  This study utilizes Independent Component Analysis (ICA) to unveil a
consistent semantic structure within embeddings of words or images. Our
approach extracts independent semantic components from the embeddings of a
pre-trained model by leveraging anisotropic information that remains after the
whitening process in Principal Component Analysis (PCA). We demonstrate that
each embedding can be expressed as a composition of a few intrinsic
interpretable axes and that these semantic axes remain consistent across
different languages, algorithms, and modalities. The discovery of a universal
semantic structure in the geometric patterns of embeddings enhances our
understanding of the representations in embeddings.
