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Ibon Recio

We study here the emerging phenomena of an auto-associative binary
neural network where, with a probability
$c$
we added a new random
contribution to the traditional Hebbian synaptic weights. This new
term, randomly taken from a Gaussian bimodal distribution, balances
the population of synapses in our network so that we have
$80\%-20\%$
relation in E/I population ratio, imitating the balance observed in
mammals cortex. For some regions of the relevant parameters, our system
depicts standard memory and non-memory attractors as in the Hopfield
model, but as
$c$
increases the system underlies a reentrant first
order transition when the level of the underlying noise decreases
below a certain value. This results in a low noise phase where memory
disappear and where a frustrated state similar to the spin-glass phase
emerges. However and contrary to what it is expected in Hopfield model,
this low noise frustrated state occurs even in the limit of the loading
parameter
$\alpha \to 0$
which seems intriguing. Attending
to mean firing rate, we observed that the phase of frustrated memory
results in two states of non-vanishing activity, one with high activity
or Up state and the other with low activity or Down state. Using linear
stability analysis we have studied the regions in the space of relevant
parameters where different steady states are locally stable. We also
computed region where metastability emerges. We have studied in deep
our system, both theoritecally using standard mean-field techniques,
and by means of Montecarlo simulations, obtaining an almost perfect
agreement between theory and simulations. The model can be useful
to explain the emergence of Up and Down states similar to those in
mammalian cortex and to explore the conditions to induce transitions
among them.