Benchmarking Cerebellar Control

Cerebellar models have long been advocated as viable models for robot dynamics control. Building on an increasing insight in and knowledge of the biological cerebellum, many models have been greatly refined, of which some computational models have emerged with useful properties with respect to robot dynamics control. Looking at the application side, however, there is a totally different picture. Not only is there not one robot on the market which uses anything remotely connected with cerebellar control, but even in research labs most testbeds for cerebellar models are restricted to toy problems. Such applications hardly ever exceed the complexity of a 2 DoF simulated robot arm; a task which is hardly representative for the field of robotics, or relates to realistic applications. In order to bring the amalgamation of the two fields forwards, we advocate the use of a set of robotics benchmarks, on which existing and new computational cerebellar models can be comparatively tested. It is clear that the traditional approach to solve robotics dynamics loses ground with the advancing complexity of robotic structures; there is a desire for adaptive methods which can compete as traditional control methods do for traditional robots. In this paper we try to lay down the successes and problems in the fields of cerebellar modelling as well as robot dynamics control. By analyzing the common ground, a set of benchmarks is suggested which may serve as typical robot applications for cerebellar models

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas examined. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears to be a general, functional property in all cases analyzed. We then created a generic neural model to investigate adaptive learning rules that create and maintain lognormal distributions. We conclusively demonstrate that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This provides a solution to the long-standing question about the type of plasticity exhibited by intrinsic excitability

A Scalable Model of Cerebellar Adaptive Timing and Sequencing: The Recurrent Slide and Latch (RSL) Model

From the dawn of modern neural network theory, the mammalian cerebellum has been a favored object of mathematical modeling studies. Early studies focused on the fan-out, convergence, thresholding, and learned weighting of perceptual-motor signals within the cerebellar cortex. This led in the proposals of Albus (1971; 1975) and Marr (1969) to the still viable idea that the granule cell stage in the cerebellar cortex performs a sparse expansive recoding of the time-varying input vector. This recoding reveals and emphasizes combinations (of input state variables) in a distributed representation that serves as a basis for the learned, state-dependent control actions engendered by cerebellar outputs to movement related centers. Although well-grounded as such, this perspective seriously underestimates the intelligence of the cerebellar cortex. Context and state information arises asynchronously due to the heterogeneity of sources that contribute signals to compose the cerebellar input vector. These sources include radically different sensory systems - vision, kinesthesia, touch, balance and audition - as well as many stages of the motor output channel. To make optimal use of available signals, the cerebellum must be able to sift the evolving state representation for the most reliable predictors of the need for control actions, and to use those predictors even if they appear only transiently and well in advance of the optimal time for initiating the control action. Such a cerebellar adaptive timing competence has recently been experimentally verified (Perrett, Ruiz, & Mauk, 1993). This paper proposes a modification to prior, population, models for cerebellar adaptive timing and sequencing. Since it replaces a population with a single clement, the proposed Recurrent Slide and Latch (RSL) model is in one sense maximally efficient, and therefore optimal from the perspective of scalability.Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-92-J-1309, N00014-93-1-1364, N00014-95-1-0409)

The hippocampus and cerebellum in adaptively timed learning, recognition, and movement

The concepts of declarative memory and procedural memory have been used to distinguish two basic types of learning. A neural network model suggests how such memory processes work together as recognition learning, reinforcement learning, and sensory-motor learning take place during adaptive behaviors. To coordinate these processes, the hippocampal formation and cerebellum each contain circuits that learn to adaptively time their outputs. Within the model, hippocampal timing helps to maintain attention on motivationally salient goal objects during variable task-related delays, and cerebellar timing controls the release of conditioned responses. This property is part of the model's description of how cognitive-emotional interactions focus attention on motivationally valued cues, and how this process breaks down due to hippocampal ablation. The model suggests that the hippocampal mechanisms that help to rapidly draw attention to salient cues could prematurely release motor commands were not the release of these commands adaptively timed by the cerebellum. The model hippocampal system modulates cortical recognition learning without actually encoding the representational information that the cortex encodes. These properties avoid the difficulties faced by several models that propose a direct hippocampal role in recognition learning. Learning within the model hippocampal system controls adaptive timing and spatial orientation. Model properties hereby clarify how hippocampal ablations cause amnesic symptoms and difficulties with tasks which combine task delays, novelty detection, and attention towards goal objects amid distractions. When these model recognition, reinforcement, sensory-motor, and timing processes work together, they suggest how the brain can accomplish conditioning of multiple sensory events to delayed rewards, as during serial compound conditioning.Air Force Office of Scientific Research (F49620-92-J-0225, F49620-86-C-0037, 90-0128); Advanced Research Projects Agency (ONR N00014-92-J-4015); Office of Naval Research (N00014-91-J-4100, N00014-92-J-1309, N00014-92-J-1904); National Institute of Mental Health (MH-42900

Decorrelation control by the cerebellum achieves oculomotor plant compensation in simulated vestibulo-ocular reflex

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 reflex (VOR). Using an adaptive-filter 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 unifies motor and sensory cerebellar functions

Recurrent cerebellar architecture solves the motor-error problem

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

Computational Models of Timing Mechanisms in the Cerebellar Granular Layer

A long-standing question in neuroscience is how the brain controls movement that requires precisely timed muscle activations. Studies using Pavlovian delay eyeblink conditioning provide good insight into this question. In delay eyeblink conditioning, which is believed to involve the cerebellum, a subject learns an interstimulus interval (ISI) between the onsets of a conditioned stimulus (CS) such as a tone and an unconditioned stimulus such as an airpuff to the eye. After a conditioning phase, the subject’s eyes automatically close or blink when the ISI time has passed after CS onset. This timing information is thought to be represented in some way in the cerebellum. Several computational models of the cerebellum have been proposed to explain the mechanisms of time representation, and they commonly point to the granular layer network. This article will review these computational models and discuss the possible computational power of the cerebellum

Characterizing Purkinje Cell Responses and Cerebellar Influence on Fluid Licking in the Mouse

Rodents consume water by performing stereotypical, rhythmic licking movements which are believed to be driven by central pattern generating circuits located in the brainstem. Temporal aspects of rhythmic licking behavior have been shown to be represented in the olivo-cerebellar system in the form of population complex spike activity. These findings suggest that the olivo-cerebellar system is involved in the generating circuitry responsible for licking rhythm in rodents. However, the representation of licking in the simple spike activity of Purkinje cells and the consequences of loss of cerebellar function on licking behavior has not been quantified. I investigated the influence of the cerebellum on the maintenance of rhythm in murine fluid-licking. In one set of experiments, I characterized Purkinje cell activity in healthy mice during fluid licking. Use of a head-restrained preparation allowed recordings of well-isolated single units during repeated experimental sessions. Thus, a large number of neurons were tested for their relationship with behavior and detailed spatial maps of behavior related neuronal activity were generated as exemplified here with recordings from lick-related Purkinje cells in the cerebellum. The data show a multifaceted representation of licking behavior in the simple spike activity of a large population of Purkinje cells distributed across Crus I, Crus II, and lobus simplex of mouse cerebellar cortex. Lick related Purkinje cell simple spike activity was changed in a manner that was either rhythmic, in phase with the lick rhythm, or nonrhythmic with a decrease or increase in firing in relation to licks but not phasically. For rhythmically responsive units, signal modulation was marked by the introduction of a phasic variation in the frequency of spikes. A subpopulation of lick related Purkinje cells exhibited different activity patterns during short and long interlick intervals (ILIs). I examined the role of the cerebellum in fluid-licking by using several models of cerebellar ataxia with distinct causes. First, I observed fluid-licking in animals over several days to determine how the microstructure of the behavior may also be altered. The first model involved animals that underwent cerebellectomies. Surgical removal of the cerebellum resulted in significant slowing of the lick rhythm but did not affect the mouse’s ability to perform the gross licking movement. Thus, the cerebellum is involved in the modulation but not in the generation of the licking rhythm. Next, I observed changes to behavior in animals with a genetic cause to their ataxia, the Cerebellin1 (CBLN1) knockout and heterozygous mice (Morgan et al., 1988). The CBLN1 gene is a member of a family of proteins that have been found primarily in the Purkinje cell/parallel fiber synapse and is thought to stabilize the connection. Although removal of the gene does not alter the numbers of neurons or their spatial relations, the mutation results in moderate to severe ataxia. While these animals also varied significantly from their wild type counterparts in lick rate and microstructure, the changes were not all similar to the cerebellectomized model of ataxia. For example, cerebellectomized mice licked significantly slower with an average ILI of 135 ± 8 ms (mean ± S.D.) compared to 117 ± 7 ms whereas in cbln1 KO had a faster lick rate (110 ± 4 ) than wild type counterparts (121 ± 6 ), with all of these values significant with p \u3c 0.05. These observations show that the removal of the normal functions of the cerebellum can alter fluid-licking resulting in bidirectional rate changes. An alternative possibility is that there may be compensatory process. Lastly, I used a chemically-induced model of cerebellar ataxia by injecting the GABA agonist muscimol in the medial and lateral deep cerebellar nuclei. This transient cerebellar ataxia resulted in a similar slowing of the licking rhythm as in the cerebellectomized mice with the eventual recovery of the fluid-licking behavior to normal as the effect of muscimol wore off. My work to characterize the role of the cerebellum in the maintenance of fluid- licking rhythm and behavior microstructure has resulted in the development of experimental procedures for the recording of neuronal activity in awake and behaving mice. It is an important and necessary step towards neurophysiological investigation of normal and pathological mouse brain function. I have presented the first characterization of simple spike activity, the main cerebellar cortical output signal, during fluid-licking. Furthermore, my results show that the cerebellum is also involved in the control of fluid intake or homeostasis as the intervals between drinking events were abnormally long in mice with cerebellar ataxia. Electrophysiological recordings of individual Purkinje cells from the cerebellar cortex demonstrated variations in spike activity capable of influencing the rhythmicity of fluid licking. While licking still occurred with relative regularity in ataxic animals, the lick rates slowed significantly for mice with surgically induced ataxia and pharmalogically induced ataxia. For animals with a genetic origin to ataxia, lick rates increased. Regularity of licking remained evident despite the change in interlick interval duration. Any alteration of lick timing could ultimately affect the coordination of licking with other orofacial movements. Future investigations may benefit from this work by investigating if therapeutic interventions for cerebellar ataxias show a recovery of typical behavior or adapt the neurophysiological recordings to other behaviors in awake mice