神经网络中的退火——非时齐情形

Annealing in the Neural Network. II. Inhomogeneous Case

本文考虑神经网络经过非时齐退火后的极限行为,我们给出了神经网络经过非时齐退火后的分布,证明了经过非时齐退火后网络在组态空间的一个子集上是遍历的。从而网络经非时齐退火后并不能以概率为1地恢复起一个记忆,进一步地,我们证明了既使只贮存了一个最强的记忆η,网络经非时齐退火仍不能以概率为1地恢复它。

In this paper, the annealing procedure is considered for the neural network evolving as an inhomogeneous Markov chain. The exact distribution of the neural network, after annealing, is obtained. The neural network is ergodic inside a subset of the configuration space of the neural network. We thus conclude that the network, after performing the inhomogeneous annealing, is also incapable of retrieving a memory. It is pointed out that even if only one pattern η is stored strong enough, generally η can not be retrieved with probability one after taking the inbomogeneous annealing.