Linguistics

Philosophy

Pure mathematics

Interpretation (philosophy)

Theoretical computer science

Operating system

Weighting

Computer science

Embedding

Radiology

Vector space

Natural language processing

Word embedding

Mathematics

Artificial intelligence

Geometry

Medicine

Programming language

Word (group theory)

Algebra over a field

Space (punctuation)

A surprising property of word vectors is that word analogies can often be solved with vector arithmetic. However, it is unclear why arithmetic operators correspond to non-linear embedding models such as skip-gram with negative sampling (SGNS). We provide a formal explanation of this phenomenon without making the strong assumptions that past theories have made about the vector space and word distribution. Our theory has several implications. Past work has conjectured that linear substructures exist in vector spaces because relations can be represented as ratios; we prove that this holds for SGNS. We provide novel justification for the addition of SGNS word vectors by showing that it automatically down-weights the more frequent word, as weighting schemes do ad hoc. Lastly, we offer an information theoretic interpretation of Euclidean distance in vector spaces, justifying its use in capturing word dissimilarity.

Towards Understanding Linear Word Analogies