Restricted Boltzmann machines (RBMs) are energy-based neural-networks which are commonly used as the building blocks for deep architectures neural architectures. In this work, we derive a deterministic framework for the training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer (TAP) mean-field approximation of widely-connected systems with weak interactions coming from spin-glass theory. While the TAP approach has been extensively studied for fully-visible binary spin systems, our construction is generalized to latent-variable models, as well as to arbitrarily distributed real-valued spin systems with bounded support. In our numerical experiments, we demonstrate the effective deterministic training of our proposed models and are able to show interesting features of unsupervised learning which could not be directly observed with sampling. Additionally, we demonstrate how to utilize our TAP-based framework for leveraging trained RBMs as joint priors in denoising problems.

中文翻译：

---

使用受限的Boltzmann机器进行无监督学习的确定性和通用框架

受限玻尔兹曼机（RBM）是基于能量的神经网络，通常用作深度体系结构神经体系结构的构建基块。在这项工作中，我们基于自旋玻璃理论的弱相互作用的广泛连接系统的Thouless-Anderson-Palmer（TAP）平均场近似，得出了用于RBM的训练，评估和使用的确定性框架。尽管已对全可见的二元自旋系统进行了TAP方法的广泛研究，但我们的构造已推广到潜变量模型以及具有有限支持的任意分布实值自旋系统。在我们的数值实验中 我们展示了我们提出的模型的有效确定性训练，并且能够展示出无监督学习的有趣特征，这些特征无法通过采样直接观察到。此外，我们演示了如何利用基于TAP的框架来利用受过训练的RBM作为解决问题的先决条件。