Revisiting Additive Compositionality: AND, OR and NOT Operations with Word Embeddings

TL;DR

This paper introduces a post-processing method for word embeddings that improves additive compositionality and enables linear operations for OR and NOT, enhancing semantic manipulation capabilities.

Contribution

It proposes a frequency-weighted centering post-processing technique that aligns practical embeddings with theoretical assumptions and facilitates new logical operations.

Findings

Improved AND operation accuracy by 3.5x with post-processing

Successfully performed OR and NOT operations linearly on embeddings

Enhanced semantic compositionality in word embeddings

Abstract

It is well-known that typical word embedding methods such as Word2Vec and GloVe have the property that the meaning can be composed by adding up the embeddings (additive compositionality). Several theories have been proposed to explain additive compositionality, but the following questions remain unanswered: (Q1) The assumptions of those theories do not hold for the practical word embedding. (Q2) Ordinary additive compositionality can be seen as an AND operation of word meanings, but it is not well understood how other operations, such as OR and NOT, can be computed by the embeddings. We address these issues by the idea of frequency-weighted centering at its core. This paper proposes a post-processing method for bridging the gap between practical word embedding and the assumption of theory about additive compositionality as an answer to (Q1). It also gives a method for taking OR or NOT of the meaning by linear operation of word embedding as an answer to (Q2). Moreover, we confirm experimentally that the accuracy of AND operation, i.e., the ordinary additive compositionality, can be improved by our post-processing method (3.5x improvement in top-100 accuracy) and that OR and NOT operations can be performed correctly.