces a spatially varying parameter α(x) to modulate encoded Fourier components, enabling a smooth transition among low-pass, band-pass, and high-pass behaviors at different spatial locations. We further analyze the effect of the proposed filter from the neural tangent kernel (NTK) perspective and provide an NTK-inspired interpretation of how it reshapes the effective kernel spectrum. Experiments on 2D image fitting, 3D shape representation, and sparse data reconstruction demonstrate that the proposed method consistently improves reconstruction quality and leads to faster optimization compared with fixed-frequency baselines. In addition, the learned α(x) provides an intuitive visualization of spatially varying frequency preferences, which helps explain the behavior of the model on non-stationary signals. These results indicate that adaptive local frequency modulation is a practical enhancement for Fourier-encoded INRs.