形式化和学习概念的量子模型
Formalising and Learning a Quantum Model of Concepts
摘要：
在这份报告中，我们提出了一个新的建模框架的概念的基础上量子理论，并演示了如何概念表示可以从数据中自动学习。一个贡献的工作是一个彻底的范畴理论形式化我们的框架。我们声称，使用范畴理论，特别是使用弦图来描述量子过程，有助于阐明我们的量子概念建模方法的一些最重要的特征。我们的方法建立在Gardenfors的概念空间的经典框架，其中认知是通过使用凸空间，这反过来因式分解在称为域的更简单的空间几何建模。我们展示了如何从形状，颜色，大小和位置域的概念可以从简单形状的图像中学习，其中单个图像表示为量子态和量子效应的概念。概念是通过训练执行概念分类的混合经典-量子网络学习的，其中经典图像处理由卷积神经网络执行，量子表示由参数化量子电路产生。我们还使用丢弃来产生混合效果，然后可以用来学习仅适用于域子集的概念，并展示如何使用纠缠（与丢弃一起）来捕获跨域的有趣相关性。最后，我们考虑的问题，我们的量子模型的概念是否可以被认为是概念空间的Gardenfors意义。
英文摘要：
In this report we present a new modelling framework for concepts based on quantum theory, and demonstrate how the conceptual representations can be learned automatically from data. A contribution of the work is a thorough category-theoretic formalisation of our framework. We claim that the use of category theory, and in particular the use of string diagrams to describe quantum processes, helps elucidate some of the most important features of our quantum approach to concept modelling. Our approach builds upon Gardenfors' classical framework of conceptual spaces, in which cognition is modelled geometrically through the use of convex spaces, which in turn factorise in terms of simpler spaces called domains. We show how concepts from the domains of shape, colour, size and position can be learned from images of simple shapes, where individual images are represented as quantum states and concepts as quantum effects. Concepts are learned by a hybrid classical-quantum network trained to perform concept classification, where the classical image processing is carried out by a convolutional neural network and the quantum representations are produced by a parameterised quantum circuit. We also use discarding to produce mixed effects, which can then be used to learn concepts which only apply to a subset of the domains, and show how entanglement (together with discarding) can be used to capture interesting correlations across domains. Finally, we consider the question of whether our quantum models of concepts can be considered conceptual spaces in the Gardenfors sense.
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