# Learning Spatially Collaged Fourier Bases for Implicit Neural Representation

arXiv: https://arxiv.org/abs/2312.17018 · HTML: https://mlsanity.com/paper/2312.17018/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 15 references that are in the map.
- First posted on arXiv 28 Dec 2023.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [Residual Multiplicative Filter Networks for Multiscale Reconstruction](https://mlsanity.com/paper/2206.00746/) (2022)

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

- [Nonparametric Teaching of Implicit Neural Representations](https://mlsanity.com/paper/2405.10531/) (2024)
- [ASMR: Activation-sharing Multi-resolution Coordinate Networks For Efficient Inference](https://mlsanity.com/paper/2405.12398/) (2024)
- [H-SIREN: Improving implicit neural representations with hyperbolic periodic functions](https://mlsanity.com/paper/2410.04716/) (2024)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representation](https://mlsanity.com/paper/2503.10000/) (2025)
- [NTK-Guided Implicit Neural Teaching](https://mlsanity.com/paper/2511.15487/) (2025)
- [MINR: Efficient Implicit Neural Representations for Multi-Image Encoding](https://mlsanity.com/paper/2508.13471/) (2025)
- [High-Frequency First: A Two-Stage Approach for Improving Image INR](https://mlsanity.com/paper/2508.15582/) (2025)
- [Content-Aware Frequency Encoding for Implicit Neural Representations with Fourier-Chebyshev Features](https://mlsanity.com/paper/2603.01028/) (2026)
- [PatchINR: Patch-Based Implicit Neural Representations for Efficient and Scalable Inference](https://mlsanity.com/paper/2606.25534/) (2026)
- [CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fitting](https://mlsanity.com/paper/2609.18554/) (2026)

## Abstract (arXiv)

Existing approaches to Implicit Neural Representation (INR) can be interpreted as a global scene representation via a linear combination of Fourier bases of different frequencies. However, such universal basis functions can limit the representation capability in local regions where a specific component is unnecessary, resulting in unpleasant artifacts. To this end, we introduce a learnable spatial mask that effectively dispatches distinct Fourier bases into respective regions. This translates into collaging Fourier patches, thus enabling an accurate representation of complex signals. Comprehensive experiments demonstrate the superior reconstruction quality of the proposed approach over existing baselines across various INR tasks, including image fitting, video representation, and 3D shape representation. Our method outperforms all other baselines, improving the image fitting PSNR by over 3dB and 3D reconstruction to 98.81 IoU and 0.0011 Chamfer Distance.