partial-FORCE: A fast and robust online training method for recurrent neural networks

Recurrent neural networks (RNNs) are helpful tools for modeling dynamical systems by neuronal populations, but efficiently training RNNs has been a challenging topic. In recent years, a recursive least squares (RLS) based method for modifying all the recurrent connections, called the full-Force method, has been gaining attention as a fast and robust online training rule. This method introduces a second network (called the teacher reservoir) during training to provide suitable target dynamics to all the hidden units of the task-performing network (called the student network). Thanks to the RLS-based approach, the full-FORCE method can be applied to training continuous-time networks and spiking neural networks. In this study, we propose a generalized version of the full-FORCE method: the partial-FORCE method. In the proposed method, only part of the student network neurons (called supervised neurons) is supervised by only part of the teacher reservoir neurons (called supervising neurons). As a result of this relaxation, the size of the student network and that of the teacher reservoir can be different, which is biologically plausible as a possible model of the memory transfer in the brain. Furthermore, we numerically show that the partial-FORCE method converges faster and is more robust against variations in parameter values and initial conditions than the full-FORCE method, even without the price of computational cost.