Abstract
The brain needs to predict how the body reacts to motor commands, but how a network of spiking neurons can learn non-linear body dynamics using local, online and stable learning rules is unclear. Here, we present a supervised learning scheme for the feedforward and recurrent connections in a network of heterogeneous spiking neurons. The error in the output is fed back through fixed random connections with a negative gain, causing the network to follow the desired dynamics. The rule for Feedback-based Online Local Learning Of Weights (FOLLOW) is local in the sense that weight changes depend on the presynaptic activity and the error signal projected onto the postsynaptic neuron. We provide examples of learning linear, non-linear and chaotic dynamics, as well as the dynamics of a two-link arm. Under reasonable approximations, we show, using the Lyapunov method, that FOLLOW learning is uniformly stable, with the error going to zero asymptotically.
Highlights
Over the course of life, we learn many motor tasks such as holding a pen, chopping vegetables, riding a bike or playing tennis
We found that the Feedback-based Online Local Learning Of Weights (FOLLOW) scheme learned to reproduce the arm dynamics even without error feedback for a few seconds during the test phase (Figure 4 and Video 1 and Video 2), which corresponds to the time horizon needed for the planning of short arm movements
The FOLLOW learning scheme enables a spiking neural network to function as a forward predictive model that mimics a non-linear dynamical system activated by one or several time-varying inputs
Summary
Over the course of life, we learn many motor tasks such as holding a pen, chopping vegetables, riding a bike or playing tennis. To control and plan such movements, the brain must implicitly or explicitly learn forward models (Conant and Ross Ashby, 1970) that predict how our body responds to neural activity in brain areas known to be involved in motor control (Figure 1A). We wondered whether a non-linear dynamical system, such as a forward predictive model of a simplified arm, can be learned and represented in a heterogeneous network of spiking neurons by adjusting the weights of recurrent connections. Supervised learning of recurrent weights to predict or generate non-linear dynamics, given command input, is known to be difficult in networks of rate units, and even more so in networks of spiking neurons (Abbott et al, 2016). In order to be biologically plausible, a learning rule must be online that is constantly incorporating new data, as opposed to batch learning where weights are adjusted only after many examples have been seen; and local that is the quantities that modify the
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