Understanding Higher-Order Correlations Among Semantic Components in Embeddings

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 Figure 1: Heatmap visualization of 300-dimensional a maximum spanning tree of semantic components. SGNS embeddings transformed by PCA and ICA, with These findings provide deeper insights axes sorted by variance and skewness, respectively.