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About this paper
Vincent Wang-Maścianica, Nikhil Khatri
A formal graphical calculus unifies undirected tensor networks and directed computation graphs for structural tensor programming, making structural equality decidable for `einops`-like operations. The framework enables concise diagrammatic derivations of complex properties, such as the attention mask-augment duality, and provides a theoretical basis for several attention optimization strategies.
Key insights
- Structural `einops` programs can be faithfully embedded within the proposed `FinSet^op`-graded tube calculus, providing a formal representation for ubiquitous tensor operations.
- Structural equality in this fragment of tensor programming is decidable, reducible to equality of composite functions between finite sets.
- The 'Mask-Augment Duality' theorem demonstrates that masked attention is structurally equivalent to fibrewise unmasked attention over a specific display of Key/Value streams.
Summary by alphaXiv.
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