神经网络中的退火:Ⅰ.时齐情况

Annealing in the Neural Network, Ⅰ, Homogeneous Case

本文考虑神经网络经过时齐退火后的极限分布,从动力系统的随机扰动的观点出发,我们证明了极限分布将最后集中在吸引子的一个子集上,当网络可逆时,极限分布为该集合上的均匀分布,文中解释了上述现象发生的原因。

In this paper, the annealing procedure is considered for the neural network evolving as a homogeneous Markov chain. From the point of view of the perturbation of a dynamical system, we proved that the invariant measure will concentrate on a subset of attractors. The neural network, undergoing annealing procedure, will uniformly distribute on the subset when the neural network is reversible. The reason why that happens is given.