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

• URL: http://arxiv.org/abs/2401.08585v1
• Date: Mon, 6 Nov 2023 15:08:22 GMT
• Title: From Conceptual Spaces to Quantum Concepts: Formalising and Learning Structured Conceptual Models
• Authors: Sean Tull, Razin A. Shaikh, Sara Sabrina Zemljic and Stephen Clark
• Abstract summary: We present a new modelling framework for structured concepts using a category-theoretic generalisation of conceptual spaces. We show how concepts can be learned automatically from data, using two very different instantiations: one classical and one quantum.
• Score: 3.430966345969155
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Theoretical framework for quantum associative memories [0.8437187555622164]
  Associative memory refers to the ability to relate a memory with an input and targets the restoration of corrupted patterns. We develop a comprehensive framework for a quantum associative memory based on open quantum system dynamics.
  arXiv  Detail & Related papers  (2024-08-26T13:46:47Z)
• A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models [62.997667081978825]
  We build over a proposed framework for evaluating the generalization performance of generative models. We establish the first comparative race towards practical quantum advantage (PQA) between classical and quantum generative models. Our results suggest that QCBMs are more efficient in the data-limited regime than the other state-of-the-art classical generative models.
  arXiv  Detail & Related papers  (2023-03-27T22:48:28Z)
• Formalising and Learning a Quantum Model of Concepts [7.15767183672057]
  We present a new modelling framework for concepts based on quantum theory. We show how concepts from domains of shape, colour, size and position can be learned from images of simple shapes. Concepts are learned by a hybrid classical-quantum network trained to perform concept classification.
  arXiv  Detail & Related papers  (2023-02-07T10:29:40Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Quantum Structure in Human Perception [0.0]
  We investigate the ways in which the quantum structures of superposition, contextuality, and entanglement have their origins in human perception itself. Our analysis takes us from a simple quantum measurement model, along how human perception incorporates the warping mechanism of categorical perception.
  arXiv  Detail & Related papers  (2022-08-07T13:59:23Z)
• The Conceptual VAE [7.15767183672057]
  We present a new model of concepts, based on the framework of variational autoencoders. The model is inspired by, and closely related to, the Beta-VAE model of concepts. We show how the model can be used as a concept classifier, and how it can be adapted to learn from fewer labels per instance.
  arXiv  Detail & Related papers  (2022-03-21T17:27:28Z)
• Human-Centered Concept Explanations for Neural Networks [47.71169918421306]
  We introduce concept explanations including the class of Concept Activation Vectors (CAV) We then discuss approaches to automatically extract concepts, and approaches to address some of their caveats. Finally, we discuss some case studies that showcase the utility of such concept-based explanations in synthetic settings and real world applications.
  arXiv  Detail & Related papers  (2022-02-25T01:27:31Z)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)
• Formalising Concepts as Grounded Abstractions [68.24080871981869]
  This report shows how representation learning can be used to induce concepts from raw data. The main technical goal of this report is to show how techniques from representation learning can be married with a lattice-theoretic formulation of conceptual spaces.
  arXiv  Detail & Related papers  (2021-01-13T15:22:01Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.