# Continuous Neural Reparameterization as a Deep Geometric Prior for Robust Fixed-Chart UV Repair

arXiv: https://arxiv.org/abs/2606.10050 · HTML: https://mlsanity.com/paper/2606.10050/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Sign and Basis Invariant Networks for Spectral Graph Representation Learning](https://mlsanity.com/paper/2202.13013/) (2022)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [Nuvo: Neural UV Mapping for Unruly 3D Representations](https://mlsanity.com/paper/2312.05283/) (2023)
- [Boundary First Flattening](https://mlsanity.com/paper/1704.06873/) (2017)
- [AmaraSpatial-10K: A Spatially and Semantically Aligned 3D Dataset for Spatial Computing and Embodied AI](https://mlsanity.com/paper/2604.23018/) (2026)

## Abstract (arXiv)

Traditional UV unwrapping relies on direct optimization of geometric distortion energies and can fail through invalid initialization, local minima, or topological foldovers. We recast fixed-chart UV unwrapping as continuous neural reparameterization: an untrained SIREN maps per-vertex mesh features to UV coordinates, and its weights are optimized for a geometric objective. The practical contribution is a robust chart-solver recipe, combining Laplace--Beltrami spectral inputs, Tutte residual warm-up, a C2 determinant extension, an injectivity barrier, and validity-checked retry/fallback routing, rather than a claim that any single component guarantees validity or that recutting methods should be replaced. NTK--LBO diagnostics show that spectral conditioning changes update geometry, especially at initialization and mid-rank subspaces, but does not by itself predict chart success. On compact pre-cut charts and a 47-chart stratified Thingi10K/xatlas-cut benchmark, the neural solver produces zero flips on all compact charts and 42/47 valid zero-flip stratified solves. BFF and OptCuts comparisons sharpen the scope: recutting can be faster and lower-distortion when allowed, while the neural solver targets supplied-chart validity and validation-first atlas construction. On Amara Spatial generated meshes, the full atlas construction path gives packed-atlas coverage on a 25-asset set and 1000/1000 strict locally valid atlases with zero UV flips in a large-scale Rust atlas run after fallback routing.