Substantial experimental evidence suggests the cerebellum is involved in calibrating sensorimotor maps. Consistent with this involvement is the well-known, but little understood, massive cerebellar projection to maps in the superior colliculus. Map calibration would be a significant new role for the cerebellum given the ubiquity of map representations in the brain, but how it could perform such a task is unclear. Here we investigated a dynamic method for map calibration, based on electrophysiological recordings from the superior colliculus, that used a standard adaptive-filter cerebellar model. The method proved effective for complex distortions of both unimodal and bimodal maps, and also for predictive map-based tracking of moving targets. These results provide the first computational evidence for a novel role for the cerebellum in dynamic sensorimotor map calibration, of potential importance for coordinate alignment during ongoing motor control, and for map calibration in future biomimetic systems. This computational evidence also provides testable experimental predictions concerning the role of the connections between cerebellum and superior colliculus in previously observed dynamic coordinate transformations.

We present an adaptive filter model of cerebellar function applied to the calibration of a tactile sensory map to improve the accuracy of directed movements of a robotic manipulator. This is demonstrated using a platform called Bellabot that incorporates an array of biomimetic tactile whiskers, actuated using electro-active polymer artificial muscles, a camera to provide visual error feedback, and a standard industrial robotic manipulator. The algorithm learns to accommodate imperfections in the sensory map that may be as a result of poor manufacturing tolerances or damage to the sensory array. Such an ability is an important pre-requisite for robust tactile robotic systems operating in the real-world for extended periods of time. In this work the sensory maps have been purposely distorted in order to evaluate the performance of the algorithm.

Models of the cerebellar microcircuit often assume that input signals from the mossy-fibers are expanded and recoded to provide a foundation from which the Purkinje cells can synthesize output filters to implement specific input-signal transformations. Details of this process are however unclear. While previous work has shown that recurrent granule cell inhibition could in principle generate a wide variety of random outputs suitable for coding signal onsets, the more general application for temporally varying signals has yet to be demonstrated. Here we show for the first time that using a mechanism very similar to reservoir computing enables random neuronal networks in the granule cell layer to provide the necessary signal separation and extension from which Purkinje cells could construct basis filters of various time-constants. The main requirement for this is that the network operates in a state of criticality close to the edge of random chaotic behavior. We further show that the lack of recurrent excitation in the granular layer as commonly required in traditional reservoir networks can be circumvented by considering other inherent granular layer features such as inverted input signals or mGluR2 inhibition of Golgi cells. Other properties that facilitate filter construction are direct mossy fiber excitation of Golgi cells, variability of synaptic weights or input signals and output-feedback via the nucleocortical pathway. Our findings are well supported by previous experimental and theoretical work and will help to bridge the gap between system-level models and detailed models of the granular layer network.

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.

Sensory signals are often caused by one's own active movements. This raises a problem of discriminating between self-generated sensory signals and signals generated by the external world. Such discrimination is of general importance for robotic systems, where operational robustness is dependent on the correct interpretation of sensory signals. Here, we investigate this problem in the context of a whiskered robot. The whisker sensory signal comprises two components: one due to contact with an object (externally generated) and another due to active movement of the whisker (self-generated). We propose a solution to this discrimination problem based on adaptive noise cancelation, where the robot learns to predict the sensory consequences of its own movements using an adaptive filter. The filter inputs (copy of motor commands) are transformed by Laguerre functions instead of the often-used tapped-delay line, which reduces model order and, therefore, computational complexity. Results from a contact-detection task demonstrate that false positives are significantly reduced using the proposed scheme.

In this paper, a model of cerebellar function is implemented and evaluated in the control of a robot eye actuated by pneumatic artificial muscles. The investigated control problem is stabilization of the visual image in response to disturbances. This is analogous to the vestibuloocular reflex (VOR) in humans. The cerebellar model is structurally based on the adaptive filter, and the learning rule is computationally analogous to least-mean squares, where parameter adaptation at the parallel fiber/Purkinje cell synapse is driven by the correlation of the sensory error signal (carried by the climbing fiber) and the motor command signal. Convergence of the algorithm is first analyzed in simulation on a model of the robot and then tested online in both one and two degrees of freedom. The results show that this model of neural function successfully works on a real-world problem, providing empirical evidence for validating: 1) the generic cerebellar learning algorithm; 2) the function of the cerebellum in the VOR; and 3) the signal transmission between functional neural components of the VOR.

Computational analysis of neural systems is at its most useful when it uncovers principles that provide a unified account of phenomena across multiple scales and levels of description. Here we analyse a widely used model of the cerebellar contribution to sensori-motor learning to demonstrate both that its response to intrinsic and sensor noise is optimal, and that the unexpected synaptic and behavioural consequences of this optimality can explain a wide range of experimental data. The response of the Marr-Albus adaptive-filter model of the cerebellar microcircuit to noise was examined in the context of vestibulo-ocular reflex calibration. We found that, when appropriately connected, an adaptive-filter model using the covariance learning rule to adjust the weights of synapses between parallel fibres and Purkinje cells learns weight values that are optimal given the relative amount of signal and noise carried by each parallel fibre. This optimality principle is consistent with data on the cerebellar role in smooth pursuit eye movements, and predicts that many synaptic weights must be very small, providing an explanation for the experimentally observed preponderance of silent synapses. Such a preponderance has in its turn two further consequences. First, an additional inhibitory pathway from parallel fibre to Purkinje cell is required if Purkinje cell activity is to be altered in either direction from a starting point of silent synapses. Second, cerebellar learning tasks must often proceed via LTP, rather than LTD as is widely assumed. Taken together, these considerations have profound behavioural consequences, including the optimal combination of sensori-motor information, and asymmetry and hysteresis of sensori-motor learning rates.

We have described elsewhere an adaptive filter model of cerebellar learning in which the cerebellar microcircuit acts to decorrelate motor commands from their sensory consequences (Dean, Porrill, & Stone, 2002). Learning stability required the cerebellar microcircuit to be embedded in a recurrent loop, and this has been shown to lead to a simple and modular adaptive control architecture when applied to the linearized 3D vestibular ocular reflex (Porrill, Dean, & Stone, 2004). Here we investigate the properties of recurrent loop connectivity in the case of redundant and nonlinear motor systems and illustrate them using the example of kinematic control of a simulated two-joint robot arm. We demonstrate that (1) the learning rule does not require unavailable motor error signals or complex neural reference structures to estimate such signals (i.e., it solves the motor error problem) and (2) control of redundant systems is not subject to the nonconvexity problem in which incorrect average motor commands are learned for end-effector positions that can be accessed in more than one arm configuration. These properties suggest a central functional role for the closed cerebellar loops, which have been shown to be ubiquitous in motor systems (e.g., Kelly & Strick, 2003).

Classical Marr-Albus theories of cerebellar learning employ only cortical sites of plasticity. However, tests of these theories using adaptive calibration of the vestibulo-ocular reflex (VOR) have indicated plasticity in both cerebellar cortex and the brainstem. To resolve this long-standing conflict, we attempted to identify the computational role of the brainstem site, by using an adaptive filter version of the cerebellar microcircuit to model VOR calibration for changes in the oculomotor plant. With only cortical plasticity, introducing a realistic delay in the retinal-slip error signal of 100 ms prevented learning at frequencies higher than 2.5 Hz, although the VOR itself is accurate up to at least 25 Hz. However, the introduction of an additional brainstem site of plasticity, driven by the correlation between cerebellar and vestibular inputs, overcame the 2.5 Hz limitation and allowed learning of accurate high-frequency gains. This "cortex-first" learning mechanism is consistent with a wide variety of evidence concerning the role of the flocculus in VOR calibration, and complements rather than replaces the previously proposed "brainstem-first" mechanism that operates when ocular tracking mechanisms are effective. These results (i) describe a process whereby information originally learnt in one area of the brain (cerebellar cortex) can be transferred and expressed in another (brainstem), and (ii) indicate for the first time why a brainstem site of plasticity is actually required by Marr-Albus type models when high-frequency gains must be learned in the presence of error delay.