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arXiv:2303.12352

Training Multilayer Perceptrons by Sampling with Quantum Annealers

Frances Fengyi Yang, Michele Sasdelli, Tat-Jun Chin

Published Mar 22, 2023• 0 citations
arXivHTMLPDF

Abstract

A successful application of quantum annealing to machine learning is training restricted Boltzmann machines (RBM). However, many neural networks for vision applications are feedforward structures, such as multilayer perceptrons (MLP). Backpropagation is currently the most effective technique to train MLPs for supervised learning. This paper aims to be forward-looking by exploring the training of MLPs using quantum annealers. We exploit an equivalence between MLPs and energy-based models (EBM), which are a variation of RBMs with a maximum conditional likelihood objective. This leads to a strategy to train MLPs with quantum annealers as a sampling engine. We prove our setup for MLPs with sigmoid activation functions and one hidden layer, and demonstrated training of binary image classifiers on small subsets of the MNIST and Fashion-MNIST datasets using the D-Wave quantum annealer. Although problem sizes that are feasible on current annealers are limited, we obtained comprehensive results on feasible instances that validate our ideas. Our work establishes the potential of quantum computing for training MLPs.

DOI
10.48550/arxiv.2303.12352

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In Deep Learning, a well-known approach for training a Deep Neural Network starts by training a generative Deep Belief Network model, typically using Contrastive Divergence (CD), then fine-tuning the weights using backpropagation or other discriminative techniques. However, the generative training can be time-consuming due to the slow mixing of Gibbs sampling. We investigated an alternative approach that estimates model expectations of Restricted Boltzmann Machines using samples from a D-Wave quantum annealing machine. We tested this method on a coarse-grained version of the MNIST data set. In our tests we found that the quantum sampling-based training approach achieves comparable or better accuracy with significantly fewer iterations of generative training than conventional CD-based training. Further investigation is needed to determine whether similar improvements can be achieved for other data sets, and to what extent these improvements can be attributed to quantum effects.
Computer vision has a wide range of applications from medical image analysis to robotics. Over the past few years, the field has been transformed by machine learning and stands to benefit from potential advances in quantum computing. The main challenge for processing images on current and near-term quantum devices is the size of the data such devices can process. Images can be large, multidimensional and have multiple color channels. Current machine learning approaches to computer vision that exploit quantum resources require a significant amount of manual pre-processing of the images in order to be able to fit them onto the device. This paper proposes a framework to address the problem of processing large scale data on small quantum devices. This framework does not require any dataset-specific processing or information and works on large, grayscale and RGB images. Furthermore, it is capable of scaling to larger quantum hardware architectures as they become available. In the proposed approach, a classical autoencoder is trained to compress the image data to a size that can be loaded onto a quantum device. Then, a Restricted Boltzmann Machine (RBM) is trained on the D-Wave device using the compressed data, and the weights from the RBM are then used to initialize a neural network for image classification. Results are demonstrated on two MNIST datasets and two medical imaging datasets.
Energy-based models provide a natural bridge between statistical physics and machine learning by representing data through structured energy landscapes. Boltzmann machines are a particularly compelling class of such models for capturing complex interactions among latent variables, but their use in modern generative learning has been limited by the classical intractability of sampling from general (non-restricted) Boltzmann distributions. Here we develop a quantum-annealing-based framework that enables variational autoencoders with general Boltzmann priors. The framework employs three complementary annealing modes tailored to different stages of learning and deployment: diabatic quantum annealing provides unbiased Boltzmann samples for efficient training, slower annealing concentrates samples near low-energy configurations of the learned prior for unconditional generation, and conditional annealing with external fields steers the learned energy landscape toward attribute-specific regions for conditional generation and semantic editing. Using up to 2000 qubits on a D-Wave Advantage2 processor, we demonstrate stable training and high-quality generation on MNIST, Fashion-MNIST, and CelebA, achieving faster convergence and lower reconstruction loss than a Gaussian-prior VAE with the same encoder-decoder architecture. Beyond generation, the learned energy function provides out-of-distribution detection signals that add discriminative power beyond reconstruction loss. We demonstrate that these scores separate in-distribution samples from held-out digit classes in one-class MNIST experiments and improve the detection of market regime shifts in financial data. These results establish quantum annealing as a practical and controllable physical mechanism for energy-based representation learning and generative modeling beyond the reach of tractable classical approaches.
Restricted Boltzmann machines are common machine learning models that can utilize quantum annealing devices in their training processes as quantum samplers. While this approach has shown promise as an alternative to classical sampling methods, the limitations of quantum annealing hardware, such as the number of qubits and the lack of connectivity between the qubits, still pose a barrier to wide-scale adoption. We propose the use of multiple software techniques such as dropout method, passive labeling, and parallelization techniques for addressing these hardware limitations. The study found that using these techniques along with quantum sampling showed comparable results to its classical counterparts in certain contexts, while in others the increased complexity of the sampling process hindered the performance of the trained models. This means that further research into the behavior of quantum sampling needs to be done to apply quantum annealing to training tasks of more complicated RBM models.