论文标题
带有限制的玻尔兹曼机器的模式重建
Pattern reconstruction with restricted Boltzmann machines
论文作者
论文摘要
受限的玻尔兹曼机器是由可见和隐藏层制成的能量模型。我们确定了一个有效的能量函数，该功能描述了可见单元上的零温度景观，并且仅取决于隐藏层先前分布的尾巴行为。在研究这种能量函数的局部最小值的位置时，我们表明，受限的玻尔兹曼机器重建随机模式的能力确实仅取决于隐藏的先前分布的尾巴。我们发现，具有严格超级高斯尾巴的隐藏先验只会在模式检索中造成对数损失，而有效的检索则更难，而隐藏的单元则具有严格的次高斯尾巴。如果隐藏的先验具有高斯尾巴，则检索功能由隐藏单元的数量（如Hopfield模型）确定。
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).
