# Content-Aware Frequency Encoding for Implicit Neural Representations with Fourier-Chebyshev Features

arXiv: https://arxiv.org/abs/2603.01028 · HTML: https://mlsanity.com/paper/2603.01028/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 43 references that are in the map.
- First posted on arXiv 1 Mar 2026.

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

- [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)
- [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)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [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)
- [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)
- [CiaoSR: Continuous Implicit Attention-in-Attention Network for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2212.04362/) (2022)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [Seeing Implicit Neural Representations as Fourier Series](https://mlsanity.com/paper/2109.00249/) (2021)
- [Disorder-invariant Implicit Neural Representation](https://mlsanity.com/paper/2304.00837/) (2023)
- [PINs: Progressive Implicit Networks for Multi-Scale Neural Representations](https://mlsanity.com/paper/2202.04713/) (2022)
- [HIIF: Hierarchical Encoding based Implicit Image Function for Continuous Super-resolution](https://mlsanity.com/paper/2412.03748/) (2024)
- [HOSC: A Periodic Activation Function for Preserving Sharp Features in Implicit Neural Representations](https://mlsanity.com/paper/2401.10967/) (2024)
- [Learning Spatially Collaged Fourier Bases for Implicit Neural Representation](https://mlsanity.com/paper/2312.17018/) (2023)
- [Robustifying Fourier Features Embeddings for Implicit Neural Representations](https://mlsanity.com/paper/2502.05482/) (2025)
- [Towards Lossless Implicit Neural Representation via Bit Plane Decomposition](https://mlsanity.com/paper/2502.21001/) (2025)
- [Towards a Sampling Theory for Implicit Neural Representations](https://mlsanity.com/paper/2405.18410/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning Spatial-Spectral Refinement and Calibrating Complementary Observations for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2609.05303/) (2026)

## Abstract (arXiv)

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for various signal processing tasks, but their inherent spectral bias limits the ability to capture high-frequency details. Existing methods partially mitigate this issue by using Fourier-based features, which usually rely on fixed frequency bases. This forces multi-layer perceptrons (MLPs) to inefficiently compose the required frequencies, thereby constraining their representational capacity. To address this limitation, we propose Content-Aware Frequency Encoding (CAFE), which builds upon Fourier features through multiple parallel linear layers combined via a Hadamard product. CAFE can explicitly and efficiently synthesize a broader range of frequency bases, while the learned weights enable the selection of task-relevant frequencies. Furthermore, we extend this framework to CAFE+, which incorporates Chebyshev features as a complementary component to Fourier bases. This combination provides a stronger and more stable frequency representation. Extensive experiments across multiple benchmarks validate the effectiveness and efficiency of our approach, consistently achieving superior performance over existing methods. Our code is available at https://github.com/JunboKe0619/CAFE.