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A Sampling Theory Perspective on Activations for Implicit Neural Representations
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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.
Forward citations
Cited by 4 Pith papers
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FLAIR: Frequency- and Locality-Aware Implicit Neural Representations
FLAIR combines band-localized activations with wavelet-energy-guided encoding to help implicit neural representations learn sharper high-frequency details.
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VI3NR: Variance Informed Initialization for Implicit Neural Representations
A variance-matching initialization for implicit neural representations keeps preactivation variance stable for any activation function and improves image, audio, and 3D reconstruction for Gaussian and sinc activations.
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Robustifying Fourier Features Embeddings for Implicit Neural Representations
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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