Random neural network

The random neural network (RNN) is a mathematical representation of neurons or cells which exchange spiking signals. Each cell is represented by an integer whose value rises when the cell receives an excitatory spike and drops when it receives an inhibitory spike. The spikes can originate outside the network itself, or they can come from other cells in the networks. Cells whose internal excitatory state has a positive value are allowed to send out spikes of either kind to other cells in the network according to specific cell-dependent spiking rates. The model has a mathematical solution in steady-state which provides the joint probability distribution of the network in terms of the individual probabilities that each cell is excited and able to send out spikes. Computing this solution is based on solving a set of non-linear algebraic equations whose parameters are related to the spiking rates of individual cells and their connectivity to other cells, as well as the arrival rates of spikes from outside the network. The RNN also has a gradient-based learning algorithm whose computational complexity is proportional to the cube of the number of cells, and other algorithms such as reinforcement learning can also be used. The RNN has also been shown to be a universal approximator for bounded and continuous functions.