Restricted Boltzmann Machine (RBM) is an energy-based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate the exact gradient of the log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), where obtaining samples is faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results of RBM trained using quantum annealing are compared with the CD-based method. The performance of the two approaches is compared with respect to the classification accuracies, image reconstruction, and log-likelihood results. The classification accuracy results indicate comparable performances of the two methods. Image reconstruction and log-likelihood results show improved performance of the CD-based method. It is shown that the samples obtained from quantum annealer can be used to train an RBM on a 64-bit `bars and stripes' dataset with classification performance similar to an RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer could be useful as it eliminates computationally expensive MCMC steps of CD.

中文翻译：

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使用 D-Wave 量子退火器训练受限玻尔兹曼机

受限玻尔兹曼机 (RBM) 是一种基于能量的无向图模型。它通常用于无监督和有监督的机器学习。通常，RBM ​​是使用对比散度 (CD) 进行训练的。但是，使用 CD 进行训练很慢，并且无法估计对数似然成本函数的确切梯度。在这项工作中，使用量子退火器 (D-Wave 2000Q) 计算了 RBM 梯度学习的模型期望，其中获取样本比 CD 中使用的马尔可夫链蒙特卡罗 (MCMC) 更快。将使用量子退火训练的 RBM 的训练和分类结果与基于 CD 的方法进行比较。两种方法的性能在分类精度、图像重建和对数似然结果方面进行了比较。分类准确率结果表明两种方法的性能相当。图像重建和对数似然结果表明基于 CD 的方法的性能有所提高。结果表明，从量子退火器获得的样本可用于在 64 位“条形”数据集上训练 RBM，其分类性能类似于用 CD 训练的 RBM。尽管基于 CD 的训练显示了改进的学习性能，但使用量子退火器的训练可能很有用，因为它消除了计算上昂贵的 CD MCMC 步骤。分类性能类似于用 CD 训练的 RBM 的数据集。尽管基于 CD 的训练显示了改进的学习性能，但使用量子退火器的训练可能很有用，因为它消除了计算上昂贵的 CD MCMC 步骤。分类性能类似于用 CD 训练的 RBM 的数据集。尽管基于 CD 的训练显示了改进的学习性能，但使用量子退火器的训练可能很有用，因为它消除了计算上昂贵的 CD MCMC 步骤。