Graphical einops: bridging tensor networks and computation graphs

• URL: http://arxiv.org/abs/2605.31485v1
• Date: Fri, 29 May 2026 16:08:49 GMT
• Title: Graphical einops: bridging tensor networks and computation graphs
• Abstract summary: We introduce a formal graphical calculus for the structural fragment of tensor programming underlying einops.<n>The key rewrite is grade-naturality: sliding spectacles over tubes.<n>We additionally demonstrate how our rewrite system may be applied to convert attention masks into pre-processing operations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Architecture diagrams are ubiquitous in deep learning, but they are usually only representational: the tensor-program identities they suggest are still proved by prose and tensor-axis manipulation. We introduce a formal graphical calculus for the structural fragment of tensor programming underlying einops, making such diagrams proof-enabling. Our calculus represents tensor axes as nested graded tubes around a base type. The tube boundary recovers the undirected tensor-network view of axes, while the directed interior retains the operational reading of computation graphs. The key rewrite is grade-naturality: sliding spectacles over tubes. Standard equivariance proofs become short diagrammatic derivations. We additionally demonstrate how our rewrite system may be applied to convert attention masks into pre-processing operations, recovering efficient implementations of sparse attention blocks.

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