Excitatory and Inhibitory balance in Recurrent Networks

Abstract

Balanced states are theoretical models of a balance or ratio of excitation and inhibition of neurons. The dynamical patterns of networks that contain these excitatory and inhibitory neurons are characterized by the feed forward connections are the spatio-temporal patterns involved in odour representation and memory. The existing models for EI balance look at feed-forward connections, but recurrent network connections are widespread in the brain and we try to understand how the balance is achieved in recurrent networks. Excitatory- inhibitory balance is thought to play an important role in regulating the dynamic range of the network, and in preferentially gating incoming inputs. Balanced states is known to maximize the coding capacity of a network, i.e. the states of the network become more stable and more states become accessible. The idea is that having a balance gave the maximum number of potential states(Chowdhary and Assisi, 2019). The specific patterns that a network generates is constrained by the topology of the network and the number of such patterns that are stable is maximised when excitation and inhibition are balanced, there are a large number of states and the number of possible solutions is maximum when balanced. The recurrent network connectivity in the motor cortex is used to operate for generating the muscle activation patterns(Capaday et al., 2009). Research has shown that recurrent network connections are widespread in the brain. Here we investigate about the different properties and analytical models of the neurons in recurrent networks in their balanced states. We also try to make derivatives of sudoku model and try to get more stable solutions compared to that of others. We also arrive at some interesting results of multi-frequency locking and splay phase solutions when we tried to analyse the 4 partite network as a cue for the 4x4 sudoku network.