# Sobek: Streaming Equivariant Tensor Product Convolutions

arXiv: https://arxiv.org/abs/2607.18074 · HTML: https://mlsanity.com/paper/2607.18074/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 23 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 19 of 19)

- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [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)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [An Efficient Sparse Kernel Generator for O(3)-Equivariant Deep Networks](https://mlsanity.com/paper/2501.13986/) (2025)
- [The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Products](https://mlsanity.com/paper/2506.13523/) (2025)
- [Equivariant Neural Operator Learning with Graphon Convolution](https://mlsanity.com/paper/2311.10908/) (2023)
- [Speeding Up MACE: Low-Precision Tricks for Equivarient Force Fields](https://mlsanity.com/paper/2510.23621/) (2025)

## Built on by (most cited first, 1 of 1)

- [FlashCart: Fast Cartesian Tensor Products for Equivariant Interatomic Potentials](https://mlsanity.com/paper/2610.06409/) (2026)

## Abstract (arXiv)

Equivariant graph neural networks repeatedly apply edge-conditioned tensor-product convolutions over graph edges. Conventional implementations materialize edge-specific weights, messages, and adjoints, causing tensor-product workspace and memory traffic to grow rapidly with graph size and operator width. This limits feasible workloads and can prevent larger problems from fully utilizing the GPU. We show that these edge-sized intermediates are artifacts of the execution schedule, not requirements of the equivariant operator. By reassociating radial projection, spherical-harmonic coupling, and graph aggregation, edge-local products can be consumed directly into bounded receiver-side state. The resulting streaming formulation preserves fully connected multiplicity mixing and extends through forward, backward, and double backward. We implement this formulation in Sobek, a generated-CUDA backend, and evaluate it across edge-scaling regimes and varied feature structures. Across two operator families and all three differentiation orders, Sobek is faster in all 75 capacity-matched comparisons, with speedups ranging from 1.2× to 49.7×, and reduces peak allocated memory by up to 99%. It also executes workloads up to two orders of magnitude beyond OpenEquivariance's capacity while retaining near-peak throughput. These results show that edge-scaled tensor-product workspace is a property of the conventional schedule, not of equivariant convolution itself.