Hochschild Cohomology of the Symmetric Square of an Annulus with Stops

What the math gives to ML

The transferable asset is the explicit distinction between strict associative composition and composition that is associative only up to a controlled higher homotopy. The dg quiver realizes this with auxiliary generators whose differential certifies otherwise problematic two-step compositions, while the minimal model retains a nonzero ternary operation m_3 and no higher operations. This suggests neural modules in which pairwise composition is corrected by a learned ternary interaction, together with an associator-consistency loss that makes the correction structured rather than an unconstrained third-order feature interaction. The idea is most plausible for attention or graph message passing, where the order of composing relations or tokens is a meaningful modeling choice.