グラフィカルeinops：テンソルネットワークと計算グラフの橋渡し
Graphical einops: bridging tensor networks and computation graphs
einopsのテンソル操作を形式的な図的計算体系として表現し、軸の操作を視覚的に証明可能にする手法を提案した論文。
著者: Vincent Wang-Maścianica, Nikhil Khatri
分類: cs.LG, math.CT
原文アブストラクト
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.