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

TL;DR

This paper investigates how a combination of Hebbian learning and random Gaussian contributions to synaptic weights in neural networks leads to the emergence of frustrated, spin-glass-like states that coexist with memory states, especially at low temperatures.

Contribution

It introduces a model with mixed synaptic weights that mimics cortical E/I balance and reveals the emergence of frustrated states even at zero loading, expanding understanding of neural network dynamics.

Findings

Frustrated states emerge below a critical temperature T_t.

Frustrated states coexist with memory attractors in certain parameter regimes.

The model's predictions are validated by both mean-field analysis and Monte Carlo simulations.

Abstract

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 ...