An analog VLSI recurrent neural network learning a continuous-time trajectory

Real-time algorithms for gradient descent supervised learning in recurrent dynamical neural networks fail to support scalable VLSI implementation, due to their complexity which grows sharply with the network dimension. We present an alternative implementation in analog VLSI, which employs a stochastic perturbation algorithm to observe the gradient of the error index directly on the network in random directions of the parameter space, thereby avoiding the tedious task of deriving the gradient from an explicit model of the network dynamics. The network contains six fully recurrent neurons with continuous-time dynamics, providing 42 free parameters which comprise connection strengths and thresholds. The chip implementing the network includes local provisions supporting both the learning and storage of the parameters, integrated in a scalable architecture which can be readily expanded for applications of learning recurrent dynamical networks requiring larger dimensionality. We describe and characterize the functional elements comprising the implemented recurrent network and integrated learning system, and include experimental results obtained from training the network to represent a quadrature-phase oscillator.