Alignment and stability of embeddings: measurement and inference improvement

TL;DR

This paper introduces formal definitions and novel metrics for embedding alignment and stability, demonstrating their importance through synthetic and real-world experiments, and showing that proper alignment significantly improves dynamic network inference accuracy.

Contribution

It provides the first formal definitions of embedding alignment, proposes new metrics for measuring alignment and stability, and empirically demonstrates their impact on RL methods.

Findings

Misalignment worsens RL performance in real-world tasks.

Aligning embeddings improves prediction accuracy by up to 90%.

Both static and dynamic RL methods are susceptible to misalignment.

Abstract

Representation learning (RL) methods learn objects' latent embeddings where information is preserved by distances. Since distances are invariant to certain linear transformations, one may obtain different embeddings while preserving the same information. In dynamic systems, a temporal difference in embeddings may be explained by the stability of the system or by the misalignment of embeddings due to arbitrary transformations. In the literature, embedding alignment has not been defined formally, explored theoretically, or analyzed empirically. Here, we explore the embedding alignment and its parts, provide the first formal definitions, propose novel metrics to measure alignment and stability, and show their suitability through synthetic experiments. Real-world experiments show that both static and dynamic RL methods are prone to produce misaligned embeddings and such misalignment worsens the performance of dynamic network inference tasks. By ensuring alignment, the prediction accuracy raises by up to 90% in static and by 40% in dynamic RL methods.