In this article we present a new modelling framework for structured concepts
using a category-theoretic generalisation of conceptual spaces, and show how
the conceptual representations can be learned automatically from data, using
two very different instantiations: one classical and one quantum. 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 approach. We build 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 concepts
are represented as Gaussians in the classical implementation, and quantum
effects in the quantum one. In the classical case we develop a new model which
is inspired by the Beta-VAE model of concepts, but is designed to be more
closely connected with language, so that the names of concepts form part of the
graphical model. In the quantum case, 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.
Finally, we consider the question of whether our quantum models of concepts can
be considered conceptual spaces in the Gardenfors sense.

本文提出了一个新的模型框架，使用范畴论的概念空间广义化，并展示了如何从数据中自动地学习概念表示，包括经典和量子两种不同的实例化。通过范畴论的形式化，我们详细阐述了该框架的基本原理。我们认为使用范畴论，特别是使用弦图来描述量子过程，可以帮助阐明我们方法的一些重要特点。在现有的概念空间框架基础上，我们从简单形状的图像中学习了形状、颜色、大小和位置等概念，在经典实现中概念表示为高斯函数，在量子实现中表示为量子效应。在经典情况下，我们开发了一个新的模型，受到概念的 Beta-VAE 模型启发，但更紧密地与语言相连接，使得概念的名称成为图形模型的一部分。在量子情况下，概念通过一个混合的经典 - 量子网络进行学习，该网络通过卷积神经网络进行经典图像处理，并通过参数化量子电路生成量子表示。最后，我们考虑了我们的量子概念模型是否可以被视为 Gardenfors 意义上的概念空间。

从概念空间到量子概念：形式化和学习结构化概念模型

From Conceptual Spaces to Quantum Concepts: Formalising and Learning  Structured Conceptual Models

The last decade has seen huge progress in the development of advanced machine
learning models; however, those models are powerless unless human users can
interpret them. Here we show how the mind's construction of concepts and
meaning can be used to create more interpretable machine learning models. By
proposing a novel method of classifying concepts, in terms of 'form' and
'function', we elucidate the nature of meaning and offer proposals to improve
model understandability. As machine learning begins to permeate daily life,
interpretable models may serve as a bridge between domain-expert authors and
non-expert users.

本文探讨如何利用概念和意义的构建方式来创建更易理解的机器学习模型，通过提出分类概念的新方法，即 “形式” 和 “功能”，阐明了意义的本质，并提出了提高模型可理解性的建议。