Several variants of a stochastic local search process for constructing the synaptic weights of an Ising perceptron are studied. In this process, binary patterns are sequentially presented to the Ising perceptron and are then learned as the synaptic weight configuration is modified through a chain of single- or double-weight flips within the compatible weight configuration space of the earlier learned patterns. This process is able to reach a storage capacity of $α\approx 0.63$ for pattern length N = 101 and $α\approx 0.41$ for N = 1001. If in addition a relearning process is exploited, the learning performance is further improved to a storage capacity of $α\approx 0.80$ for N = 101 and $α\approx 0.42$ for N=1001. We found that, for a given learning task, the solutions constructed by the random walk learning process are separated by a typical Hamming distance, which decreases with the constraint density $α$ of the learning task; at a fixed value of $α$, the width of the Hamming distance distributions decreases with $N$.
Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments
我们研究了各种一维无序模型中动力学量的分布，这些模型的临界行为由无限随机不动点描述。在{ \it无序接触过程}中，在固定随机环境中定义的猝灭生存概率$\mathcal{P}(t)$在临界点处表现出多标度性，这意味着当$t\to\infty$时，$\mathcal{P}(t)=t^{-δ}$，其中（环境和时间相关的）指数$δ$具有普适极限分布.利用强无序重整化群方法，在半无限格点的端点处解析地确定了极限分布，发现极限分布是指数分布，而在无限格点处，则基于数值结果，给出了小、大$δ$的极限行为的表达式.用同样的方法，我们还证明了随机环境中的随机游动问题{ \it random walks in random environments}中的猝灭生存概率也是指数极限分布的多尺度问题.此外，还发现{ \it随机横场伊辛链}的自旋-自旋自相关函数在重正化水平上具有与接触过程的生存概率相似的形式.因此，可以建立两个问题中相应的极限分布之间的关系。最后讨论了该模型中自发磁化强度的分布。
