Product Interaction: An Algebraic Formalism for Deep Learning Architectures

arXiv:2602.02573v2 Announce Type: replace-cross Abstract: Modern neural architectures are largely developed as distinct empirical constructions, despite recurring principles across convolutional, attention, state-space, and equivariant models. We introduce Product Interactions, an algebraic formalism that unifies these architectures under a common construction principle and turns their design into a systematic procedure. The core shift is representing data as algebraic elements and treating multiplication, rather than linear transformation alone, as a primitive architectural operation. Archite

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