arXiv:2607.08101 2026 Architecture 1 ideas extracted · analyzed Aug 30, 2026
The paper introduces a discrete Laplace transform of a polytope's support function, producing a lattice partition function whose derivatives encode moments of integer directions. The transferable asset is the combination of convex support functions, exact lattice summation, and positive-semidefinite covariance structure. A practical neural analogue is a learnable convex-polytope attention or embedding layer in which query-dependent features are derived from the log partition function and its gradient, with finite lattice truncation making the construction directly implementable.
Replace or augment conventional dot-product attention with features generated by a convex polytope's lattice Laplace partition function. For a query-dependent point inside a learnable polytope, the log-partition gradient is the expected lattice direction under a Gibbs distribution, while its Hessian is a covariance matrix that supplies curvature-aware features.