Restricted Boltzmann machines are energy models made of a visible and a hidden layer. We identify an effective energy function describing the zero-temperature landscape on the visible units and depending only on the tail behaviour of the hidden layer prior distribution. Studying the location of the local minima of such an energy function, we show that the ability of a restricted Boltzmann machine to reconstruct a random pattern depends indeed only on the tail of the hidden prior distribution. We find that hidden priors with strictly super-Gaussian tails give only a logarithmic loss in pattern retrieval, while an efficient retrieval is much harder with hidden units with strictly sub-Gaussian tails; if the hidden prior has Gaussian tails, the retrieval capability is determined by the number of hidden units (as in the Hopfield model).

翻译：受限玻尔兹曼机是由可见层与隐藏层构成的能量模型。我们定义了一个描述可见单元零温度景观的有效能量函数，该函数仅取决于隐藏层先验分布的尾部特征。通过研究该能量函数局部极小值的位置，我们证明受限玻尔兹曼机重建随机模式的能力确实仅依赖于隐藏先验分布的尾部形态。研究发现：当隐藏先验具有严格超高斯尾部时，模式检索仅产生对数级损失；而使用严格次高斯尾部的隐藏单元时，高效检索将变得极为困难；若隐藏先验具有高斯尾部，其检索能力则由隐藏单元数量决定（类似于Hopfield模型）。