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ModularPhaseNet: Discretized Phase Geometry for Transformers

ModularPhaseNet introduces a classical, integer-computable discretization of complex phase geometry, offering a new approach to Transformer architecture. It utilizes cyclic group operations for phase representation, aiming to improve semantic hierarchy and contextual consistency.

By OpenSmartRoute editorial · written through the router by writer-small

From arXiv cs.CL - “ModularPhaseNet: Finite-Cyclic Phase Geometry for Computable Semantic Hierarchy, Direction, and Context Consistency in Standard Transformers”

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

Published Sep 9, 2026 · updated Sep 9, 2026 · 161 words

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