# NSTR: Neural Spectral Transport Representation for Space-Varying Frequency Fields

arXiv: https://arxiv.org/abs/2511.18384 · HTML: https://mlsanity.com/paper/2511.18384/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 21 references that are in the map.
- First posted on arXiv 23 Nov 2025.

## Builds on (most cited first, 17 of 17)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles](https://mlsanity.com/paper/2505.19914/) (2025)
- [FLEX: Continuous Agent Evolution via Forward Learning from Experience](https://mlsanity.com/paper/2511.06449/) (2025)
- [RefConv: Re-parameterized Refocusing Convolution for Powerful ConvNets](https://mlsanity.com/paper/2310.10563/) (2023)
- [FalconNet: Factorization for the Light-weight ConvNets](https://mlsanity.com/paper/2306.06365/) (2023)
- [X-MLP: A Patch Embedding-Free MLP Architecture for Vision](https://mlsanity.com/paper/2307.00592/) (2023)
- [SA-GD: Improved Gradient Descent Learning Strategy with Simulated Annealing](https://mlsanity.com/paper/2107.07558/) (2021)
- [Jitter: Random Jittering Loss Function](https://mlsanity.com/paper/2106.13749/) (2021)
- [Encoding Semantic Priors into the Weights of Implicit Neural Representation](https://mlsanity.com/paper/2406.04178/) (2024)
- [Reborn Mechanism: Rethinking the Negative Phase Information Flow in Convolutional Neural Network](https://mlsanity.com/paper/2106.07026/) (2021)
- [Interflow: Aggregating Multi-layer Feature Mappings with Attention Mechanism](https://mlsanity.com/paper/2106.14073/) (2021)
- [Evolution: A Unified Formula for Feature Operators from a High-level Perspective](https://mlsanity.com/paper/2305.14409/) (2023)
- [Learn to Enhance the Negative Information in Convolutional Neural Network](https://mlsanity.com/paper/2306.10536/) (2023)
- [Conv-INR: Convolutional Implicit Neural Representation for Multimodal Visual Signals](https://mlsanity.com/paper/2406.04249/) (2024)
- [Split-Layer: Enhancing Implicit Neural Representation by Maximizing the Dimensionality of Feature Space](https://mlsanity.com/paper/2511.10142/) (2025)

## Abstract (arXiv)

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 textitglobal 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 Neural Spectral Transport Representation (NSTR), the first INR framework that explicitly models a spatially varying local frequency field. NSTR introduces a learnable 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 Fθ enforcing nabla S(x) ≈ Fθ(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.