Distributional hypothesis as isomorphism between word-word co-occurrence and analogical parallelograms.

Area of Science:

• Computational linguistics
• Natural Language Processing (NLP)
• Cognitive Science

Background:

• Modern NLP relies on vector space models where words are high-dimensional vectors.
• Word vectors exhibit geometric structures, like "parallelograms," enabling analogical reasoning (e.g., A:B::C:D).
• The emergence of these geometric properties in NLP models remains incompletely understood.

Purpose of the Study:

• To investigate the hypothesis that parallelogram arrangements of word vectors are inherent in language's co-occurrence statistics.
• To explore data-centric explanations for geometric structures in word embeddings, diverging from model-centric approaches.
• To provide a refined distributional hypothesis linking linguistic structure to word co-occurrence patterns.

Main Methods:

• Analyzing the decomposition of bigram co-occurrence matrices to enable analogical reasoning.
• Constructing a small artificial corpus to generate word vectors and observe geometric formations.
• Examining the statistical properties of word co-occurrence data.

Main Results:

• Analogical reasoning was shown to be achievable through the decomposition of bigram co-occurrence matrices.
• The formation of a parallelepiped, a more complex geometric structure than a parallelogram, was demonstrated in an artificial corpus.
• Evidence suggests that geometric properties of word vectors are rooted in the statistical structure of language data.

Conclusions:

• The study supports the hypothesis that word vector geometry, including parallelogram formations, originates from language's co-occurrence statistics.
• A refined distributional hypothesis is proposed, highlighting an isomorphism between linguistic symmetry/exchangeability and word co-occurrence patterns.
• Findings suggest focusing on data properties offers a new perspective on understanding semantic representation in NLP.