Generalized quantum similarity learning

TL;DR

This paper introduces GQSim, a quantum network-based method for learning flexible, task-dependent similarity measures that can be asymmetric and handle data from different spaces, with theoretical guarantees and practical applications.

Contribution

The paper proposes a novel quantum network approach for learning data-dependent similarity measures, extending beyond symmetric distances and enabling cross-space comparisons.

Findings

Similarity measures can extract salient data features.

The method is theoretically guaranteed to perform well.

Applications include classification, graph completion, and generative modeling.

Abstract

The similarity between objects is significant in a broad range of areas. While similarity can be measured using off-the-shelf distance functions, they may fail to capture the inherent meaning of similarity, which tends to depend on the underlying data and task. Moreover, conventional distance functions limit the space of similarity measures to be symmetric and do not directly allow comparing objects from different spaces. We propose using quantum networks (GQSim) for learning task-dependent (a)symmetric similarity between data that need not have the same dimensionality. We analyze the properties of such similarity function analytically (for a simple case) and numerically (for a complex case) and showthat these similarity measures can extract salient features of the data. We also demonstrate that the similarity measure derived using this technique is $(\epsilon,\gamma,\tau)$-good, resulting in theoretically guaranteed performance. Finally, we conclude by applying this technique for three relevant applications - Classification, Graph Completion, Generative modeling.