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A Sampling Theory Perspective on Activations for Implicit Neural Representations

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arxiv 2402.05427 v1 pith:VDUXFYFD submitted 2024-02-08 cs.LG

Hemanth Saratchandran , Sameera Ramasinghe , Violetta Shevchenko , Alexander Long , Simon Lucey This is my paper · ORCID
classification cs.LG
keywords activationsinrssamplingtheoryencodingimplicitneuralperspective
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks

    cs.LG 2026-07 conditional novelty 7.0 of 10

    Learned replacement non-linearities show transformers are rarely optimal for algorithmic tasks, with benefits that are task-specific, while language/code gains are smaller and more transferable.

  2. FLAIR: Frequency- and Locality-Aware Implicit Neural Representations

    cs.CV 2025-08 unverdicted novelty 6.0 of 10

    FLAIR combines band-localized activations with wavelet-energy-guided encoding to help implicit neural representations learn sharper high-frequency details.

  3. Robustifying Fourier Features Embeddings for Implicit Neural Representations

    cs.CV 2025-02 conditional novelty 6.0 of 10

    A bias-free MLP filter applied multiplicatively to Fourier features, with a line-search learning-rate controller, reduces noise and improves implicit neural representation fitting across images, shapes, and NeRF.

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