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Local Homeostatic Regulation of the Spectral Radius of Echo-State Networks
Frontiers in Computational Neuroscience ( IF 3.2 ) Pub Date : 2021-01-25 , DOI: 10.3389/fncom.2021.587721
Fabian Schubert 1 , Claudius Gros 1
Affiliation  

Recurrent cortical networks provide reservoirs of states that are thought to play a crucial role for sequential information processing in the brain. However, classical reservoir computing requires manual adjustments of global network parameters, particularly of the spectral radius of the recurrent synaptic weight matrix. It is hence not clear if the spectral radius is accessible to biological neural networks. Using random matrix theory, we show that the spectral radius is related to local properties of the neuronal dynamics whenever the overall dynamical state is only weakly correlated. This result allows us to introduce two local homeostatic synaptic scaling mechanisms, termed flow control and variance control, that implicitly drive the spectral radius toward the desired value. For both mechanisms the spectral radius is autonomously adapted while the network receives and processes inputs under working conditions. We demonstrate the effectiveness of the two adaptation mechanisms under different external input protocols. Moreover, we evaluated the network performance after adaptation by training the network to perform a time-delayed XOR operation on binary sequences. As our main result, we found that flow control reliably regulates the spectral radius for different types of input statistics. Precise tuning is however negatively affected when interneural correlations are substantial. Furthermore, we found a consistent task performance over a wide range of input strengths/variances. Variance control did however not yield the desired spectral radii with the same precision, being less consistent across different input strengths. Given the effectiveness and remarkably simple mathematical form of flow control, we conclude that self-consistent local control of the spectral radius via an implicit adaptation scheme is an interesting and biological plausible alternative to conventional methods using set point homeostatic feedback controls of neural firing.



中文翻译:

回波态网络频谱半径的局部稳态调节

循环皮质网络提供了状态库,这些状态库被认为在大脑的顺序信息处理中发挥着至关重要的作用。然而,经典的储层计算需要手动调整全局网络参数,特别是循环突触权重矩阵的谱半径。因此,尚不清楚生物神经网络是否可以访问光谱半径。使用随机矩阵理论,我们表明,当整体动态状态仅弱相关时,谱半径与神经元动态的局部特性相关。这一结果使我们能够引入两种局部稳态突触缩放机制,称为流量控制和方差控制,它们隐式地将谱半径驱动到所需值。对于这两种机制,当网络在工作条件下接收和处理输入时,频谱半径会自动适应。我们证明了两种适应机制在不同外部输入协议下的有效性。此外,我们通过训练网络对二进制序列执行延时异或运算来评估适应后的网络性能。作为我们的主要结果,我们发现流量控制可以可靠地调节不同类型的输入统计数据的谱半径。然而,当神经间相关性很大时,精确调整就会受到负面影响。此外,我们发现在各种输入强度/方差下任务表现都是一致的。然而,方差控制并没有以相同的精度产生所需的光谱半径,在不同的输入强度上不太一致。考虑到流量控制的有效性和非常简单的数学形式,我们得出结论,通过隐式适应方案对光谱半径进行自洽局部控制是使用神经放电设定点稳态反馈控制的传统方法的一种有趣且生物学上合理的替代方法。

更新日期:2021-02-24
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