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We study emerging phenomena in binary neural networks where, with aprobability c synaptic intensities are chosen according with a Hebbianprescription, and with probability (1-c) there is an extra random contributionto synaptic weights. This new term, randomly taken from a Gaussian bimodaldistribution, balances the synaptic population in the network so that one has80-20 relation in E/I population ratio, mimicking the balance observed inmammals cortex. For some regions of the relevant parameters, our system depictsstandard memory (at low temperature) and non-memory attractors (at hightemperature). However, as c decreases and the level of the underlying noisealso decreases below a certain temperature T_t, a kind of memory-frustratedstate, which resembles spin-glass behavior, sharply emerges. Contrary to whatoccurs in Hopfield-like neural networks, the frustrated state appears here evenin the limit of the loading parameter alpha-->0. Moreover, we observed that thefrustrated state in fact corresponds to two states of non-vanishing activityuncorrelated with stored memories, associated, respectively, to a high activityor Up state and to a low activity or Down state. Using a linear stabilityanalysis, we found regions in the space of relevant parameters for locallystable steady states and demonstrated that frustrated states coexist withmemory attractors below T_t. Then, multistability between memory and frustratedstates is present for relatively small c, and metastability of memoryattractors can emerge as c decreases even more. We studied our system usingstandard mean-field techniques and with Monte Carlo simulations, obtaining aperfect agreement between theory and simulations. Our study can be useful to...

Emergence of low noise \emph{frustrated} states in E/I balanced neural networks