Cerebellar Learning by Decorrelation Control
Paul Dean and John Porrill
Centre for Signal Processing in Neuroimaging and Systems Neuroscience, Department of Psychology, University of Sheffield , UK
Models of the cerebellar algorithm need to satisfy both biological and computational constraints. We have focussed on the latter, by simulating calibration of the vestibulo-ocular reflex (VOR) using linearised dynamics, an adaptive filter to represent cerebellar cortex, and a standard covariance learning rule. The simulations have addressed the following issues.
- How could the cerebellum learn correct motor commands, given it receives sensory not motor error signals? The covariance learning rule can be used to decorrelate motor commands from sensory error. It thus overcomes a potentially very serious problem for Marr-Albus type models, without resorting to complex and possibly unworkable schemes such as feedback error learning. The architectural feature required for decorrelation control is that a copy of motor commands be sent to the flocculus. Such recurrent architecture appears to be a very common feature of cerebellar connectivity.
- Is the role of the cerebellum sensory rather than motor? Since successful calibration of the VOR delivers a retinal slip signal that is uncontaminated by the animal's own movements, it would appear that the cerebellum necessarily has both sensory and motor functions. However, VOR calibration differs from interference-cancellation, a role suggested for cerebellar precursor structures, because the interference is removed by moving the sensor rather than by internal signal processing. This crucial difference in strategy may be related to the evolution of climbing fibres, since they can in principle convey an error signal that differs from cerebellar output (i.e. Purkinje cell firing) which is used as the error signal for interference cancellation.
- Why does VOR calibration require a site of plasticity outside cerebellar cortex? The basic problem with the VOR is that the putative error signal of retinal slip is delayed by ~100 ms, leading to unstable learning above ~2.5 Hz. The simplest way of achieving accurate VOR performance up to 25 Hz is to use cerebellar cortical output as a teaching signal for the brainstem, where a value related to VOR gain can be stored. This mechanism depends upon the viscoelastic properties of the oculomotor plant for its efficacy.
- Why are most synapses between parallel fibres (PF) and Purkinje cells (PC) silent? The covariance learning rule at PF/PC synapses means that, given additive noise on PFs, learnt synaptic weights are proportional to root mean square PF signal and inversely proportional to mean square PF noise. This minimises the contribution of PF noise to errors in PC output. As a consequence PFs carrying noise alone have their synaptic weights driven to zero. The evidence that 80-85% of synapses are in fact silent suggests that a high proportion of PF’s carrying information irrelevant to the task of any given PC. The prevalence of silent synapses is likely to produce asymmetries and hysteresis in cerebellar learning rates.
This computational approach, inasmuch as it solves important control problems, is likely to be of interest to (for example) robotics even if biologically mistaken. However, for understanding the actual cerebellum biological fidelity is of course crucial. Can the biological and computational approaches meet?
