论文标题
迈向揭示多稳定神经网络的结构的一步
A Step Towards Uncovering The Structure of Multistable Neural Networks
论文作者
论文摘要
我们研究了复发性神经网络中的连通性如何决定并由网络活动的多稳态解决方案确定。为了获得分析性障碍性，我们让神经激活成为非平滑的重力步进功能。这种非线性将相位空间划分为具有不同但线性动力学的区域。在每个区域中，存在一个稳定的平衡状态，或者网络活动流到该地区的外部。稳定状态通过其在突触重量矩阵上的半阳性约束来识别。限制可以通过它们对连接的迹象或优势的影响来隔离。得出并证明了网络拓扑，符号稳定性，权重矩阵分解，模式完成和模式耦合的确切结果。我们的工作可能为更复杂的复发神经网络奠定了基础。
We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function. This nonlinearity partitions the phase space into regions with different, yet linear dynamics. In each region either a stable equilibrium state exists, or network activity flows to outside of the region. The stable states are identified by their semipositivity constraints on the synaptic weight matrix. The restrictions can be separated by their effects on the signs or the strengths of the connections. Exact results on network topology, sign stability, weight matrix factorization, pattern completion and pattern coupling are derived and proven. Our work may lay the foundation for multistability in more complex recurrent neural networks.
