  We study emerging phenomena in binary neural networks where, with a
probability c synaptic intensities are chosen according with a Hebbian
prescription, and with probability (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 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 c decreases and the level of the underlying noise
also decreases below a certain temperature 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 alpha-->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. Then, multistability between memory and frustrated
states is present for relatively small c, and metastability of memory
attractors can emerge as 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
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