Improved Implicit Neural Representation with Fourier Reparameterized Training
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Abstract (arXiv)
Implicit Neural Representation (INR) as a mighty representation paradigm has achieved success in various computer vision tasks recently. Due to the low-frequency bias issue of vanilla multi-layer perceptron (MLP), existing methods have investigated advanced techniques, such as positional encoding and periodic activation function, to improve the accuracy of INR. In this paper, we connect the network training bias with the reparameterization technique and theoretically prove that weight reparameterization could provide us a chance to alleviate the spectral bias of MLP. Based on our theoretical analysis, we propose a Fourier reparameterization method which learns coefficient matrix of fixed Fourier bases to compose the weights of MLP. We evaluate the proposed Fourier reparameterization method on different INR tasks with various MLP architectures, including vanilla MLP, MLP with positional encoding and MLP with advanced activation function, etc. The superiority approximation results on different MLP architectures clearly validate the advantage of our proposed method. Armed with our Fourier reparameterization method, better INR with more textures and less artifacts can be learned from the training data.
Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). Builds on 37 of its 49 references that are in the map. First posted on arXiv 15 Jan 2024.
Builds on
37 of 49 references.
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Citing papers per year: 2024: 5; 2025: 17; 2026: 14.
36 papers.
Sort:
- 2024Where Do We Stand with Implicit Neural Representations? A Technical and Performance Surveycited by 41
- 2025Do We Always Need the Simplicity Bias? Looking for Optimal Inductive Biases in the Wildcited by 13
- 2024Inductive Gradient Adjustment For Spectral Bias In Implicit Neural Representationscited by 8
- 2024Implicit Neural Representations with Fourier Kolmogorov-Arnold Networkscited by 4
- 2025Continuous Representation Methods, Theories, and Applications: An Overview and Perspectivescited by 4
- 2025PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modelingcited by 4
- 2025SASNet: Spatially-Adaptive Sinusoidal Networks for INRscited by 3
- 2025MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representationcited by 2
- 2025LIFT: Latent Implicit Functions for Task- and Data-Agnostic Encodingcited by 2
- 2025Exploring Kernel Transformations for Implicit Neural Representationscited by 2
- 2025Cross-Frequency Implicit Neural Representation with Self-Evolving Parameterscited by 2
- 2025Fourier-Modulated Implicit Neural Representation for Multispectral Satellite Image Compressioncited by 2
24 more
- 2025Learning Pixel-adaptive Multi-layer Perceptrons for Real-time Image Enhancementcited by 2
- 2025Spectral Bottleneck in Sinusoidal Representation Networks: Noise is All You Needcited by 2
- 2025FM-SIREN & FM-FINER: Implicit Neural Representation Using Nyquist-based Orthogonalitycited by 2
- 2026Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Datacited by 2
- 2024SeCo-INR: Semantically Conditioned Implicit Neural Representations for Improved Medical Image Super-Resolutioncited by 1
- 2025QFGN: A Quantum Approach to High-Fidelity Implicit Neural Representationscited by 1
- 2025COSMO-INR: Complex Sinusoidal Modulation for Implicit Neural Representationscited by 1
- 2026Neu-PiG: Neural Preconditioned Grids for Fast Dynamic Surface Reconstruction on Long Sequencescited by 1
- 2026Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recoverycited by 1
- 2026Implicit Neural Representations: A Signal Processing Perspectivecited by 1
- 2024SL2A-INR: Single-Layer Learnable Activation for Implicit Neural Representationcited by 0
- 2025LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEscited by 0
- 2025FLAIR: Frequency- and Locality-Aware Implicit Neural Representationscited by 0
- 2025Adaptive Training of INRs via Pruning and Densificationcited by 0
- 2026Neural Operator-Grounded Continuous Tensor Function Representation and Its Applicationscited by 0
- 2026Coordinate Encoding on Linear Grids for Physics-Informed Neural Networkscited by 0
- 2026Neural Fields for NV-Center Inverse Sensingcited by 0
- 2026ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representationcited by 0
- 2026Jacobi-Anger Method for Deterministic Initialization in Implicit Neural Representationcited by 0
- 2026FiRe: Frequency Reparameterization as a Preconditioner for Periodic Implicit Neural Representationscited by 0
- 2026Coarse-to-fine Framework for Generative MEF via Implicit Neural Representationcited by 0
- 2026See the Change, Keep the Flow: Unsupervised Action Segmentation via Spectral-Temporal Representation Learningcited by 0
- 2026CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fittingcited by 0
- 2026Hierarchical Frequency-Domain Compression of Implicit Geometric Representations for Large-Scale Point Cloudscited by 0
- 2026Hierarchical Frequency-Domain Compression of Implicit Geometric Representations for Large-Scale Point Clouds26 Sep 2026
- 2026CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fitting16 Sep 2026
- 2026See the Change, Keep the Flow: Unsupervised Action Segmentation via Spectral-Temporal Representation Learning30 Aug 2026
- 2026Coarse-to-fine Framework for Generative MEF via Implicit Neural Representation20 Jul 2026
- 2026FiRe: Frequency Reparameterization as a Preconditioner for Periodic Implicit Neural Representations28 Jun 2026
- 2026Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Data25 Jun 2026
- 2026Jacobi-Anger Method for Deterministic Initialization in Implicit Neural Representation4 Jun 2026
- 2026ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation21 May 2026
- 2026Neural Fields for NV-Center Inverse Sensing13 May 2026
- 2026Implicit Neural Representations: A Signal Processing Perspective16 Apr 2026
- 2026Coordinate Encoding on Linear Grids for Physics-Informed Neural Networks24 Mar 2026
- 2026Neural Operator-Grounded Continuous Tensor Function Representation and Its Applications2 Mar 2026
24 more
- 2026Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery1 Mar 2026
- 2026Neu-PiG: Neural Preconditioned Grids for Fast Dynamic Surface Reconstruction on Long Sequences25 Feb 2026
- 2025Adaptive Training of INRs via Pruning and Densification27 Oct 2025
- 2025FM-SIREN & FM-FINER: Implicit Neural Representation Using Nyquist-based Orthogonality27 Sep 2025
- 2025Spectral Bottleneck in Sinusoidal Representation Networks: Noise is All You Need9 Sep 2025
- 2025FLAIR: Frequency- and Locality-Aware Implicit Neural Representations19 Aug 2025
- 2025Learning Pixel-adaptive Multi-layer Perceptrons for Real-time Image Enhancement16 Jul 2025
- 2025LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs21 Jun 2025
- 2025PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling15 Jun 2025
- 2025Fourier-Modulated Implicit Neural Representation for Multispectral Satellite Image Compression2 Jun 2025
- 2025Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives21 May 2025
- 2025COSMO-INR: Complex Sinusoidal Modulation for Implicit Neural Representations16 May 2025
- 2025QFGN: A Quantum Approach to High-Fidelity Implicit Neural Representations26 Apr 2025
- 2025Cross-Frequency Implicit Neural Representation with Self-Evolving Parameters15 Apr 2025
- 2025Exploring Kernel Transformations for Implicit Neural Representations7 Apr 2025
- 2025LIFT: Latent Implicit Functions for Task- and Data-Agnostic Encoding19 Mar 2025
- 2025Do We Always Need the Simplicity Bias? Looking for Optimal Inductive Biases in the Wild13 Mar 2025
- 2025MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representation13 Mar 2025
- 2025SASNet: Spatially-Adaptive Sinusoidal Networks for INRs12 Mar 2025
- 2024Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey6 Nov 2024
- 2024Inductive Gradient Adjustment For Spectral Bias In Implicit Neural Representations17 Oct 2024
- 2024SL2A-INR: Single-Layer Learnable Activation for Implicit Neural Representation17 Sep 2024
- 2024Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks14 Sep 2024
- 2024SeCo-INR: Semantically Conditioned Implicit Neural Representations for Improved Medical Image Super-Resolution2 Sep 2024
- 2024Where Do We Stand with Implicit Neural Representations? A Technical and Performance Surveycited by 41
- 2025Do We Always Need the Simplicity Bias? Looking for Optimal Inductive Biases in the Wildcited by 13
- 2024Inductive Gradient Adjustment For Spectral Bias In Implicit Neural Representationscited by 8
- 2024Implicit Neural Representations with Fourier Kolmogorov-Arnold Networkscited by 4
- 2025Continuous Representation Methods, Theories, and Applications: An Overview and Perspectivescited by 4
- 2025PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modelingcited by 4
- 2025SASNet: Spatially-Adaptive Sinusoidal Networks for INRscited by 3
- 2025MetricGrids: Arbitrary Nonlinear Approximation with Elementary Metric Grids based Implicit Neural Representationcited by 2
- 2025LIFT: Latent Implicit Functions for Task- and Data-Agnostic Encodingcited by 2
- 2025Exploring Kernel Transformations for Implicit Neural Representationscited by 2
- 2025Cross-Frequency Implicit Neural Representation with Self-Evolving Parameterscited by 2
- 2025Fourier-Modulated Implicit Neural Representation for Multispectral Satellite Image Compressioncited by 2
12 most cited of 36 All 36 (JSON)
- 2026Hierarchical Frequency-Domain Compression of Implicit Geometric Representations for Large-Scale Point Clouds26 Sep 2026
- 2026CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fitting16 Sep 2026
- 2026See the Change, Keep the Flow: Unsupervised Action Segmentation via Spectral-Temporal Representation Learning30 Aug 2026
- 2026Coarse-to-fine Framework for Generative MEF via Implicit Neural Representation20 Jul 2026
- 2026FiRe: Frequency Reparameterization as a Preconditioner for Periodic Implicit Neural Representations28 Jun 2026
- 2026Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Data25 Jun 2026
- 2026Jacobi-Anger Method for Deterministic Initialization in Implicit Neural Representation4 Jun 2026
- 2026ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation21 May 2026
- 2026Neural Fields for NV-Center Inverse Sensing13 May 2026
- 2026Implicit Neural Representations: A Signal Processing Perspective16 Apr 2026
- 2026Coordinate Encoding on Linear Grids for Physics-Informed Neural Networks24 Mar 2026
- 2026Neural Operator-Grounded Continuous Tensor Function Representation and Its Applications2 Mar 2026
12 newest of 36 All 36 (JSON)