同步和冗余：对神经学习和决策的鲁棒性的影响
Synchronization and Redundancy: Implications for Robustness of Neural Learning and Decision Making
摘要：
大脑中的学习和决策是对生存至关重要的关键过程，但这些过程是由非理想的生物构建模块实现的，可能会造成重大错误。我们定量地探讨大脑如何利用两种普遍存在的机制，冗余和同步，来应对这种固有的错误来源。特别是，我们考虑一个神经过程，其目标是通过实现非线性梯度动力学来学习决策函数。然而，动态，假设被破坏的扰动建模的错误，这可能是由于生物学的限制，固有的神经元噪声，和不完善的测量。我们发现，错误，以及相关的不确定性周围的学习解决方案，可以控制在很大程度上通过权衡多个冗余神经系统之间的同步强度对噪声幅度。这种冗余系统之间的耦合的影响是量化的网络拉普拉斯算子的频谱，我们讨论的作用，网络拓扑结构的同步和减少噪声的影响。一系列的情况下，我们的模型在脑科学中出现的机制进行了讨论，我们提请注意实验证据表明，能够实现感兴趣的计算在这里可以发现在几个尺度上的皮层电路。最后，模拟比较理论界的相关经验量表明，我们得到的理论估计可以是紧的。
英文摘要：
Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by non-ideal biological building blocks which can impose significant error. We explore quantitatively how the brain might cope with this inherent source of error by taking advantage of two ubiquitous mechanisms, redundancy and synchronization. In particular we consider a neural process whose goal is to learn a decision function by implementing a nonlinear gradient dynamics. The dynamics, however, are assumed to be corrupted by perturbations modeling the error which might be incurred due to limitations of the biology, intrinsic neuronal noise, and imperfect measurements. We show that error, and the associated uncertainty surrounding a learned solution, can be controlled in large part by trading off synchronization strength among multiple redundant neural systems against the noise amplitude. The impact of the coupling between such redundant systems is quantified by the spectrum of the network Laplacian, and we discuss the role of network topology in synchronization and in reducing the effect of noise. A range of situations in which the mechanisms we model arise in brain science are discussed, and we draw attention to experimental evidence suggesting that cortical circuits capable of implementing the computations of interest here can be found on several scales. Finally, simulations comparing theoretical bounds to the relevant empirical quantities show that the theoretical estimates we derive can be tight.
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