# Disorder-invariant Implicit Neural Representation

arXiv: https://arxiv.org/abs/2304.00837 · HTML: https://mlsanity.com/paper/2304.00837/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 60 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 30 of 34)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [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)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (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)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [On the Inductive Bias of Neural Tangent Kernels](https://mlsanity.com/paper/1905.12173/) (2019)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [The Convergence Rate of Neural Networks for Learned Functions of Different Frequencies](https://mlsanity.com/paper/1906.00425/) (2019)
- [Neural Lumigraph Rendering](https://mlsanity.com/paper/2103.11571/) (2021)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [ReLU Fields: The Little Non-linearity That Could](https://mlsanity.com/paper/2205.10824/) (2022)
- [E-NeRV: Expedite Neural Video Representation with Disentangled Spatial-Temporal Context](https://mlsanity.com/paper/2207.08132/) (2022)
- [ObjectFolder 2.0: A Multisensory Object Dataset for Sim2Real Transfer](https://mlsanity.com/paper/2204.02389/) (2022)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation](https://mlsanity.com/paper/2005.03991/) (2020)
- [DINER: Disorder-Invariant Implicit Neural Representation](https://mlsanity.com/paper/2211.07871/) (2022)
- [Scalable Neural Video Representations with Learnable Positional Features](https://mlsanity.com/paper/2210.06823/) (2022)
- [Polynomial Neural Fields for Subband Decomposition and Manipulation](https://mlsanity.com/paper/2302.04862/) (2023)

## Built on by (most cited first, 27 of 27)

- [Nonparametric Teaching of Implicit Neural Representations](https://mlsanity.com/paper/2405.10531/) (2024)
- [From Chaos to Clarity: 3DGS in the Dark](https://mlsanity.com/paper/2406.08300/) (2024)
- [FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representation](https://mlsanity.com/paper/2407.19434/) (2024)
- [RHINO: Regularizing the Hash-based Implicit Neural Representation](https://mlsanity.com/paper/2309.12642/) (2023)
- [Inductive Gradient Adjustment For Spectral Bias In Implicit Neural Representations](https://mlsanity.com/paper/2410.13271/) (2024)
- [Optimizing Rank for High-Fidelity Implicit Neural Representations](https://mlsanity.com/paper/2512.14366/) (2025)
- [Continuous 3D Myocardial Motion Tracking via Echocardiography](https://mlsanity.com/paper/2310.02792/) (2023)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Towards the Spectral bias Alleviation by Normalizations in Coordinate Networks](https://mlsanity.com/paper/2407.17834/) (2024)
- [Predicting the Encoding Error of SIRENs](https://mlsanity.com/paper/2410.21645/) (2024)
- [V2V3D: View-to-View Denoised 3D Reconstruction for Light-Field Microscopy](https://mlsanity.com/paper/2504.07853/) (2025)
- [WIPES: Wavelet-based Visual Primitives](https://mlsanity.com/paper/2508.12615/) (2025)
- [Spectral Bottleneck in Sinusoidal Representation Networks: Noise is All You Need](https://mlsanity.com/paper/2509.09719/) (2025)
- [Knowledge Distillation for Continual Learning of Biomedical Neural Fields](https://mlsanity.com/paper/2511.21409/) (2025)
- [Neural Poisson Solver: A Universal and Continuous Framework for Natural Signal Blending](https://mlsanity.com/paper/2407.08457/) (2024)
- [PNR: Physics-informed Neural Representation for high-resolution LFM reconstruction](https://mlsanity.com/paper/2409.18223/) (2024)
- [Self-supervised Deep Unrolled Model with Implicit Neural Representation Regularization for Accelerating MRI Reconstruction](https://mlsanity.com/paper/2510.06611/) (2025)
- [Content-Aware Frequency Encoding for Implicit Neural Representations with Fourier-Chebyshev Features](https://mlsanity.com/paper/2603.01028/) (2026)
- [SL2A-INR: Single-Layer Learnable Activation for Implicit Neural Representation](https://mlsanity.com/paper/2409.10836/) (2024)
- [Rapid Whole Brain Motion-robust Mesoscale In-vivo MR Imaging using Multi-scale Implicit Neural Representation](https://mlsanity.com/paper/2502.08634/) (2025)
- [QuadINR: Hardware-Efficient Implicit Neural Representations Through Quadratic Activation](https://mlsanity.com/paper/2508.14374/) (2025)
- [The Inlet Rank Collapse in Implicit Neural Representations: Diagnosis and Unified Remedy](https://mlsanity.com/paper/2602.01526/) (2026)
- [Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations](https://mlsanity.com/paper/2604.02846/) (2026)
- [Frequency-Decomposed INR for NIR-Assisted Low-Light RGB Image Denoising](https://mlsanity.com/paper/2604.16800/) (2026)
- [Three-Step Conditional Diffusion 3D Reconstruction for Light-Field Microscopy](https://mlsanity.com/paper/2605.24959/) (2026)
- [Texture-preserving implicit neural representation for Cone beam CT truncated reconstruction](https://mlsanity.com/paper/2606.06039/) (2026)
- [ASTRA: Asynchronous Spatio-Temporal Reconstruction via Trajectory Alignment](https://mlsanity.com/paper/2608.02006/) (2026)

## Abstract (arXiv)

Implicit neural representation (INR) characterizes the attributes of a signal as a function of corresponding coordinates which emerges as a sharp weapon for solving inverse problems. However, the expressive power of INR is limited by the spectral bias in the network training. In this paper, we find that such a frequency-related problem could be greatly solved by re-arranging the coordinates of the input signal, for which we propose the disorder-invariant implicit neural representation (DINER) by augmenting a hash-table to a traditional INR backbone. Given discrete signals sharing the same histogram of attributes and different arrangement orders, the hash-table could project the coordinates into the same distribution for which the mapped signal can be better modeled using the subsequent INR network, leading to significantly alleviated spectral bias. Furthermore, the expressive power of the DINER is determined by the width of the hash-table. Different width corresponds to different geometrical elements in the attribute space, textite.g., 1D curve, 2D curved-plane and 3D curved-volume when the width is set as 1, 2 and 3, respectively. More covered areas of the geometrical elements result in stronger expressive power. Experiments not only reveal the generalization of the DINER for different INR backbones (MLP vs. SIREN) and various tasks (image/video representation, phase retrieval, refractive index recovery, and neural radiance field optimization) but also show the superiority over the state-of-the-art algorithms both in quality and speed. textitProject page: urlhttps://ezio77.github.io/DINER-website/