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Collective Stability of Networks of Winner-Take-All Circuits

机译：胜者通吃电路网络的集体稳定性

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摘要

The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual cortex are consistent with the recurrent excitation and inhibitory feedback required for cooperative-competitive circuits such as the soft winner-take-all (WTA). WTA circuits offer interesting computational properties such as selective amplification, signal restoration, and decision making. But these properties depend on the signal gain derived from positive feedback, and so there is a critical trade-off between providing feedback strong enough to support the sophisticated computations while maintaining overall circuit stability. The issue of stability is all the more intriguing when one considers that the WTAs are expected to be densely distributed through the superficial layers and that they are at least partially interconnected. We consider how to reason about stability in very large distributed networks of such circuits. We approach this problem by approximating the regular cortical architecture as many interconnected cooperative-competitive modules. We demonstrate that by properly understanding the behavior of this small computational module, one can reason over the stability and convergence of very large networks composed of these modules. We obtain parameter ranges in which the WTA circuit operates in a high-gain regime, is stable, and can be aggregated arbitrarily to form large, stable networks. We use nonlinear contraction theory to establish conditions for stability in the fully nonlinear case and verify these solutions using numerical simulations. The derived bounds allow modes of operation in which the WTA network is multistable and exhibits state-dependent persistent activities. Our approach is sufficiently general to reason systematically about the stability of any network, biological or technological, composed of networks of small modules that express competition through shared inhibition.
机译：新皮层具有明显统一的神经元组织，表明在整个范围内都采用了共同的加工原理。特别是，在视觉皮层表层观察到的连通性模式与诸如软性获胜者通吃（WTA）之类的竞争性竞争性电路所需的循环激励和抑制性反馈一致。 WTA电路提供了有趣的计算属性，例如选择性放大，信号恢复和决策。但是这些特性取决于从正反馈中获得的信号增益，因此在提供足够强大的反馈以支持复杂的计算同时保持总体电路稳定性之间存在一个重大的折衷。当人们认为WTA期望通过表层密集分布并且它们至少部分互连时，稳定性的问题就更加令人着迷。我们考虑如何推理这种电路的大型分布式网络中的稳定性。我们通过将常规皮质结构近似为许多相互关联的协作竞争模块来解决此问题。我们证明，通过正确理解这一小型计算模块的行为，可以推断出由这些模块组成的非常大的网络的稳定性和收敛性。我们获得WTA电路在高增益状态下运行，稳定并且可以任意汇总以形成大型稳定网络的参数范围。我们使用非线性收缩理论来建立完全非线性情况下的稳定性条件，并使用数值模拟来验证这些解决方案。派生的边界允许WTA网络是多稳态并表现出状态相关的持续活动的操作模式。我们的方法具有足够的通用性，可以系统地推断由小模块网络组成的，通过共享抑制表达竞争的任何生物或技术网络的稳定性。

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  • 来源
    《Neural computation》 |2011年第3期|p.735-773|共39页
  • 作者

    Ueli Rutishauser; Rodney J. Douglas; Jean-Jacques Slotine;

  • 作者单位

    Department of Neural Systems and Coding, Max Planck Institute for Brain Research, Frankfurt am Main, Hessen 60528, Germany;

    Institute of Neuroinformatics, University and ETH Zurich, Zurich, 8057, Switzerland;

    Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge,MA 02142, U.S.A.;

  • 收录信息 美国《科学引文索引》(SCI);美国《化学文摘》(CA);
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