ModularPhaseNet proposes a method to modify standard Transformer architectures. It introduces a finite-phase encoder, a quotient-filtration hierarchy module, and a group-valued connection module. These components operate on real-valued hidden states, with the auxiliary phase channel quantized into a cyclic subgroup. The method represents a continuous phase as z = g^a mod p, using group multiplication and division for phase composition and relative phase, respectively. This approach induces a conceptual hierarchy through filtration of cyclic quotients, representing semantic direction with oriented relative group elements, and measuring contextual consistency via gauge-invariant cycle holonomy. Training utilizes distributions in the real group algebra or Gumbel-Softmax, while inference employs exact modular exponentiation and precomputed tables. The paper presents quantization-distortion bounds and proofs of gauge invariance and discrete integrability. The central hypothesis is that these discrete invariants improve hierarchy recovery, discourse alignment, contradiction detection, and calibrated hallucination-risk prediction under a controlled compute budget. The experiments described in Section 14 have not yet been carried out.
Source: https://arxiv.org/abs/2609.06000