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Pattern Completion in Symmetric Threshold-Linear Networks

机译:对称阈值线性网络中的模式完成

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摘要

Threshold-linear networks are a common class of firing rate models that describe recurrent interactions among neurons. Unlike their linear counterparts, these networks generically possess multiple stable fixed points (steady states), making them viable candidates for memory encoding and retrieval. In this work, we characterize stable fixed points of general threshold-linear networks with constant external drive and discover constraints on the coexistence of fixed points involving different subsets of active neurons. In the case of symmetric networks, we prove the following antichain property: if a set of neurons is the support of a stable fixed point, then no proper subset or superset of can support a stable fixed point. Symmetric threshold-linear networks thus appear to be well suited for pattern completion, since the dynamics are guaranteed not to get stuck in a subset or superset of a stored pattern. We also show that for any graph G, we can construct a network whose stable fixed points correspond precisely to the maximal cliques of G. As an application, we design network decoders for place field codes and demonstrate their efficacy for error correction and pattern completion. The proofs of our main results build on the theory of permitted sets in threshold-linear networks, including recently developed connections to classical distance geometry.
机译:阈值线性网络是一类常见的点火速率模型,用于描述神经元之间的反复相互作用。与它们的线性对应物不同,这些网络通常具有多个稳定的固定点(稳态),使其成为可行的内存编码和检索候选对象。在这项工作中,我们刻画了具有恒定外部驱动力的一般阈值线性网络的稳定不动点,并发现了涉及活跃神经元不同子集的不动点并存的约束。在对称网络的情况下,我们证明了以下反链特性:如果一组神经元是稳定定点的支持,则没有适当的子集或超集可以支持稳定定点。因此,对称阈值线性网络似乎非常适合模式完成,因为可以保证动态不会陷入存储模式的子集或超集中。我们还表明,对于任何图G,我们都可以构建一个稳定的固定点正好对应于G的最大集团的网络。作为一种应用,我们设计了用于位置场代码的网络解码器,并展示了其对纠错和图案完成的功效。我们主要结果的证明建立在阈值线性网络的允许集理论上,包括最近开发的与经典距离几何的连接。

著录项

  • 来源
    《Neural computation》 |2016年第12期|2825-2852|共28页
  • 作者单位

    Department of Mathematics Pennsylvania State University University Park PA 16802 U.S.A. ccurto@psu.edu;

    Department of Mathematics Pennsylvania State University University Park PA 16802 U.S.A. and School of Mathematical Sciences University of Northern Colorado Greeley CO 80639 U.S.A. katherine.morrison@unco.edu;

  • 收录信息 美国《科学引文索引》(SCI);美国《化学文摘》(CA);
  • 原文格式 PDF
  • 正文语种 eng
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