Sobek: Streaming Equivariant Tensor Product Convolutions
2026-07-20 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study how a certain kind of graph neural network (equivariant graph neural networks) usually does lots of work for each edge in a graph, which uses a lot of memory and slows things down. They found that much of this heavy memory use comes from the way the computations are organized, not from the math itself. By changing the calculation order, they made a new method that uses less memory and runs much faster. They built this into a system called Sobek and showed it works well for different tests, handling bigger problems and saving a lot of memory compared to previous approaches.
equivariant graph neural networkstensor-product convolutionsedge-conditioned weightsspherical harmonicsradial projectiongraph aggregationCUDA backenddifferentiation ordersmemory optimizationstreaming formulation
Authors
Vladimir Chorošajev, Cédric Bény
Abstract
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 $1.2\times$ to $49.7\times$, 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.