Guido Montúfar

Symmetries in deep networks don't automatically yield conservation laws under gradient flow; this geometric framework pinpoints exactly when Noether-style invariants hold across layers, completely mapping the conserved quantities of multi-head and grouped-query attention.

This work formalizes causal regions as polyhedral regions with fixed causal sets and derive upper and lower bounds on the maximal number of causal regions in both shallow and multilayer feedforward spiking networks.

RL can now discover more diverse triangulations of complex polytopes than specialized geometric algorithms, opening avenues for automated exploration in fields like Calabi-Yau manifold construction.