论文标题
密集的关联记忆中的公差与突触噪声
Tolerance versus synaptic noise in dense associative memories
论文作者
论文摘要
联想神经网络的检索能力可能会因不同种类的噪声而损害：快速噪声（这使神经元更容易容易发生失败），缓慢的噪声（由于存储的记忆中的干扰）和突触噪声（由于学习过程中可能存在的缺陷或存储阶段）。在这项工作中，我们考虑了密集的关联神经网络，在没有快速噪声的情况下，神经元可以在$ p $上相互作用，我们研究了缓慢和突触噪声的相互作用。特别是，我们利用关联神经网络和受限的玻尔兹曼机器之间的二元性，分析了损坏的信息，不完美的学习和存储错误的效果。对于$ p = 2 $（对应于Hopfield模型），如果记忆的数量$ k $ scales作为网络大小，则任何突触噪声中断的源。对于$ p> 2 $，在相对较低的载荷制度$ k \ sim n $中，突触噪声可容忍至一定界限，具体取决于结构的密度。
The retrieval capabilities of associative neural networks can be impaired by different kinds of noise: the fast noise (which makes neurons more prone to failure), the slow noise (stemming from interference among stored memories), and synaptic noise (due to possible flaws during the learning or the storing stage). In this work we consider dense associative neural networks, where neurons can interact in $p$-plets, in the absence of fast noise, and we investigate the interplay of slow and synaptic noise. In particular, leveraging on the duality between associative neural networks and restricted Boltzmann machines, we analyze the effect of corrupted information, imperfect learning and storing errors. For $p=2$ (corresponding to the Hopfield model) any source of synaptic noise breaks-down retrieval if the number of memories $K$ scales as the network size. For $p>2$, in the relatively low-load regime $K \sim N$, synaptic noise is tolerated up to a certain bound, depending on the density of the structure.
