Adaptive-filter Models of the Cerebellum: Computational Analysis

Abstract

Many current models of the cerebellar cortical microcircuit are equivalent to an adaptive filter using the covariance learning rule. The adaptive filter is a development of the original Marr–Albus framework that deals naturally with continuous time-varying signals, thus addressing the issue of 'timing' in cerebellar function, and it can be connected in a variety of ways to other parts of the system, consistent with the microzonal organization of cerebellar cortex. However, its computational capacities are not well understood. Here we summarise the results of recent work that has focused on two of its intrinsic properties. First, an adaptive filter seeks to decorrelate its (mossy fibre) inputs from a (climbing fibre) teaching signal. This procedure can be used both for sensory processing, e.g. removal of interference from sensory signals, and for learning accurate motor commands, by decorrelating an efference copy of those commands from a sensory signal of inaccuracy. As a model of the cerebellum the adaptive filter thus forms a natural link between events at the cellular level, such as forms of synaptic plasticity and the learning rules they embody, and intelligent behaviour at the system level. Secondly, it has been shown that the covariance learning rule enables the filter to handle input and intrinsic noise optimally. Such optimality may underlie the recently described role of the cerebellum in producing accurate smooth pursuit eye movements in the face of sensory noise. Moreover, it has the consequence of driving most input weights to very small values, consistent with experimental data that many parallel-fibre synapses are normally silent. The effectiveness of silent synapses can only be altered by LTP, so learning tasks depending on a reduction of Purkinje cell firing require the synapses to be embedded in a second, inhibitory pathway from parallel fibre to Purkinje cell. This pathway and the appropriate climbing-fibre related plasticity have been described experimentally, and its presence has implications for asymmetries and hysteresis in behavioural learning rates that are also consistent with experimental observations. These computational properties of the adaptive filter suggest that it is both powerful and realistic enough to be a suitable candidate model of the cerebellar cortical microcircuit.