Unified Interpretation of Softmax Cross-Entropy and Negative Sampling: With Case Study for Knowledge Graph Embedding

TL;DR

This paper provides a unified theoretical interpretation of softmax cross-entropy and negative sampling loss functions in knowledge graph embedding using Bregman divergence, enabling fair comparison and validation through experiments.

Contribution

It introduces a Bregman divergence-based framework that unifies and compares softmax cross-entropy and negative sampling losses in knowledge graph embedding.

Findings

Theoretical relationship between the two loss functions is established.

Experimental validation on FB15k-237 and WN18RR datasets confirms the theory.

Abstract

In knowledge graph embedding, the theoretical relationship between the softmax cross-entropy and negative sampling loss functions has not been investigated. This makes it difficult to fairly compare the results of the two different loss functions. We attempted to solve this problem by using the Bregman divergence to provide a unified interpretation of the softmax cross-entropy and negative sampling loss functions. Under this interpretation, we can derive theoretical findings for fair comparison. Experimental results on the FB15k-237 and WN18RR datasets show that the theoretical findings are valid in practical settings.