Optimal short-term memory before the edge of chaos in driven random recurrent networks
This work addresses memory optimization in neural networks for computational neuroscience or AI, but it appears incremental as it builds on existing mean-field theory to clarify relationships among memory measures.
The study tackled the problem of how discrete-time nonlinear recurrent neural networks store time-varying small input signals, showing that short-term memory measures like memory capacity peak before the edge of chaos, with network contributions optimized in this regime.
The ability of discrete-time nonlinear recurrent neural networks to store time-varying small input signals is investigated by mean-field theory. The combination of a small input strength and mean-field assumptions makes it possible to derive an approximate expression for the conditional probability density of the state of a neuron given a past input signal. From this conditional probability density, we can analytically calculate short-term memory measures, such as memory capacity, mutual information, and Fisher information, and determine the relationships among these measures, which have not been clarified to date to the best of our knowledge. We show that the network contribution of these short-term memory measures peaks before the edge of chaos, where the dynamics of input-driven networks is stable but corresponding systems without input signals are unstable.