Pietro Vertechi, Wieland Brendel, Christian K. Machens
Learning in recurrent neural networks has been a topic fraught with difficulties and problems. We here report substantial progress in the unsupervised learning of recurrent networks that can keep track of an input signal. Specifically, we show how these networks can learn to efficiently represent their present and past inputs, based on local learning rules only. Our results are based on several key insights. First, we develop a local learning rule for the recurrent weights whose main aim is to drive the network into a regime where, on average, feedforward signal inputs are canceled by recurrent inputs. We show that this learning rule minimizes a cost function. Second, we develop a local learning rule for the feedforward weights that, based on networks in which recurrent inputs already predict feedforward inputs, further minimizes the cost. Third, we show how the learning rules can be modified such that the network can directly encode non-whitened inputs. Fourth, we show that these learning rules can also be applied to a network that feeds a time-delayed version of the network output back into itself. As a consequence, the network starts to efficiently represent both its signal inputs and their history. We develop our main theory for linear networks, but then sketch how the learning rules could be transferred to balanced, spiking networks.