mlsanityData to 7 Oct 2026

A Sampling Theory Perspective on Activations for Implicit Neural Representations

arXiv 2402.05427 ↗First posted 8 Feb 2024cs.LGcited by 23

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Abstract (arXiv)

Implicit Neural Representations (INRs) have gained popularity for encoding signals as compact, differentiable entities. While commonly using techniques like Fourier positional encodings or non-traditional activation functions (e.g., Gaussian, sinusoid, or wavelets) to capture high-frequency content, their properties lack exploration within a unified theoretical framework. Addressing this gap, we conduct a comprehensive analysis of these activations from a sampling theory perspective. Our investigation reveals that sinc activations, previously unused in conjunction with INRs, are theoretically optimal for signal encoding. Additionally, we establish a connection between dynamical systems and INRs, leveraging sampling theory to bridge these two paradigms.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 12 of its 49 references that are in the map. First posted on arXiv 8 Feb 2024.

Builds on

12 of 49 references.

References · 12

  1. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  2. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  3. 2018On the Spectral Bias of Neural Networkscited by 1,321
  4. 2020Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humanscited by 634
  5. 2022DynIBaR: Neural Dynamic Image-Based Renderingcited by 224
  6. 2023WIRE: Wavelet Implicit Neural Representationscited by 220
  7. 2021Implicit Neural Representations for Image Compressioncited by 161
  8. 2021Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPscited by 134
  9. 2022Trading Positional Complexity vs. Deepness in Coordinate Networkscited by 16
  10. 2023FlowIBR: Leveraging Pre-Training for Efficient Neural Image-Based Rendering of Dynamic Scenescited by 14
  11. 2023Curvature-Aware Training for Coordinate Networkscited by 8
  12. 2021Learning Positional Embeddings for Coordinate-MLPscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 7; 2025: 12; 2026: 4.

23 papers.

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  1. 2024Where Do We Stand with Implicit Neural Representations? A Technical and Performance Surveycited by 41
  2. 2024Tuning the Frequencies: Robust Training for Sinusoidal Neural Networkscited by 18
  3. 2024Fast Training of Sinusoidal Neural Fields via Scaling Initializationcited by 11
  4. 2024Neural Experts: Mixture of Experts for Implicit Neural Representationscited by 9
  5. 2024Preconditioners for the Stochastic Training of Neural Fieldscited by 5
  6. 2024H-SIREN: Improving implicit neural representations with hyperbolic periodic functionscited by 5
  7. 2025DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functionscited by 4
  8. 2024Model-based learning for multi-antenna multi-frequency location-to-channel mappingcited by 3
  9. 2025SASNet: Spatially-Adaptive Sinusoidal Networks for INRscited by 3
  10. 2025Enhancing Transformers Through Conditioned Embedded Tokenscited by 3
  11. 2025Spectral Bottleneck in Sinusoidal Representation Networks: Noise is All You Needcited by 2
  12. 2026Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Taskscited by 2
11 more
  1. 2025VI3NR: Variance Informed Initialization for Implicit Neural Representationscited by 1
  2. 2025COSMO-INR: Complex Sinusoidal Modulation for Implicit Neural Representationscited by 1
  3. 2025Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systemscited by 1
  4. 2025TabINR: An Implicit Neural Representation Framework for Tabular Data Imputationcited by 1
  5. 2025From Tables to Signals: Revealing Spectral Adaptivity in TabPFNcited by 1
  6. 2026Implicit Neural Representations: A Signal Processing Perspectivecited by 1
  7. 2025FLAIR: Frequency- and Locality-Aware Implicit Neural Representationscited by 0
  8. 2025QuadINR: Hardware-Efficient Implicit Neural Representations Through Quadratic Activationcited by 0
  9. 2025Adaptive Training of INRs via Pruning and Densificationcited by 0
  10. 2026HOSC: A Periodic Activation with Saturation Control for High-Fidelity Implicit Neural Representationscited by 0
  11. 2026Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representationscited by 0