{"ID":2837969,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.18384","arxiv_id":"2511.18384","title":"NSTR: Neural Spectral Transport Representation for Space-Varying Frequency Fields","abstract":"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.","short_abstract":"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....","url_abs":"https://arxiv.org/abs/2511.18384","url_pdf":"https://arxiv.org/pdf/2511.18384v2","authors":"[\"Plein Versace\"]","published":"2025-11-23T10:24:12Z","proceeding":"cs.SD","tasks":"[\"cs.SD\",\"cs.AI\"]","methods":"[]","has_code":false}