# Symmetry-aware super-resolution of crystal orientation maps via invariant latent-space learning

arXiv: https://arxiv.org/abs/2609.10898 · HTML: https://mlsanity.com/paper/2609.10898/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Single Image Super-Resolution via a Holistic Attention Network](https://mlsanity.com/paper/2008.08767/) (2020)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Q-RBSA: High-Resolution 3D EBSD Map Generation Using An Efficient Quaternion Transformer Network](https://mlsanity.com/paper/2303.10722/) (2023)

## Abstract (arXiv)

Crystal-orientation maps are physical fields defined only up to crystal symmetry; electron backscatter diffraction (EBSD) resolves them experimentally, but acquisition-time constraints limit spatial resolution. Unlike conventional images, EBSD data lie on the quotient space SO(3)/G, where G is the crystal-symmetry group. Standard Euclidean interpolation can therefore mix symmetry-equivalent representations and blur grain boundaries. We introduce the Symmetry-Group-Aware Super-Resolution Attention Network (SG-SRAN), which incorporates crystal symmetry and boundary preservation by design. A frozen, locally isometric encoder maps equivalent orientations to a common latent representation in which Euclidean distance approximates misorientation. Super-resolution is performed in this space, with each high-resolution token restricted to a feature-consistent local support to prevent cross-boundary mixing. A dictionary-based decoder then recovers valid orientations. Across FCC and HCP benchmarks, SG-SRAN matches 15-16 million parameter backbones using only 27-49k trainable parameters, while achieving the lowest p68 errors, highest inverse-pole-figure fidelity, and zero-shot transfer to unseen alloys.