Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not directly accessible due to its computational complexity, and Markov-chain sampling is invoked to analyze the learned probability distribution. For training and eventual applications, it is thus desirable to have a sampler that is both accurate and efficient. We highlight that these two goals generally compete with each other and cannot be achieved simultaneously. More specifically, we identify and quantitatively characterize three regimes of RBM learning: independent learning, where the accuracy improves without losing efficiency; correlation learning, where higher accuracy entails lower efficiency; and degradation, where both accuracy and efficiency no longer improve or even deteriorate. These findings are based on numerical experiments and heuristic arguments.

受限玻尔兹曼机 (RBM) 为无监督机器学习提供了一种通用架构，原则上可以以任意精度逼近任何目标概率分布。然而，RBM ​​模型由于其计算复杂性通常不能直接访问，并且调用马尔可夫链采样来分析学习的概率分布。因此，对于训练和最终应用，需要一个既准确又高效的采样器。我们强调，这两个目标通常相互竞争，不能同时实现。更具体地说，我们确定并定量描述了 RBM 学习的三种方案：独立学习，其中准确性提高而不损失效率；相关学习，更高的准确性需要更低的效率；和退化，准确性和效率都不再提高甚至恶化。这些发现基于数值实验和启发式论证。