# A Sampling Theory Perspective on Activations for Implicit Neural Representations

arXiv: https://arxiv.org/abs/2402.05427 · HTML: https://mlsanity.com/paper/2402.05427/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [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)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humans](https://mlsanity.com/paper/2012.15838/) (2020)
- [DynIBaR: Neural Dynamic Image-Based Rendering](https://mlsanity.com/paper/2211.11082/) (2022)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [Trading Positional Complexity vs. Deepness in Coordinate Networks](https://mlsanity.com/paper/2205.08987/) (2022)
- [FlowIBR: Leveraging Pre-Training for Efficient Neural Image-Based Rendering of Dynamic Scenes](https://mlsanity.com/paper/2309.05418/) (2023)
- [Curvature-Aware Training for Coordinate Networks](https://mlsanity.com/paper/2305.08552/) (2023)
- [Learning Positional Embeddings for Coordinate-MLPs](https://mlsanity.com/paper/2112.11577/) (2021)

## Built on by (most cited first, 24 of 24)

- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [Fast Training of Sinusoidal Neural Fields via Scaling Initialization](https://mlsanity.com/paper/2410.04779/) (2024)
- [Neural Experts: Mixture of Experts for Implicit Neural Representations](https://mlsanity.com/paper/2410.21643/) (2024)
- [Preconditioners for the Stochastic Training of Neural Fields](https://mlsanity.com/paper/2402.08784/) (2024)
- [H-SIREN: Improving implicit neural representations with hyperbolic periodic functions](https://mlsanity.com/paper/2410.04716/) (2024)
- [DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions](https://mlsanity.com/paper/2501.12369/) (2025)
- [From Tables to Signals: Revealing Spectral Adaptivity in TabPFN](https://mlsanity.com/paper/2511.18278/) (2025)
- [Model-based learning for multi-antenna multi-frequency location-to-channel mapping](https://mlsanity.com/paper/2407.07719/) (2024)
- [SASNet: Spatially-Adaptive Sinusoidal Networks for INRs](https://mlsanity.com/paper/2503.09750/) (2025)
- [Enhancing Transformers Through Conditioned Embedded Tokens](https://mlsanity.com/paper/2505.12789/) (2025)
- [Spectral Bottleneck in Sinusoidal Representation Networks: Noise is All You Need](https://mlsanity.com/paper/2509.09719/) (2025)
- [Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks](https://mlsanity.com/paper/2607.17624/) (2026)
- [VI3NR: Variance Informed Initialization for Implicit Neural Representations](https://mlsanity.com/paper/2504.19270/) (2025)
- [COSMO-INR: Complex Sinusoidal Modulation for Implicit Neural Representations](https://mlsanity.com/paper/2505.11640/) (2025)
- [Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2509.14219/) (2025)
- [TabINR: An Implicit Neural Representation Framework for Tabular Data Imputation](https://mlsanity.com/paper/2510.01136/) (2025)
- [Implicit Neural Representations: A Signal Processing Perspective](https://mlsanity.com/paper/2604.15047/) (2026)
- [FLAIR: Frequency- and Locality-Aware Implicit Neural Representations](https://mlsanity.com/paper/2508.13544/) (2025)
- [QuadINR: Hardware-Efficient Implicit Neural Representations Through Quadratic Activation](https://mlsanity.com/paper/2508.14374/) (2025)
- [Adaptive Training of INRs via Pruning and Densification](https://mlsanity.com/paper/2510.23943/) (2025)
- [HOSC: A Periodic Activation with Saturation Control for High-Fidelity Implicit Neural Representations](https://mlsanity.com/paper/2601.07870/) (2026)
- [Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations](https://mlsanity.com/paper/2604.02846/) (2026)
- [Learnable Spectral Activations](https://mlsanity.com/paper/2610.07419/) (2026)

## 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.