ModularPhaseNet: Finite-Cyclic Phase Geometry for Computable Semantic Hierarchy, Direction, and Context Consistency in Standard Transformers

תקציר מקורי באנגליתarXiv:2609.06000v1 Announce Type: cross Abstract: We propose ModularPhaseNet, a classical and integer-computable discretization of the continuous complex phase geometry introduced in QuantumPhaseNet. The real-valued hidden states of a standard Transformer are retained, while only an auxiliary phase channel is quantized into a cyclic subgroup G = <g> of order q | (p-1) in the multiplicative group of F_p. A continuous phase e^{i phi} is represented by z = g^a mod p; phase composition becomes group multiplication, relative phase becomes group division, conceptual hierarchy is induced by a filtration of cyclic quotients, semantic direction is represented by oriented relative group elements, and contextual consistency is measured by gauge-invariant cycle holonomy. The method introduces three co