We show that discrete synaptic weights can be efficiently used for learning
in large scale neural systems, and lead to unanticipated computational
performance. We focus on the representative case of learning random patterns
with binary synapses in single layer networks. The standard statistical
analysis shows that this problem is exponentially dominated by isolated
solutions that are extremely hard to find algorithmically. Here, we introduce a
novel method that allows us to find analytical evidence for the existence of
subdominant and extremely dense regions of solutions. Numerical experiments
confirm these findings. We also show that the dense regions are surprisingly
accessible by simple learning protocols, and that these synaptic configurations
are robust to perturbations and generalize better than typical solutions. These
outcomes extend to synapses with multiple states and to deeper neural
architectures. The large deviation measure also suggests how to design novel
algorithmic schemes for optimization based on local entropy maximization.

本文研究神经系统中的离散型突触权重在学习和优化中的应用，并通过学习随机模式来证明其性能。研究发现，这些离散型突触的特定配置可以通过简单学习协议轻松获得，并对干扰具有稳健性。同时，基于局部熵最大化的大偏差度量也提出了一些新的优化算法方案。

离散突触的神经网络中亚支配稠密区域实现简单学习与高计算性能

Subdominant Dense Clusters Allow for Simple Learning and High  Computational Performance in Neural Networks with Discrete Synapses

We prove rigorously the well-known result of Gardner about the typical
fractional volume of interactions between N spins which solve the problem of
storing a given set of random patterns. The Gardner formula for this volume in
the limit N,p \to \infty, p/N \to \alpha is proven for all values of \alpha.
Besides, we prove a useful criterion of the factorisation of all the
correlation functions for a class of spin glass model.

本文从理论上证明了 Gardner 的熟知结论，即解决给定随机模式存储问题的 N 个自旋相互作用的典型非整体体积。对于所有的 α 值，证明了在极限 N，p→∞，p/N→α 情况下，该体积的 Gardner 公式。此外，我们还针对一类自旋玻璃模型证明了所有相关函数因式分解的有用准则。