论文标题
限制性玻尔兹曼机器中学习的动态均值理论
A Dynamical Mean-Field Theory for Learning in Restricted Boltzmann Machines
论文作者
论文摘要
我们定义了一种用于计算受限玻尔兹曼机器中磁化的消息通话算法，该算法是在两部分图上引入的二分图上的模型，该模型作为神经网络模型，用于旋转配置的概率分布。为了建模旋转耦合之间的非平凡统计依赖性，我们假设矩形耦合矩阵是从任意的双重旋转不变的随机矩阵集合中得出的。使用统计力学的动力学功能方法，我们精确地分析了大型系统限制中该算法的动力学。我们证明了算法在稳定性标准下的全局收敛性，并计算渐近收敛速率，显示出与数值模拟的极好一致性。
We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To model nontrivial statistical dependencies between the spins' couplings, we assume that the rectangular coupling matrix is drawn from an arbitrary bi-rotation invariant random matrix ensemble. Using the dynamical functional method of statistical mechanics we exactly analyze the dynamics of the algorithm in the large system limit. We prove the global convergence of the algorithm under a stability criterion and compute asymptotic convergence rates showing excellent agreement with numerical simulations.
