Initial investigations of the cerebellar microcircuit inspired the Marr-Albus theoretical framework of cerebellar function. We review recent developments in the experimental understanding of cerebellar microcircuit characteristics and in the computational analysis of Marr-Albus models. We conclude that many Marr-Albus models are in effect adaptive filters, and that evidence for symmetrical long-term potentiation and long-term depression, interneuron plasticity, silent parallel fibre synapses and recurrent mossy fibre connectivity is strikingly congruent with predictions from adaptive-filter models of cerebellar function. This congruence suggests that insights from adaptive-filter theory might help to address outstanding issues of cerebellar function, including both microcircuit processing and extra-cerebellar connectivity.

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We address the following question: Is there a difference (D) between the amount of time for auditory and visual stimuli to be perceived? On each of 1000 trials, observers were presented with a light-sound pair, separated by a stimulus onset asynchrony (SOA) between -250 ms (sound first) and +250 ms. Observers indicated if the light-sound pair came on simultaneously by pressing one of two (yes or no) keys. The SOA most likely to yield affirmative responses was defined as the point of subjective simultaneity (PSS). PSS values were between -21 ms (i.e. sound 21 ms before light) and +150 ms. Evidence is presented that each PSS is observer specific. In a second experiment, each observer was tested using two observer-stimulus distances. The resultant PSS values are highly correlated (r = 0.954, p = 0.003), suggesting that each observer's PSS is stable. PSS values were significantly affected by observer-stimulus distance, suggesting that observers do not take account of changes in distance on the resultant difference in arrival times of light and sound. The difference RTd in simple reaction time to single visual and auditory stimuli was also estimated; no evidence that RTd is observer specific or stable was found. The implications of these findings for the perception of multisensory stimuli are discussed.

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We introduce decorrelation control as a candidate algorithm for the cerebellar microcircuit and demonstrate its utility for oculomotor plant compensation in a linear model of the vestibulo-ocular re ex (VOR). Using an adaptive-lter representation of cerebellar cortex and an anti-Hebbian learning rule, the algorithm learnt to compensate for the oculomotor plant by minimizing correlations between a predictor variable (eye-movement command) and a target variable (retinal slip), without requiring a motor-error signal. Because it also provides an estimate of the unpredicted component of the target variable, decorrelation control can simplify both motor coordination and sensory acquisition. It thus uni es motor and sensory cerebellar functions.

Cerebellar function is increasingly discussed in terms of engineering schemes for motor control and signal processing that involve internal models. To address the relation between the cerebellum and internal models, we adopt the chip metaphor that has been used to represent the combination of a homogeneous cerebellar cortical microcircuit with individual microzones having unique external connections. This metaphor indicates that identifying the function of a particular cerebellar chip requires knowledge of both the general microcircuit algorithm and the chip's individual connections. Here we use a popular candidate algorithm as embodied in the adaptive filter, which learns to decorrelate its inputs from a reference ('teaching', 'error') signal. This algorithm is computationally powerful enough to be used in a very wide variety of engineering applications. However, the crucial issue is whether the external connectivity required by such applications can be implemented biologically. We argue that some applications appear to be in principle biologically implausible: these include the Smith predictor and Kalman filter (for state estimation), and the feedback-error-learning scheme for adaptive inverse control. However, even for plausible schemes, such as forward models for noise cancellation and novelty-detection, and the recurrent architecture for adaptive inverse control, there is unlikely to be a simple mapping between microzone function and internal model structure. This initial analysis suggests that cerebellar involvement in particular behaviours is therefore unlikely to have a neat classification into categories such as 'forward model'. It is more likely that cerebellar microzones learn a task-specific adaptive-filter operation which combines a number of signal-processing roles.

The pattern of retinal binocular disparities acquired by a fixating visual system depends on both the depth structure of the scene and the viewing geometry. This paper treats the problem of interpreting the disparity pattern in terms of scene structure without relying on estimates of fixation position from eye movement control and proprioception mechanisms. We propose a sequential decomposition of this interpretation process into disparity correction, which is used to compute three-dimensional structure up to a relief transformation, and disparity normalization, which is used to resolve the relief ambiguity to obtain metric structure. We point out that the disparity normalization stage can often be omitted, since relief transformations preserve important properties such as depth ordering and coplanarity. Based on this framework we analyse three previously proposed computational models of disparity processing; the Mayhew and Longuet-Higgins model, the deformation model and the polar angle disparity model. We show how these models are related, and argue that none of them can account satisfactorily for available psychophysical data. We therefore propose an alternative model, regional disparity correction. Using this model we derive predictions for a number of experiments based on vertical disparity manipulations, and compare them to available experimental data. The paper is concluded with a summary and a discussion of the possible architectures and mechanisms underling stereopsis in the human visual system.

Current views of cerebellar function have been heavily influenced by the models of Marr and Albus, who suggested that the climbing fibre input to the cerebellum acts as a teaching signal for motor learning. It is commonly assumed that this teaching signal must be motor error (the difference between actual and correct motor command), but this approach requires complex neural structures to estimate unobservable motor error from its observed sensory consequences. We have proposed elsewhere a recurrent decorrelation control architecture in which Marr-Albus models learn without requiring motor error. Here, we prove convergence for this architecture and demonstrate important advantages for the modular control of systems with multiple degrees of freedom. These results are illustrated by modelling adaptive plant compensation for the three-dimensional vestibular ocular reflex. This provides a functional role for recurrent cerebellar connectivity, which may be a generic anatomical feature of projections between regions of cerebral and cerebellar cortex.