A D-axis composition algebra on (vector, matrix-power) tuples provides associative per-axis operators and an interchange law when axis matrices commute, recovering RoPE, affine embedding composition, and SSM-style recurrences as special cases.
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Directional Non-Commutative Monoidal Structures for Compositional Embeddings in Machine Learning
A D-axis composition algebra on (vector, matrix-power) tuples provides associative per-axis operators and an interchange law when axis matrices commute, recovering RoPE, affine embedding composition, and SSM-style recurrences as special cases.