A Sampling Theory Perspective on Activations for Implicit Neural Representations
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909098942922752 |
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| author | Saratchandran, Hemanth Ramasinghe, Sameera Shevchenko, Violetta Long, Alexander Lucey, Simon |
| author_facet | Saratchandran, Hemanth Ramasinghe, Sameera Shevchenko, Violetta Long, Alexander Lucey, Simon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Sampling Theory Perspective on Activations for Implicit Neural Representations Saratchandran, Hemanth Ramasinghe, Sameera Shevchenko, Violetta Long, Alexander Lucey, Simon Machine Learning 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. |
| title | A Sampling Theory Perspective on Activations for Implicit Neural Representations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.05427 |