arXiv:2607.00238 2026 Architecture 2 ideas extracted · analyzed Aug 29, 2026
The paper turns a Riemann function with perfect-matching weight into a finite diagram of vector spaces whose differential, kernel, cokernel, and Euler characteristic exactly encode the function and its dual. The transferable asset is not the Riemann-function application itself, but a compact incidence/sheaf calculus: local linear maps can be assembled into global cohomology dimensions, while periodicity produces weight-sharing actions on infinite index sets. This suggests neural modules with explicit sparse matching routes and measurable kernel/cokernel channels, rather than ordinary unconstrained message passing. The strongest practical tests are a periodic sparse routing layer for grid or sequence tokens and an Euler-characteristic consistency regularizer.
Replace dense token-to-token mixing on a 2D grid by a learned or fixed periodic perfect-matching route. Each source coordinate is connected to exactly one destination coordinate, and the same matching pattern is translated across periods, producing sparse, parameter-shared aggregation with predictable equivariance.
Represent a neural block as a five-object diagram with source spaces B1,B2,B3, target spaces A1,A2, and only the incidence maps allowed by the paper. Penalize excessive cokernel dimension, or explicitly retain it as a controlled residual channel, so inconsistent information is exposed instead of silently discarded by arbitrary projections.