Theory of Neural Dynamics Group, Max Planck Institute for Brain Research, 60438 Frankfurt, Germany
Proc Natl Acad Sci U S A. 2018 Mar 27;115(13):3464-3469. doi: 10.1073/pnas.1700080115. Epub 2018 Mar 12.
A hallmark of cortical circuits is their versatility. They can perform multiple fundamental computations such as normalization, memory storage, and rhythm generation. Yet it is far from clear how such versatility can be achieved in a single circuit, given that specialized models are often needed to replicate each computation. Here, we show that the stabilized supralinear network (SSN) model, which was originally proposed for sensory integration phenomena such as contrast invariance, normalization, and surround suppression, can give rise to dynamic cortical features of working memory, persistent activity, and rhythm generation. We study the SSN model analytically and uncover regimes where it can provide a substrate for working memory by supporting two stable steady states. Furthermore, we prove that the SSN model can sustain finite firing rates following input withdrawal and present an exact connectivity condition for such persistent activity. In addition, we show that the SSN model can undergo a supercritical Hopf bifurcation and generate global oscillations. Based on the SSN model, we outline the synaptic and neuronal mechanisms underlying computational versatility of cortical circuits. Our work shows that the SSN is an exactly solvable nonlinear recurrent neural network model that could pave the way for a unified theory of cortical function.
皮质电路的一个特点是其多功能性。它们可以执行多种基本计算，如归一化、存储记忆和产生节律。然而，鉴于通常需要专门的模型来复制每个计算，目前尚不清楚如何在单个电路中实现这种多功能性。在这里，我们表明，最初为感觉整合现象（如对比度不变性、归一化和周围抑制）提出的稳定超线性网络（SSN）模型，可以产生工作记忆、持续活动和节律产生的动态皮质特征。我们对 SSN 模型进行了分析，并揭示了在哪些情况下，它可以通过支持两个稳定的稳态来为工作记忆提供基础。此外，我们证明了 SSN 模型可以在输入撤回后维持有限的放电率，并提出了这种持续活动的确切连接条件。此外，我们还表明，SSN 模型可以经历超临界 Hopf 分岔并产生全局振荡。基于 SSN 模型，我们概述了皮质电路计算多功能性的突触和神经元机制。我们的工作表明，SSN 是一个可精确求解的非线性递归神经网络模型，它可能为皮质功能的统一理论铺平道路。
