Transfer-RLS method and transfer-FORCE learning for simple and fast training of reservoir computing models

Reservoir computing is a machine learning framework derived from a special type of recurrent neural network. Following recent advances in physical reservoir computing, some reservoir computing devices are thought to be promising as energy-efficient machine learning hardware for real-time information processing. To realize efficient online learning with low-power reservoir computing devices, it is beneficial to develop fast convergence learning methods with simpler operations. This study proposes a training method located in the middle between the recursive least squares (RLS) method and the least mean squares (LMS) method, which are standard online learning methods for reservoir computing models. The RLS method converges fast but requires updates of a huge matrix called a gain matrix, whereas the LMS method does not use a gain matrix but converges very slow. On the other hand, the proposed method called a transfer-RLS method does not require updates of the gain matrix in the main-training phase by updating that in advance (i.e., in a pre-training phase). As a result, the transfer-RLS method can work with simpler operations than the original RLS method without sacrificing much convergence speed. We numerically and analytically show that the transfer-RLS method converges much faster than the LMS method. Furthermore, we show that a modified version of the transfer-RLS method (called transfer-FORCE learning) can be applied to the first-order reduced and controlled error (FORCE) learning for a reservoir computing model with a closed-loop, which is challenging to train.