Improved Representation of Asymmetrical Distances with Interval Quasimetric Embeddings

TL;DR

This paper introduces Interval Quasimetric Embeddings (IQE), a novel approach that effectively models asymmetrical distances in machine learning, demonstrating superior approximation, generalization, and efficiency over previous methods.

Contribution

The paper proposes IQE, satisfying four key properties for quasimetric models, and shows its advantages through three quasimetric learning experiments.

Findings

IQE achieves better approximation of asymmetrical distances.

IQE demonstrates improved generalization in learning tasks.

IQE outperforms prior methods in efficiency and accuracy.

Abstract

Asymmetrical distance structures (quasimetrics) are ubiquitous in our lives and are gaining more attention in machine learning applications. Imposing such quasimetric structures in model representations has been shown to improve many tasks, including reinforcement learning (RL) and causal relation learning. In this work, we present four desirable properties in such quasimetric models, and show how prior works fail at them. We propose Interval Quasimetric Embedding (IQE), which is designed to satisfy all four criteria. On three quasimetric learning experiments, IQEs show strong approximation and generalization abilities, leading to better performance and improved efficiency over prior methods. Project Page: https://www.tongzhouwang.info/interval_quasimetric_embedding Quasimetric Learning Code Package: https://www.github.com/quasimetric-learning/torch-quasimetric