Emergence of low noise frustrated states in E/I balanced neural networks

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• 作者：I. Recio ^{numero.doce@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; J.J. Torres ; ^{jtorres@onsager.ugr.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Balanced neural networks ; Frustrated activity states ; Up/Down neural states
• 刊名：Neural Networks
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：84
• 期：Complete
• 页码：91-101
• 全文大小：1462 K

文摘

We study emerging phenomena in binary neural networks where, with a probability 11f9f00e9c8d10c7de3d528f37fb" title="Click to view the MathML source">c$c$ synaptic intensities are chosen according with a Hebbian prescription, and with probability (1−c)$(1-c)$ there is an extra random contribution to synaptic weights. This new term, randomly taken from a Gaussian bimodal distribution, balances the synaptic population in the network so that one has 80%−20%$80\%-20\%$ relation in E/I population ratio, mimicking the balance observed in mammals cortex. For some regions of the relevant parameters, our system depicts standard memory (at low temperature) and non-memory attractors (at high temperature). However, as 11f9f00e9c8d10c7de3d528f37fb" title="Click to view the MathML source">c$c$ decreases and the level of the underlying noise also decreases below a certain temperature T_t$T_t$, a kind of memory-frustrated state, which resembles spin-glass behavior, sharply emerges. Contrary to what occurs in Hopfield-like neural networks, the frustrated state appears here even in the limit of the loading parameter α→0$\alpha \to 0$. Moreover, we observed that the frustrated state in fact corresponds to two states of non-vanishing activity uncorrelated with stored memories, associated, respectively, to a high activity or Up state and to a low activity or Down state. Using a linear stability analysis, we found regions in the space of relevant parameters for locally stable steady states and demonstrated that frustrated states coexist with memory attractors below T_t$T_t$. Then, multistability between memory and frustrated states is present for relatively small 11f9f00e9c8d10c7de3d528f37fb" title="Click to view the MathML source">c$c$, and metastability of memory attractors can emerge as 11f9f00e9c8d10c7de3d528f37fb" title="Click to view the MathML source">c$c$ decreases even more. We studied our system using standard mean-field techniques and with Monte Carlo simulations, obtaining a perfect agreement between theory and simulations. Our study can be useful to explain the role of synapse heterogeneity on the emergence of stable Up and Down states not associated to memory attractors, and to explore the conditions to induce transitions among them, as in sleep–wake transitions.