Pattern Completion in Symmetric Threshold-Linear Networks
Pattern Completion in Symmetric Threshold-Linear Networks
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DOI：
10.1162/neco_a_00869
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发表时间：
2016-12-01
影响因子：
2.9
通讯作者：
Morrison, Katherine
中科院分区：
文献类型：
--
作者：
Curto, Carina;Morrison, Katherine
阈值线性网络是一类常见的放电速率模型，描述神经元之间的循环相互作用。与线性网络不同，这些网络通常具有多个稳定的不动点（稳定状态），这使它们成为记忆编码和检索的可行候选者。在这项工作中，我们描述了具有恒定外部驱动的一般阈值线性网络的稳定不动点，并发现了涉及不同活动神经元子集的不动点共存的约束。在对称网络的情况下，我们证明了以下反链性质：如果一组神经元是稳定不动点的支持，则没有合适的子集或超集可以支持稳定不动点。因此，对称阈值-线性网络似乎非常适合模式补全，因为动态保证不会卡在存储模式的子集或超集中。我们还证明了对于任意图G，我们都可以构造一个网络，其稳定不动点精确对应于G的最大团。作为应用，我们设计了位置域码的网络解码器，并证明了其纠错和补全的有效性。我们的主要结果的证明建立在阈值线性网络的允许集理论的基础上，包括最近发展到经典距离几何的联系。
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.