# Single-Core Superscalar Optimization of Clifford Neural Layers

arXiv: https://arxiv.org/abs/2510.03290 · HTML: https://mlsanity.com/paper/2510.03290/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalism](https://mlsanity.com/paper/2211.07482/) (2022)

## Abstract (arXiv)

Within the growing interest in the physical sciences in developing networks with equivariance properties, Clifford neural layers shine as one approach that delivers E(n) and O(n) equivariances given specific group actions. In this paper, we analyze the inner structure of the computation within Clifford convolutional layers and propose and implement several optimizations to speed up the inference process while maintaining correctness. In particular, we begin by analyzing the theoretical foundations of Clifford algebras to eliminate redundant matrix allocations and computations, then systematically apply established optimization techniques to enhance performance further. We report a final average speedup of 21.35x over the baseline implementation of eleven functions and runtimes comparable to and faster than the original PyTorch implementation in six cases. In the remaining cases, we achieve performance in the same order of magnitude as the original library.