WavePhaseNet: A DFT-Based Method for Constructing Semantic Conceptual Hierarchy Structures (SCHS)
Kiyotaka Kasubuchi, Kazuo Fukiya

TL;DR
WavePhaseNet introduces a DFT-based approach to construct semantic hierarchy structures in language models, enabling better semantic manipulation and reduced hallucination by decomposing embeddings into frequency components.
Contribution
The paper presents WavePhaseNet, a novel method that explicitly constructs semantic hierarchy structures using DFT, and applies cohomological regularization for semantic consistency in language models.
Findings
DFT decomposes semantic information into frequency bands.
Reducing embedding dimensions to ~3,000 preserves meaning.
Cohomological regularization improves semantic consistency.
Abstract
This paper reformulates Transformer/Attention mechanisms in Large Language Models (LLMs) through measure theory and frequency analysis, theoretically demonstrating that hallucination is an inevitable structural limitation. The embedding space functions as a conditional expectation over a {\sigma}-algebra, and its failure to be isomorphic to the semantic truth set fundamentally causes logical consistency breakdown. WavePhaseNet Method The authors propose WavePhaseNet, which explicitly constructs a Semantic Conceptual Hierarchy Structure (SCHS) using Discrete Fourier Transform (DFT). By applying DFT along the sequence dimension, semantic information is decomposed into frequency bands: low-frequency components capture global meaning and intent, while high-frequency components represent local syntax and expression. This staged separation enables precise semantic manipulation in diagonalized…
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Taxonomy
TopicsTopic Modeling · Computational and Text Analysis Methods · Big Data and Digital Economy
