The random neural network (RNN) is a mathematical representation of an interconnected network of neurons or cells which exchange spiking signals. It was invented by Erol Gelenbe and is linked to the G-network model of queueing networks as well as to Gene Regulatory Network models. Each cell state 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 is a recurrent model, i.e. a neural network that is allowed to have complex feedback loops.
A highly energy-efficient implementation of random neural networks was demonstrated by Krishna Palem et al. using the Probabilistic CMOS or PCMOS technology and was shown to be c. 226–300 times more efficient in terms of Energy-Performance-Product.
RNNs are also related to artificial neural networks, which (like the random neural network) have gradient-based learning algorithms. The learning algorithm for an n-node random neural network that includes feedback loops (it is also a recurrent neural network) is of computational complexity O(n^3) (the number of computations is proportional to the cube of n, the number of neurons). The random neural network can also be used with other learning algorithms such as reinforcement learning can also be used. The RNN has been shown to be a universal approximator for bounded and continuous functions.