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.

翻译：将量子退火成功应用于机器学习的一个典型例子是训练受限玻尔兹曼机（RBM）。然而，许多面向视觉应用的神经网络采用前馈结构，例如多层感知机（MLP）。反向传播是目前监督学习中最有效的MLP训练技术。本文旨在以前瞻性视角探索利用量子退火器训练MLP的方法。我们利用MLP与基于能量的模型（EBM）之间的等价性——EBM是带有最大条件似然目标的RBM变体——提出了一种以量子退火器作为采样引擎来训练MLP的策略。我们为具有sigmoid激活函数和单隐藏层的MLP验证了该框架，并在MNIST和Fashion-MNIST数据集的较小子集上，使用D-Wave量子退火器演示了二值图像分类器的训练。尽管当前退火器可处理的问题规模有限，但我们已在可行实例上获得了全面的结果，验证了我们的构想。本研究证明了量子计算在训练MLP方面的潜力。