arXiv review-Quantum Capsule Networks
Liu et al. (Tsinghua University, Shanghai Qi Zhi Institute)
Artificial Intelligence incorporates two important complementary approaches namely connectionism and symbolism. Connectionism aims to model intelligence as an emergent phenomenon by connecting a large number of neurons while symbolic AI is based on logic, deduction, and higher-level symbolic representations. Recent attempts focus on uniting these two approaches leading to the development of Capsule Networks (CapsNets).
The building block of capsule networks is a so-called ‘capsule’ which is a group of neurons represented by a vector to encode different features of an observable entity such as shape, color, texture, deformation, etc. The information is then transferred through capsule layers hierarchically i.e. the capsule in the higher-level layer is predicated upon its geometric relationship with the lower-level one. This routing mechanism used in CapsNets can preserve the geometric relationships amongst entities and hence have more intrinsic explainability than regular (classical) Neural Networks (NNs). Inspired by the advantages of classical CapsNets, the authors in this paper propose a quantum capsule network (QCapsNet) to explore a potential quantum advantage over the classical counterpart. In QCapsNets, interacting qubits are encapsulated into a capsule as the building block of the architecture.
QCapsNets consist of three crucial components; i) the preprocessing layers, ii) the capsule layers, and iii) the quantum dynamic routing process. Firstly, the model’s input is fed into the preprocessing layers to extract some preliminary features. These features are then encapsulated into several quantum states and then sent to the capsule layers. Inside each capsule, there are a group of interacting qubits building up a sub-quantum neural network (sub-QNN). To enable the feed-forward process between the two adjacent capsule layers, a quantum dynamic routing algorithm is proposed. This routing algorithm operates with a certain routing probability which is dynamically updated with the geometric relationship between capsule layers.
For benchmarking the performance of QCapsNets against classification accuracy, numerical experiments were performed on three proposed models of QCapsNets, each with different sub-QNNs i.e. i) parameterized quantum circuit (PQC), ii) deep quantum feed-forward neural network (DQFNN), and iii) post-selection deep quantum feedforward neural network (post-DQFNN). The QCapsNets is then applied to the classification of handwritten digit images in the MNIST dataset. The results demonstrate that the inaccuracy of all three QCapsNets is reduced to less than 2 × 10^(−2) as the number of parameters increases. Also, the proposed quantum dynamic routing algorithm is able to evaluate the distance measure of quantum states in parallel, and thus is suggested to achieve an exponential speedup over its classical counterpart, given the same number of parameters. No rigorous proof has been established with this regard though.
Furthermore, the work tests the efficiency of QCapsNets in making critical decisions. To achieve this, the QCapsNet is attached to a classical encoder (CNN) and a classical decoder (feed-forward network). The whole network is used to reconstruct the input image from the MNIST dataset. The results demonstrate that the potential to encode information in each capsule seems to grow close to exponentially, just as the Hilbert space grows exponentially with respect to the number of qubits, implying a potential for quantum advantage compared to classical CapsNets.
This work suggests QCapsNets as an efficient approach demonstrating state-of-the-art accuracy among quantum classifiers. It is claimed that by means of geometric relationships, QCapsNets can capture the essential features of the input data, and then encapsulate them into the output capsule of which one specific subspace could correspond to a human-understandable feature of the input data.
QCapsNets can act as guide towards explainable quantum artificial intelligence, with some potential directions to explore being consideration of other distance measures to quantify the geometric relationships between capsule states, and exploration of the robustness of QCapsNets against adversarial perturbations as compared to traditional quantum classifiers.
Originally published at https://quandco.com.
