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INR-Bench: A Unified Benchmark for Implicit Neural Representations in Multi-Domain Regression and Reconstruction

Linfei Li, Fengyi Zhang, Zhong Wang, Lin Zhang, Ying Shen

TL;DR

This work analyzes how architectural choices (MLP vs. KAN), positional encoding, and nonlinear primitives shape the frequency behavior of implicit neural representations through Neural Tangent Kernel theory. It introduces INR-Bench, the first unified benchmark for multimodal INR tasks, evaluating 56 Coordinate-MLP variants and 22 Coordinate-KAN variants across 9 forward and inverse tasks, with public code. Key findings show that KANs exhibit weaker low-frequency spectral bias but higher training complexity, while a fully learnable FKAN positional encoding improves convergence and generalization for non-periodic activations; forward tasks benefit from NeRF/RFF encodings in some cases, whereas complex radiance fields may favor fixed encodings. Overall, Coordinate-MLPs generally provide robust performance and faster training, but carefully chosen bases and encodings (notably FKAN) can unlock substantial gains in high-frequency learning and inverse reasoning, guiding future INR design for multimodal applications.

Abstract

Implicit Neural Representations (INRs) have gained success in various signal processing tasks due to their advantages of continuity and infinite resolution. However, the factors influencing their effectiveness and limitations remain underexplored. To better understand these factors, we leverage insights from Neural Tangent Kernel (NTK) theory to analyze how model architectures (classic MLP and emerging KAN), positional encoding, and nonlinear primitives affect the response to signals of varying frequencies. Building on this analysis, we introduce INR-Bench, the first comprehensive benchmark specifically designed for multimodal INR tasks. It includes 56 variants of Coordinate-MLP models (featuring 4 types of positional encoding and 14 activation functions) and 22 Coordinate-KAN models with distinct basis functions, evaluated across 9 implicit multimodal tasks. These tasks cover both forward and inverse problems, offering a robust platform to highlight the strengths and limitations of different neural models, thereby establishing a solid foundation for future research. The code and dataset are available at https://github.com/lif314/INR-Bench.

INR-Bench: A Unified Benchmark for Implicit Neural Representations in Multi-Domain Regression and Reconstruction

TL;DR

This work analyzes how architectural choices (MLP vs. KAN), positional encoding, and nonlinear primitives shape the frequency behavior of implicit neural representations through Neural Tangent Kernel theory. It introduces INR-Bench, the first unified benchmark for multimodal INR tasks, evaluating 56 Coordinate-MLP variants and 22 Coordinate-KAN variants across 9 forward and inverse tasks, with public code. Key findings show that KANs exhibit weaker low-frequency spectral bias but higher training complexity, while a fully learnable FKAN positional encoding improves convergence and generalization for non-periodic activations; forward tasks benefit from NeRF/RFF encodings in some cases, whereas complex radiance fields may favor fixed encodings. Overall, Coordinate-MLPs generally provide robust performance and faster training, but carefully chosen bases and encodings (notably FKAN) can unlock substantial gains in high-frequency learning and inverse reasoning, guiding future INR design for multimodal applications.

Abstract

Implicit Neural Representations (INRs) have gained success in various signal processing tasks due to their advantages of continuity and infinite resolution. However, the factors influencing their effectiveness and limitations remain underexplored. To better understand these factors, we leverage insights from Neural Tangent Kernel (NTK) theory to analyze how model architectures (classic MLP and emerging KAN), positional encoding, and nonlinear primitives affect the response to signals of varying frequencies. Building on this analysis, we introduce INR-Bench, the first comprehensive benchmark specifically designed for multimodal INR tasks. It includes 56 variants of Coordinate-MLP models (featuring 4 types of positional encoding and 14 activation functions) and 22 Coordinate-KAN models with distinct basis functions, evaluated across 9 implicit multimodal tasks. These tasks cover both forward and inverse problems, offering a robust platform to highlight the strengths and limitations of different neural models, thereby establishing a solid foundation for future research. The code and dataset are available at https://github.com/lif314/INR-Bench.

Paper Structure

This paper contains 33 sections, 2 theorems, 167 equations, 18 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. INR-Bench
  4. Coordinate Models
  5. Positional Encoding
  6. Nonlinear Primitives
  7. Experiments
  8. INR Models for Benchmarking
  9. INR Tasks for Benchmarking
  10. Signal Representation
  11. Inverse Problems
  12. Benchmark Leaderboard and Insights
  13. Conclusion
  14. Coordinate-KANs
  15. 22 Basis Functions of Coordinate-KANs
  16. ...and 18 more sections

Key Result

Corollary 3.1

Spectral Bias of INR Models. During training, each component of the training error $| \mathbf{e}_{\text{train}}|_i$ decays exponentially, with the decay rate determined by the NTK eigenvalues $\lambda_i$ and learning rate $\eta$,

Figures (18)

  • Figure 1: The network of vanilla NeRF. The image is sourced from mildenhall2020nerf.
  • Figure 2: The network of NGP. The image is sourced from muller2022ngp.
  • Figure 4: Various normalization techniques (image source: cai2024towards).
  • Figure 5: Qualitative experimental results related to image representation tasks.
  • Figure 6: Qualitative experimental results related to image representation tasks.
  • ...and 13 more figures

Theorems & Definitions (2)

  • Corollary 3.1
  • Theorem A.1