# Regularize implicit neural representation by itself

arXiv: https://arxiv.org/abs/2303.15484 · HTML: https://mlsanity.com/paper/2303.15484/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 39 references that are in the map.
- First posted on arXiv 27 Mar 2023.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [Towards Understanding the Spectral Bias of Deep Learning](https://mlsanity.com/paper/1912.01198/) (2019)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Implicit Regularization for Optimal Sparse Recovery](https://mlsanity.com/paper/1909.05122/) (2019)
- [Image Restoration using Total Variation Regularized Deep Image Prior](https://mlsanity.com/paper/1810.12864/) (2018)
- [Implicit Neural Video Compression](https://mlsanity.com/paper/2112.11312/) (2021)
- [Theory of the Frequency Principle for General Deep Neural Networks](https://mlsanity.com/paper/1906.09235/) (2019)
- [Neural Tangent Kernel: A Survey](https://mlsanity.com/paper/2208.13614/) (2022)
- [A Multi-Implicit Neural Representation for Fonts](https://mlsanity.com/paper/2106.06866/) (2021)
- [SqueezeNeRF: Further factorized FastNeRF for memory-efficient inference](https://mlsanity.com/paper/2204.02585/) (2022)
- [CURE: Curvature Regularization For Missing Data Recovery](https://mlsanity.com/paper/1901.09548/) (2019)
- [A regularized deep matrix factorized model of matrix completion for image restoration](https://mlsanity.com/paper/2007.14581/) (2020)
- [Adaptive and Implicit Regularization for Matrix Completion](https://mlsanity.com/paper/2208.05640/) (2022)

## Built on by (most cited first, 13 of 13)

- [Boosting Neural Representations for Videos with a Conditional Decoder](https://mlsanity.com/paper/2402.18152/) (2024)
- [Nonparametric Teaching of Implicit Neural Representations](https://mlsanity.com/paper/2405.10531/) (2024)
- [RHINO: Regularizing the Hash-based Implicit Neural Representation](https://mlsanity.com/paper/2309.12642/) (2023)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Multiplane Prior Guided Few-Shot Aerial Scene Rendering](https://mlsanity.com/paper/2406.04961/) (2024)
- [Cross-Frequency Implicit Neural Representation with Self-Evolving Parameters](https://mlsanity.com/paper/2504.10929/) (2025)
- [NTK-Guided Implicit Neural Teaching](https://mlsanity.com/paper/2511.15487/) (2025)
- [SpikeMM: Flexi-Magnification of High-Speed Micro-Motions](https://mlsanity.com/paper/2406.00383/) (2024)
- [FANeRV: Frequency Separation and Augmentation based Neural Representation for Video](https://mlsanity.com/paper/2504.06755/) (2025)
- [Enhancing Robustness of Implicit Neural Representations Against Weight Perturbations](https://mlsanity.com/paper/2508.13481/) (2025)
- [Implicit Neural Representations: A Signal Processing Perspective](https://mlsanity.com/paper/2604.15047/) (2026)
- [Long-Term Prediction Accuracy Improvement of Data-Driven Medium-Range Global Weather Forecast](https://mlsanity.com/paper/2407.01598/) (2024)
- [Dynamical Implicit Neural Representations](https://mlsanity.com/paper/2511.21787/) (2025)

## Abstract (arXiv)

This paper proposes a regularizer called Implicit Neural Representation Regularizer (INRR) to improve the generalization ability of the Implicit Neural Representation (INR). The INR is a fully connected network that can represent signals with details not restricted by grid resolution. However, its generalization ability could be improved, especially with non-uniformly sampled data. The proposed INRR is based on learned Dirichlet Energy (DE) that measures similarities between rows/columns of the matrix. The smoothness of the Laplacian matrix is further integrated by parameterizing DE with a tiny INR. INRR improves the generalization of INR in signal representation by perfectly integrating the signal's self-similarity with the smoothness of the Laplacian matrix. Through well-designed numerical experiments, the paper also reveals a series of properties derived from INRR, including momentum methods like convergence trajectory and multi-scale similarity. Moreover, the proposed method could improve the performance of other signal representation methods.