Error-based or target-based? A unifying framework for learning in recurrent spiking networks

Learning in biological or artificial networks means changing the laws governing the network dynamics in order to better behave in a specific situation. In the field of supervised learning, two complementary approaches stand out: error-based and target-based learning. However, there exists no consensus on which is better suited for which task, and what is the most biologically plausible. Here we propose a comprehensive theoretical framework that includes these two frameworks as special cases. This novel theoretical formulation offers major insights into the differences between the two approaches. In particular, we show how target-based naturally emerges from error-based when the number of constraints on the target dynamics, and as a consequence on the internal network dynamics, is comparable to the degrees of freedom of the network. Moreover, given the experimental evidences on the relevance that spikes have in biological networks, we investigate the role of coding with specific patterns of spikes by introducing a parameter that defines the tolerance to precise spike timing during learning. Our approach naturally lends itself to Imitation Learning (and Behavioral Cloning in particular) and we apply it to solve relevant closed-loop tasks such as the button-and-food task, and the 2D Bipedal Walker. We show that a high dimensionality feedback structure is extremely important when it is necessary to solve a task that requires retaining memory for a long time (button-and-food). On the other hand, we find that coding with specific patterns of spikes enables optimal performances in a motor task (the 2D Bipedal Walker). Finally, we show that our theoretical formulation suggests protocols to deduce the structure of learning feedback in biological networks.