Multiscale analysis of slow-fast neuronal learning models with noise.
Multiscale analysis of slow-fast neuronal learning models with noise.
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DOI：
10.1186/2190-8567-2-13
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发表时间：
2012-11-22
影响因子：
2.3
通讯作者：
Wainrib G
中科院分区：
文献类型：
--
作者：
Galtier M;Wainrib G
本文讨论了时间平均方法的应用程序，经常性的网络噪声神经元进行缓慢和无监督的修改其连接矩阵称为学习。三个时间尺度出现这些模型：（i）快速的神经元动力学，（ii）中间外部输入系统，（iii）缓慢的学习机制。基于这种时间尺度分离，我们应用扩展的数学理论的随机平均与周期性的强迫，以获得一个减少确定性模型的连接动态。我们专注于一类模型，其中活动是线性的，以了解几个学习规则（赫布，跟踪或反对称学习）的特异性。在弱连接状态下，我们研究了平衡连接性，它收集了网络关于输入的全部“知识”。我们开发了一个渐近方法来近似这个平衡。我们发现，对称部分的连接后学习编码的相关结构的输入，而反对称部分对应于输入和它们的时间导数之间的互相关。此外，时间尺度比出现作为一个重要的参数，揭示时间相关性。
This paper deals with the application of temporal averaging methods to recurrent networks of noisy neurons undergoing a slow and unsupervised modification of their connectivity matrix called learning. Three time-scales arise for these models: (i) the fast neuronal dynamics, (ii) the intermediate external input to the system, and (iii) the slow learning mechanisms. Based on this time-scale separation, we apply an extension of the mathematical theory of stochastic averaging with periodic forcing in order to derive a reduced deterministic model for the connectivity dynamics. We focus on a class of models where the activity is linear to understand the specificity of several learning rules (Hebbian, trace or anti-symmetric learning). In a weakly connected regime, we study the equilibrium connectivity which gathers the entire ‘knowledge’ of the network about the inputs. We develop an asymptotic method to approximate this equilibrium. We show that the symmetric part of the connectivity post-learning encodes the correlation structure of the inputs, whereas the anti-symmetric part corresponds to the cross correlation between the inputs and their time derivative. Moreover, the time-scales ratio appears as an important parameter revealing temporal correlations.