An analysis of the gamma memory in dynamic neural networks

Presents a vector space framework to study short-term memory filters in dynamic neural networks. The authors define parameters to quantify the function of feedforward and recursive linear memory filters. They show, using vector spaces, what is the optimization problem solved by the PEs of the first hidden layer of the single input focused network architecture. Due to the special properties of the gamma bases, recursion brings an extra parameter lambda (the time constant of the leaky integrator) that displaces the memory manifold towards the desired signal when the mean square error is minimized. In contrast, for the feedforward memory filter the angle between the desired signal and the memory manifold is fixed for a given memory order. The adaptation of the feedback parameter can be done using gradient descent, but the optimization is nonconvex.