Understanding Higher-Order Correlations Among Semantic Components in Embeddings
This work provides incremental insights into embedding interpretability for researchers in natural language processing and machine learning.
The paper tackled the problem of non-independencies between semantic components estimated by Independent Component Analysis (ICA) in embeddings, quantifying these using higher-order correlations and showing that large correlations indicate strong semantic associations and shared word meanings.
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.