{"slug": "sobek-streaming-equivariant-tensor-product-convolutions", "title": "Sobek: Streaming Equivariant Tensor Product Convolutions", "summary": "Researchers have developed Sobek, a generated-CUDA backend for streaming equivariant tensor product convolutions that eliminates edge-sized intermediates, achieving speedups of 1.2× to 49.7× and reducing peak memory by up to 99% across all 75 capacity-matched comparisons. The method, described in a paper submitted on July 20, 2026, enables workloads up to two orders of magnitude larger than OpenEquivariance while maintaining near-peak throughput.", "body_md": "# Computer Science > Machine Learning\n\n[Submitted on 20 Jul 2026]\n\n# Title:Sobek: Streaming Equivariant Tensor Product Convolutions\n\n[View PDF](/pdf/2607.18074)\n\n[HTML (experimental)](https://arxiv.org/html/2607.18074v1)\n\nAbstract: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.\n\nWe 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.\n\nWe 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.\n\n## Submission history\n\nFrom: Vladimir Chorošajev [[view email](/show-email/f6115ad5/2607.18074)]\n\n**[v1]** Mon, 20 Jul 2026 15:43:21 UTC (113 KB)\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer\n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers\n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps\n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations\n\n*(*[What are Smart Citations?](https://www.scite.ai/))# Code, Data and Media Associated with this Article\n\nalphaXiv\n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers\n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub\n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub\n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face\n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast\n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower\n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender\n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\nIArxiv Recommender\n\n*(*[What is IArxiv?](https://iarxiv.org/about))# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.\n\nHave an idea for a project that will add value for arXiv's community? [ Learn more about arXivLabs](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/sobek-streaming-equivariant-tensor-product-convolutions", "canonical_source": "https://arxiv.org/abs/2607.18074", "published_at": "2026-07-21 11:07:06+00:00", "updated_at": "2026-07-21 11:22:44.781344+00:00", "lang": "en", "topics": ["machine-learning", "neural-networks", "ai-research", "ai-infrastructure"], "entities": ["Sobek", "OpenEquivariance", "Vladimir Chorošajev"], "alternates": {"html": "https://wpnews.pro/news/sobek-streaming-equivariant-tensor-product-convolutions", "markdown": "https://wpnews.pro/news/sobek-streaming-equivariant-tensor-product-convolutions.md", "text": "https://wpnews.pro/news/sobek-streaming-equivariant-tensor-product-convolutions.txt", "jsonld": "https://wpnews.pro/news/sobek-streaming-equivariant-tensor-product-convolutions.jsonld"}}