Liquid computing on and off the edge of chaos with a striatal microcircuit

In reinforcement learning theories of the basal ganglia, there is a need for the expected rewards corresponding to relevant environmental states to be maintained and modified during the learning process. However, the representation of these states that allows them to be associated with reward expectations remains unclear. Previous studies have tended to rely on pre-defined partitioning of states encoded by disjunct neuronal groups or sparse topological drives. A more likely scenario is that striatal neurons are involved in the encoding of multiple different states through their spike patterns, and that an appropriate partitioning of an environment is learned on the basis of task constraints, thus minimizing the number of states involved in solving a particular task. Here we show that striatal activity is sufficient to implement a liquid state, an important prerequisite for such a computation, whereby transient patterns of striatal activity are mapped onto the relevant states. We develop a simple small scale model of the striatum which can reproduce key features of the experimentally observed activity of the major cell types of the striatum. We then use the activity of this network as input for the supervised training of four simple linear readouts to learn three different functions on a plane, where the network is stimulated with the spike coded position of the agent. We discover that the network configuration that best reproduces striatal activity statistics lies on the edge of chaos and has good performance on all three tasks, but that in general, the edge of chaos is a poor predictor of network performance.