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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2511.18384 |
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| _version_ | 1866913017543786496 |
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| author | Versace, Plein |
| author_facet | Versace, Plein |
| contents | Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, audio, and 3D scenes. However, existing INR frameworks -- including MLPs with Fourier features, SIREN, and multiresolution hash grids -- implicitly assume a \textit{global and stationary} spectral basis. This assumption is fundamentally misaligned with real-world signals whose frequency characteristics vary significantly across space, exhibiting local high-frequency textures, smooth regions, and frequency drift phenomena. We propose \textbf{Neural Spectral Transport Representation (NSTR)}, the first INR framework that \textbf{explicitly models a spatially varying local frequency field}. NSTR introduces a learnable \emph{frequency transport equation}, a PDE that governs how local spectral compositions evolve across space. Given a learnable local spectrum field $S(x)$ and a frequency transport network $F_θ$ enforcing $\nabla S(x) \approx F_θ(x, S(x))$, NSTR reconstructs signals by spatially modulating a compact set of global sinusoidal bases. This formulation enables strong local adaptivity and offers a new level of interpretability via visualizing frequency flows. Experiments on 2D image regression, audio reconstruction, and implicit 3D geometry show that NSTR achieves significantly better accuracy-parameter trade-offs than SIREN, Fourier-feature MLPs, and Instant-NGP. NSTR requires fewer global frequencies, converges faster, and naturally explains signal structure through spectral transport fields. We believe NSTR opens a new direction in INR research by introducing explicit modeling of space-varying spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | NSTR: Neural Spectral Transport Representation for Space-Varying Frequency Fields Versace, Plein Sound Artificial Intelligence Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, audio, and 3D scenes. However, existing INR frameworks -- including MLPs with Fourier features, SIREN, and multiresolution hash grids -- implicitly assume a \textit{global and stationary} spectral basis. This assumption is fundamentally misaligned with real-world signals whose frequency characteristics vary significantly across space, exhibiting local high-frequency textures, smooth regions, and frequency drift phenomena. We propose \textbf{Neural Spectral Transport Representation (NSTR)}, the first INR framework that \textbf{explicitly models a spatially varying local frequency field}. NSTR introduces a learnable \emph{frequency transport equation}, a PDE that governs how local spectral compositions evolve across space. Given a learnable local spectrum field $S(x)$ and a frequency transport network $F_θ$ enforcing $\nabla S(x) \approx F_θ(x, S(x))$, NSTR reconstructs signals by spatially modulating a compact set of global sinusoidal bases. This formulation enables strong local adaptivity and offers a new level of interpretability via visualizing frequency flows. Experiments on 2D image regression, audio reconstruction, and implicit 3D geometry show that NSTR achieves significantly better accuracy-parameter trade-offs than SIREN, Fourier-feature MLPs, and Instant-NGP. NSTR requires fewer global frequencies, converges faster, and naturally explains signal structure through spectral transport fields. We believe NSTR opens a new direction in INR research by introducing explicit modeling of space-varying spectrum. |
| title | NSTR: Neural Spectral Transport Representation for Space-Varying Frequency Fields |
| topic | Sound Artificial Intelligence |
| url | https://arxiv.org/abs/2511.18384 |