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.

The Robot Vibrissal System: Understanding Mammalian Sensorimotor Co-ordination Through Biomimetics

“…The mapping of this scheme onto the cerebellar microcircuit is illustrated in figure 7. We have previously investigated the computational properties of this model for adaptive motor control (Dean, Porrill et al, 2002;Dean and Porrill, 2008;Porrill, Dean et al, 2004;Porrill and Dean, 2007), and others have proposed that it could be used in principle to learn forward models (see for review). However, our vibrissal noise study was, to our knowledge, the first instance of the adaptive-filter model of the cerebellum being applied to learning a specific forward model (i.e.…”

Computational Structure of the Cerebellar Molecular Layer

“…With respect to what Marr referred to as "the representation of the input and output" (Marr 1982), or in other words, what this cortical circuitry needs to compute, while there is some variation among theories, almost all assume that cerebellar circuitry computes some function that directly creates or modifies patterns of muscle activations and synergies. Within that broad assumption, most theories then consider one of two not necessarily mutually exclusive presumed requirements for motor control: the dependence of motor coordination on the precise timing of muscle contractions (Carrillo et al 2008;D'Angelo and De Zeeuw 2009;Dean and Porrill 2008;Dean et al 2010b;Heck et al 2007;Ioffe et al 2007;Jacobson et al 2008;Kawato and Gomi 1992; (Cajal 1911), modified slightly by Ito (Ito 2001). These basic excitatory connections represent the reduced form of cerebellar cortex found in most cerebellar models and theories.…”

“…Regardless of whether models or theories assume the molecular layer implements a timing (Carrillo et al 2008;D'Angelo and De Zeeuw 2009;Dean and Porrill 2008;Dean et al 2010b;Heck et al 2007;Ioffe et al 2007;Jacobson et al 2008;Kawato and Gomi 1992;Kitazawa and Wolpert 2005;Ohyama et al 2003;Yamazaki and Tanaka 2009), or learning function (Apps and Garwicz 2005;Bell et al 2008;D'Angelo and De Zeeuw 2009;Dean et al 2010b;Empson and Knopfel 2010;Ito 2006;Kitazawa and Wolpert 2005;Lisberger 2009;Molinari et al 2007;Ohyama et al 2010;Shadmehr and Krakauer 2008) or some combination of the two, or implements an adaptive filter (Dean et al 2010b;Requarth and Sawtell 2011) or an inverse kinematic model (Lisberger 2009), or some combination of the two, all existing algorithmic speculations regarding molecular layer circuitry make one overarching assumption: that parallel fiber input directly drives Purkinje cell output. While it seems reasonable to assume that an excitatory input as massive as that of the parallel fibers would directly drive somatic spiking, the experimental fact is that there is little experimental evidence that they do (Bell and Grimm 1969;Bower and Woolston 1983;Brown and Ariel 2009;Chu et al 2011a, b;Cohen and Yarom 1998;De Jaeger and Proteau 2003;de Solages et al 2008;Dizon and Khodakhah 2011;Eccles et al 1972b;Heck et al 2007;…”

“…First, most modern models and theories of cerebellar cortex explicitly exclude molecular layer inhibition (Carrillo et al 2008;de Gruijl et al 2009;Dean and Porrill 2008;Dean et al 2010a;Ohyama et al 2003;Traub et al 2008;yamazaki and Tanaka 2007), and those in which it is included assume it provides the traditional role of sculpting excitatory responses (Chauvet and Chauvet 1999;De Jaeger and Proteau 2003;Hong and Optican 2008;Mauk and Ohyama 2004;Silkis 2000;Steuber et al 2007;Wulff et al 2009). If the new modeling results are correct, the physiological relationship between parallel fiber excitation and molecular layer inhibition is far more complex, active, subtle, and interesting than simple inhibitory sculpting, and is likely of fundamental importance in the cerebellar processing of afferent information.…”

Adaptive Cancelation of Self-Generated Sensory Signals in a Whisking Robot

“…The cerebellum is a natural candidate for this role because of the resemblance of the cerebellar microcircuit to the adaptive filter [43], [44]. The cerebellum has also been particularly associated with the concept of learning internal dynamical models [12], [13], [45].…”