arXiv 2201.023102022-01-07quant-phcs.LGstat.ML

广义量子相似性学习

Generalized quantum similarity learning

Agnostiq Inc.（Agnostiq 公司）

Santosh Kumar Radha, Casey Jao

摘要：

对象之间的相似性在广泛的领域中是显著的。虽然可以使用现成的距离函数来测量相似性，但它们可能无法捕获相似性的内在含义，这往往取决于底层数据和任务。此外，传统的距离函数将相似性度量的空间限制为对称的，并且不直接允许比较来自不同空间的对象。我们建议使用量子网络（GQSim）来学习任务相关的（a）不需要具有相同维度的数据之间的对称相似性。我们分析了这种相似性函数的性质解析（对于一个简单的情况下）和数值（对于一个复杂的情况下），并showthese相似性措施可以提取显着的数据特征。我们还表明，使用这种技术得到的相似性度量是$(ε,γ,τ)$ -好，从而在理论上保证性能。最后，我们总结了三个相关的应用程序-分类，图完成，生成式建模应用这种技术。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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