Gradient Learning in Spiking Neural Networks by Dynamic Perturbation of Conductances

We present a method of estimating the gradient of an objective function with respect to the synaptic weights of a spiking neural network. The method works by measuring the fluctuations in the objective function in response to dynamic perturbation of the membrane conductances of the neurons. It is compatible with recurrent networks of conductance-based model neurons with dynamic synapses. The method can be interpreted as a biologically plausible synaptic learning rule, if the dynamic perturbations are generated by a special class of “empiric” synapses driven by random spike trains from an external source.

Figure 1

Neurons in a recurrent network (actor), connected by plastic (modifiable) weights $W$. A global reinforcement signal $R$ is broadcast by a critic to all neurons in the network. In addition, each neuron $i$ receives an empiric synapse carrying perturbing input ${\xi }_i(t)$ from an external experimenter.