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Co-occurrences between two words provide useful insights into the semanticsof those words. Consequently, numerous prior work on word embedding learninghave used co-occurrences between two words as the training signal for learningword embeddings. However, in natural language texts it is common for multiplewords to be related and co-occurring in the same context. We extend the notionof co-occurrences to cover $k(\geq\!\!2)$-way co-occurrences among a set of$k$-words. Specifically, we prove a theoretical relationship between the jointprobability of $k(\geq\!\!2)$ words, and the sum of $\ell_2$ norms of theirembeddings. Next, we propose a learning objective motivated by our theoreticalresult that utilises $k$-way co-occurrences for learning word embeddings. Ourexperimental results show that the derived theoretical relationship does indeedhold empirically, and despite data sparsity, for some smaller $k$ values,$k$-way embeddings perform comparably or better than $2$-way embeddings in arange of tasks.

Using $k$-way Co-occurrences for Learning Word Embeddings