stylistic:tone, structural:reformatting, information:classification
Theories and computational models

The large base of knowledge about the anatomical structure and behavioral functions of the cerebellum have made it a fertile ground for theorizing—there are perhaps more theories of the function of the cerebellum than of any other part of the brain. The most basic distinction among them is between "learning theories" and "performance theories"—that is, theories that make use of synaptic plasticity within the cerebellum to account for its role in learning, versus theories that account for aspects of ongoing behavior on the basis of cerebellar signal processing. Several theories of both types have been formulated as mathematical models and simulated using computers.

Perhaps the earliest "performance" theory was the "delay line" hypothesis of Valentino Braitenberg. The original theory put forth by Braitenberg and Roger Atwood in 1958 proposed that slow propagation of signals along parallel fibers imposes predictable delays that allow the cerebellum to detect time relationships within a certain window. Experimental data did not support the original form of the theory, but Braitenberg continued to argue for modified versions. The hypothesis that the cerebellum functions essentially as a timing system has also been advocated by Richard Ivry. Another influential "performance" theory is the Tensor network theory of Pellionisz and Llinás, which provided an advanced mathematical formulation of the idea that the fundamental computation performed by the cerebellum is to transform sensory into motor coordinates.

Theories in the "learning" category almost all derive from publications by Marr and Albus. Marr's 1969 paper proposed that the cerebellum is a device for learning to associate elemental movements encoded by climbing fibers with mossy fiber inputs that encode the sensory context. Albus proposed in 1971 that a cerebellar Purkinje cell functions as a perceptron, a neurally inspired abstract learning device. The most basic difference between the Marr and Albus theories is that Marr assumed that climbing fiber activity would cause parallel fiber synapses to be strengthened, whereas Albus proposed that they would be weakened. Albus also formulated his version as a software algorithm he called a CMAC (Cerebellar Model Articulation Controller), which has been tested in a number of applications.