[2607.18074] Sobek: Streaming Equivariant Tensor Product Convolutions

Skip to main content

Search arXiv

Press Enter to search · Advanced search

-->

Computer Science > Machine Learning

arXiv:2607.18074 (cs)

[Submitted on 20 Jul 2026]

Title:Sobek: Streaming Equivariant Tensor Product Convolutions

Authors:Vladimir Chorošajev, Cédric Bény<br>View a PDF of the paper titled Sobek: Streaming Equivariant Tensor Product Convolutions, by Vladimir Choro\v{s}ajev and 1 other authors

View PDF<br>HTML (experimental)

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.

Subjects:

Machine Learning (cs.LG)

Cite as:<br>arXiv:2607.18074 [cs.LG]

(or<br>arXiv:2607.18074v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.18074

Focus to learn more

arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Vladimir Chorošajev [view email]<br>[v1]<br>Mon, 20 Jul 2026 15:43:21 UTC (113 KB)

Full-text links:<br>Access Paper:

View a PDF of the paper titled Sobek: Streaming Equivariant Tensor Product Convolutions, by Vladimir Choro\v{s}ajev and 1 other authors<br>View PDF<br>HTML (experimental)<br>TeX Source

view license

Current browse context:

cs.LG

next >

new<br>recent<br>| 2026-07

Change to browse by:

cs

References & Citations

NASA ADS<br>Google Scholar

Semantic Scholar

export BibTeX citation<br>Loading...

BibTeX formatted citation

&times;

loading...

Data provided by:

Bookmark

Bibliographic Tools

Bibliographic and Citation Tools

Bibliographic Explorer Toggle

Bibliographic Explorer (What is the Explorer?)

Connected Papers Toggle

Connected Papers (What is Connected Papers?)

Litmaps Toggle

Litmaps (What is Litmaps?)

scite.ai Toggle

scite Smart Citations (What are Smart Citations?)

Code, Data, Media

Code, Data and Media Associated with this Article

alphaXiv Toggle

alphaXiv (What is alphaXiv?)

Links to Code Toggle

CatalyzeX Code Finder for Papers (What is CatalyzeX?)

DagsHub Toggle

DagsHub (What is DagsHub?)

GotitPub Toggle

Gotit.pub (What is GotitPub?)

Huggingface Toggle

Hugging Face (What is Huggingface?)

ScienceCast Toggle

ScienceCast (What is ScienceCast?)

Demos

Demos

Replicate Toggle

Replicate (What is Replicate?)

Spaces Toggle

Hugging Face Spaces (What is Spaces?)

Spaces Toggle

TXYZ.AI (What is TXYZ.AI?)

Related Papers

Recommenders and Search Tools

Link to Influence Flower

Influence Flower (What are Influence Flowers?)

Core recommender toggle

CORE Recommender (What is CORE?)

IArxiv recommender toggle

IArxiv Recommender<br>(What is IArxiv?)

Author

Venue

Institution

Topic

About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both 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.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Which authors of this paper are endorsers? |<br>Disable MathJax (What is MathJax?)

Major funding support from