Understanding Higher-Order Correlations Among Semantic Components in Embeddings

2024/09/30 by Momose Oyama, Oyama, Momose, Hiroaki Yamagiwa +3 · 1 citation
Computer Science · #Computation and Language (cs.CL) #FOS: Computer and information sciences #Semantic Web and Ontologies

paper · pdf · doi:10.48550/arxiv.2409.19919

openalex publication_date 2024/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Independent Component Analysis (ICA) offers interpretable semantic components of embeddings. While ICA theory assumes that embeddings can be linearly decomposed into independent components, real-world data often do not satisfy this assumption. Consequently, non-independencies remain between the estimated components, which ICA cannot eliminate. We quantified these non-independencies using higher-order correlations and demonstrated that when the higher-order correlation between two components is large, it indicates a strong semantic association between them, along with many words sharing common meanings with both components. The entire structure of non-independencies was visualized using a maximum spanning tree of semantic components. These findings provide deeper insights into embeddings through ICA.

Cited by

• Quantifying Compositionality of Classic and State-of-the-Art Embeddings

Related

• Exploring Intra and Inter-language Consistency in Embeddings with ICA
• Discovering Universal Geometry in Embeddings with ICA
• Axis Tour: Word Tour Determines the Order of Axes in ICA-transformed Embeddings
• Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings
• Encoding Prior Knowledge with Eigenword Embeddings