# Cross-Frequency Implicit Neural Representation with Self-Evolving Parameters

arXiv: https://arxiv.org/abs/2504.10929 · HTML: https://mlsanity.com/paper/2504.10929/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 52 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 30 of 37)

- [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)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [State of the Art on Neural Rendering](https://mlsanity.com/paper/2004.03805/) (2020)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Adversarial Generation of Continuous Images](https://mlsanity.com/paper/2011.12026/) (2020)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Wavelet Convolutions for Large Receptive Fields](https://mlsanity.com/paper/2407.05848/) (2024)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [Implicit Neural Spatial Representations for Time-dependent PDEs](https://mlsanity.com/paper/2210.00124/) (2022)
- [Self-Supervised Arbitrary-Scale Point Clouds Upsampling via Implicit Neural Representation](https://mlsanity.com/paper/2204.08196/) (2022)
- [Efficient Multi-scale Network with Learnable Discrete Wavelet Transform for Blind Motion Deblurring](https://mlsanity.com/paper/2401.00027/) (2023)

## Built on by (most cited first, 3 of 3)

- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Multi-resolution Enhancement for Full Spectrum Neural Representations](https://mlsanity.com/paper/2509.15494/) (2025)
- [S3-PnP: Plug-and-Play Denoising for Scientific Imaging with Self-Supervised Score Priors](https://mlsanity.com/paper/2610.18458/) (2026)

## Abstract (arXiv)

Implicit neural representation (INR) has emerged as a powerful paradigm for visual data representation. However, classical INR methods represent data in the original space mixed with different frequency components, and several feature encoding parameters (e.g., the frequency parameter ω or the rank R) need manual configurations. In this work, we propose a self-evolving cross-frequency INR using the Haar wavelet transform (termed CF-INR), which decouples data into four frequency components and employs INRs in the wavelet space. CF-INR allows the characterization of different frequency components separately, thus enabling higher accuracy for data representation. To more precisely characterize cross-frequency components, we propose a cross-frequency tensor decomposition paradigm for CF-INR with self-evolving parameters, which automatically updates the rank parameter R and the frequency parameter ω for each frequency component through self-evolving optimization. This self-evolution paradigm eliminates the laborious manual tuning of these parameters, and learns a customized cross-frequency feature encoding configuration for each dataset. We evaluate CF-INR on a variety of visual data representation and recovery tasks, including image regression, inpainting, denoising, and cloud removal. Extensive experiments demonstrate that CF-INR outperforms state-of-the-art methods in each case.