On Compositionality in Data Embedding

Representing data items as vectors in a space is a common practice in machine learning, where it often goes under the name of “data embedding”. This representation is typically learnt from known relations that exist in the original data, such as co-occurrence of words, or connections in graphs. A property of these embeddings is known as compositionality, whereby the vector representation of an item can be decomposed into different parts, which can be understood separately. This property, first observed in the case of word embeddings, could help with various challenges of modern AI: detection of unwanted bias in the representation, explainability of AI decisions based on these representations, and the possibility of performing analogical reasoning or counterfactual question answering. One important direction of research is to understand the origins, properties and limitations of compositional data embeddings, with the idea of going beyond word embeddings. In this paper, we propose two methods to test for this property, demonstrating their use in the case of sentence embedding and knowledge graph embedding.