Generalized quantum similarity learning
This addresses the limitation of conventional distance functions in capturing meaningful, task-specific similarities for various applications, though it appears incremental as it builds on quantum networks for similarity learning.
The paper tackles the problem of learning task-dependent similarity measures that can be asymmetric and compare objects from different spaces, proposing a quantum network approach (GQSim) that is shown to be theoretically guaranteed and applied to classification, graph completion, and generative modeling.
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 $(ε,γ,τ)$-good, resulting in theoretically guaranteed performance. Finally, we conclude by applying this technique for three relevant applications - Classification, Graph Completion, Generative modeling.