# QSV: Quat-Sphere-Vision for Coupled Quaternion Attention on Spherical Lattices

arXiv: https://arxiv.org/abs/2609.30592 · HTML: https://mlsanity.com/paper/2609.30592/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 44 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Escaping the Big Data Paradigm with Compact Transformers](https://mlsanity.com/paper/2104.05704/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Rotary Position Embedding for Vision Transformer](https://mlsanity.com/paper/2403.13298/) (2024)
- [TrivialAugment: Tuning-free Yet State-of-the-Art Data Augmentation](https://mlsanity.com/paper/2103.10158/) (2021)
- [Synthesizer: Rethinking Self-Attention in Transformer Models](https://mlsanity.com/paper/2005.00743/) (2020)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [Stabilizing Transformer Training by Preventing Attention Entropy Collapse](https://mlsanity.com/paper/2303.06296/) (2023)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [PointMixer: MLP-Mixer for Point Cloud Understanding](https://mlsanity.com/paper/2111.11187/) (2021)
- [Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with 1/n Parameters](https://mlsanity.com/paper/2102.08597/) (2021)
- [3D-Rotation-Equivariant Quaternion Neural Networks](https://mlsanity.com/paper/1911.09040/) (2019)
- [No Routing Needed Between Capsules](https://mlsanity.com/paper/2001.09136/) (2020)
- [Lightweight and Efficient Neural Natural Language Processing with Quaternion Networks](https://mlsanity.com/paper/1906.04393/) (2019)
- [Quaternion Convolutional Neural Networks for End-to-End Automatic Speech Recognition](https://mlsanity.com/paper/1806.07789/) (2018)
- [Improving the Robustness of Capsule Networks to Image Affine Transformations](https://mlsanity.com/paper/1911.07968/) (2019)
- [HEAL-SWIN: A Vision Transformer On The Sphere](https://mlsanity.com/paper/2307.07313/) (2023)
- [Scratching Visual Transformer's Back with Uniform Attention](https://mlsanity.com/paper/2210.08457/) (2022)
- [Is Random Attention Sufficient for Sequence Modeling? Disentangling Trainable Components in the Transformer](https://mlsanity.com/paper/2506.01115/) (2025)

## Abstract (arXiv)

In standard attention, three separately learned projections decide how strongly a token attends to each neighbor (WQ, WK) and how the attended features are transformed before aggregation (WV). We study Quat-Sphere-Vision (QSV), a sparse spherical vision model that replaces this projection triple with a single learned unit quaternion per token: the relative quaternion rij = qi* otimes qj supplies both the attention logit operatornameRe(rij) and a sandwich-product feature transport x mapsto rij otimes x otimes rij*, with messages passed over sparse kNN graphs on concentric Fibonacci spheres. Ablations that change only the targeted component show the two roles to be asymmetric. Removing the transport reduces test accuracy by about four percentage points on CIFAR-10 and CIFAR-100 (single runs per CIFAR-100 variant), while replacing the learned attention weights with uniform averaging leaves it essentially unchanged. Parameter-matched controls then remove the geometry itself: standard attention on the same graph exceeds QSV (mean 87.3% vs. 85.9%), and the same model on a flat 2D lattice reaches 91.1%, within 2.1 points of a ResNet-20 trained under the same pipeline (single run). In the coupled kernel, nearly all of the learned pairwise computation resides in the transport channel.