Principles of operation of a cerebellar learning circuit

A cerebellar population coding model for sensorimotor learning

The cerebellum is crucial for sensorimotor adaptation, using error information to keep the sensorimotor system well-calibrated. Here we introduce a population-coding model to explain how cerebellar-dependent learning is modulated by contextual variation. The model consists of a two-layer network, designed to capture activity in both the cerebellar cortex and deep cerebellar nuclei. A core feature of the model is that within each layer, the processing units are tuned to both movement direction and the direction of movement error. The model captures a large range of contextual effects including interference from prior learning and the influence of error uncertainty and volatility. While these effects have traditionally been taken to indicate meta learning or context-dependent memory within the adaptation system, our results show that they are emergent properties that arise from the population dynamics within the cerebellum. Our results provide a novel framework to understand how the nervous system responds to variable environments.

Synaptic weight dynamics underlying systems consolidation of a memory

Systems consolidation is a common feature of learning and memory systems, in which a long-term memory initially stored in one brain region becomes persistently stored in another region. We studied the dynamics of systems consolidation in simple circuit architectures modeling core features of many memory systems: an early- and late-learning brain region and two sites of plasticity. We show that the synaptic dynamics of the circuit during consolidation of an analog memory can be understood as a temporal integration process, by which transient changes in activity driven by plasticity in the early-learning area are accumulated into persistent synaptic changes at the late-learning site. This simple principle leads to two constraints on the circuit operation for consolidation to be implemented successfully. First, the plasticity rule at the late-learning site must stably support a continuum of possible outputs for a given input. We show that this is readily achieved by heterosynaptic but not standard Hebbian rules, that it naturally leads to a speed-accuracy tradeoff in systems consolidation, and that it provides a concrete circuit instantiation for how systems consolidation solves the stability-plasticity dilemma. Second, to turn off the consolidation process and prevent erroneous changes at the late-learning site, neural activity in the early-learning area must be reset to its baseline activity. We propose two biologically plausible implementations for this reset that suggest novel roles for core elements of the cerebellar circuit.

Cerebellar associative learning underlies skilled reach adaptation

The cerebellum is hypothesized to refine movement through online adjustments. We examined how such predictive control may be generated using a mouse reach paradigm, testing whether the cerebellum uses within-reach information as a predictor to adjust reach kinematics. We first identified a population-level response in Purkinje cells that scales inversely with reach velocity, pointing to the cerebellar cortex as a potential site linking kinematic predictors and anticipatory control. Next, we showed that mice can learn to compensate for a predictable reach perturbation caused by repeated, closed-loop optogenetic stimulation of pontocerebellar mossy fiber inputs. Both neural and behavioral readouts showed adaptation to position-locked mossy fiber perturbations and exhibited aftereffects when stimulation was removed. Surprisingly, position-randomized stimulation schedules drove partial adaptation but no opposing aftereffects. A model that recapitulated these findings suggests that the cerebellum may decipher cause-and-effect relationships through time-dependent generalization mechanisms.

An emergent temporal basis set robustly supports cerebellar time-series learning

The cerebellum is considered a "learning machine" essential for time interval estimation underlying motor coordination and other behaviors. Theoretical work has proposed that the cerebellum's input recipient structure, the granule cell layer (GCL), performs pattern separation of inputs that facilitates learning in Purkinje cells (P-cells). However, the relationship between input reformatting and learning has remained debated, with roles emphasized for pattern separation features from sparsification to decorrelation. We took a novel approach by training a minimalist model of the cerebellar cortex to learn complex time-series data from time-varying inputs, typical during movements. The model robustly produced temporal basis sets from these inputs, and the resultant GCL output supported better learning of temporally complex target functions than mossy fibers alone. Learning was optimized at intermediate threshold levels, supporting relatively dense granule cell activity, yet the key statistical features in GCL population activity that drove learning differed from those seen previously for classification tasks. These findings advance testable hypotheses for mechanisms of temporal basis set formation and predict that moderately dense population activity optimizes learning.NEW & NOTEWORTHY During movement, mossy fiber inputs to the cerebellum relay time-varying information with strong intrinsic relationships to ongoing movement. Are such mossy fibers signals sufficient to support Purkinje signals and learning? In a model, we show how the GCL greatly improves Purkinje learning of complex, temporally dynamic signals relative to mossy fibers alone. Learning-optimized GCL population activity was moderately dense, which retained intrinsic input variance while also performing pattern separation.

A cerebellum inspired spiking neural network as a multi-model for pattern classification and robotic trajectory prediction

Spiking neural networks were introduced to understand spatiotemporal information processing in neurons and have found their application in pattern encoding, data discrimination, and classification. Bioinspired network architectures are considered for event-driven tasks, and scientists have looked at different theories based on the architecture and functioning. Motor tasks, for example, have networks inspired by cerebellar architecture where the granular layer recodes sparse representations of the mossy fiber (MF) inputs and has more roles in motor learning. Using abstractions from cerebellar connections and learning rules of deep learning network (DLN), patterns were discriminated within datasets, and the same algorithm was used for trajectory optimization. In the current work, a cerebellum-inspired spiking neural network with dynamics of cerebellar neurons and learning mechanisms attributed to the granular layer, Purkinje cell (PC) layer, and cerebellar nuclei interconnected by excitatory and inhibitory synapses was implemented. The model’s pattern discrimination capability was tested for two tasks on standard machine learning (ML) datasets and on following a trajectory of a low-cost sensor-free robotic articulator. Tuned for supervised learning, the pattern classification capability of the cerebellum-inspired network algorithm has produced more generalized models than data-specific precision models on smaller training datasets. The model showed an accuracy of 72%, which was comparable to standard ML algorithms, such as MLP (78%), Dl4jMlpClassifier (64%), RBFNetwork (71.4%), and libSVM-linear (85.7%). The cerebellar model increased the network’s capability and decreased storage, augmenting faster computations. Additionally, the network model could also implicitly reconstruct the trajectory of a 6-degree of freedom (DOF) robotic arm with a low error rate by reconstructing the kinematic parameters. The variability between the actual and predicted trajectory points was noted to be ± 3 cm (while moving to a position in a cuboid space of 25 × 30 × 40 cm). Although a few known learning rules were implemented among known types of plasticity in the cerebellum, the network model showed a generalized processing capability for a range of signals, modulating the data through the interconnected neural populations. In addition to potential use on sensor-free or feed-forward based controllers for robotic arms and as a generalized pattern classification algorithm, this model adds implications to motor learning theory.

The influence of neck torsion and sequence of cycles on intra-trial reliability of smooth pursuit eye movement test in patients with neck pain disorders

The sensory mismatch commonly observed in patients with neck pain disorders could alter intra-trial reliability in simple implicit smooth pursuit eye movement tasks. This could be more pronounced when neck is in torsioned position (SPNT). The aim of this study was to explore the effects of neck torsion, target movement velocity and amplitude on intra-trial reliability of smooth pursuit eye movements in patients with neck pain disorders and healthy individuals. SPNT test was evaluated in 32 chronic neck pain patients and 32 healthy controls. Ten cycles were performed using video-oculography at three different velocities (20° s^-1, 30° s^-1 and 40° s^-1) and at three different amplitudes (30°, 40° and 50°) of target movement. Intra-trial reliability and differences between average gain and SPNT difference from the second to fifth cycle and from the sixth to ninth cycle were assessed using ICC_3.1 and factorial analysis of variance, respectively. Intra-trial reliability for gain and SPNT difference at all target movement amplitudes and velocities proved to be good to excellent in both observed groups. Patients with neck pain disorders presented with a trend of inferior gain performance between the sixth and ninth cycle at 30° s^-1 of target movement as compared to healthy individuals which was only evident when neck was in torsioned position. Although intra-trial reliability of smooth pursuit neck torsion test is good to excellent, the effects of learning are not as pronounced in patients with neck pain disorders.

Ventromedial Thalamus-Projecting DCN Neurons Modulate Associative Sensorimotor Responses in Mice

The deep cerebellar nuclei (DCN) integrate various inputs to the cerebellum and form the final cerebellar outputs critical for associative sensorimotor learning. However, the functional relevance of distinct neuronal subpopulations within the DCN remains poorly understood. Here, we examined a subpopulation of mouse DCN neurons whose axons specifically project to the ventromedial (Vm) thalamus (DCN^Vm neurons), and found that these neurons represent a specific subset of DCN units whose activity varies with trace eyeblink conditioning (tEBC), a classical associative sensorimotor learning task. Upon conditioning, the activity of DCN^Vm neurons signaled the performance of conditioned eyeblink responses (CRs). Optogenetic activation and inhibition of the DCN^Vm neurons in well-trained mice amplified and diminished the CRs, respectively. Chemogenetic manipulation of the DCN^Vm neurons had no effects on non-associative motor coordination. Furthermore, optogenetic activation of the DCN^Vm neurons caused rapid elevated firing activity in the cingulate cortex, a brain area critical for bridging the time gap between sensory stimuli and motor execution during tEBC. Together, our data highlights DCN^Vm neurons' function and delineates their kinematic parameters that modulate the strength of associative sensorimotor responses.

Passive Motor Learning: Oculomotor Adaptation in the Absence of Behavioral Errors

Motor adaptation is commonly thought to be a trial-and-error process in which the accuracy of movement improves with repetition of behavior. We challenged this view by testing whether erroneous movements are necessary for motor adaptation. In the eye movement system, the association between movements and errors can be disentangled, since errors in the predicted stimulus trajectory can be perceived even without movements. We modified a smooth pursuit eye movement adaptation paradigm in which monkeys learn to make an eye movement that predicts an upcoming change in target direction. We trained the monkeys to fixate on a target while covertly, an additional target initially moved in one direction and then changed direction after 250 ms. The monkeys showed a learned response to infrequent probe trials in which they were instructed to follow the moving target. Additional experiments confirmed that probing learning or residual eye movements during fixation did not drive learning. These results show that motor adaptation can be elicited in the absence of movement and provide an animal model for studying the implementation of passive motor learning. Current models assume that the interaction between movement and error signals underlies adaptive motor learning. Our results point to other mechanisms that may drive learning in the absence of movement.

Diversity and dynamism in the cerebellum

The past several years have brought revelations and paradigm shifts in research on the cerebellum. Historically viewed as a simple sensorimotor controller with homogeneous architecture, the cerebellum is increasingly implicated in cognitive functions. It possesses an impressive diversity of molecular, cellular and circuit mechanisms, embedded in a dynamic, recurrent circuit architecture. Recent insights about the diversity and dynamism of the cerebellum provide a roadmap for the next decade of cerebellar research, challenging some old concepts, reinvigorating others and defining major new research directions.

Long-term effects of cerebellar anodal transcranial direct current stimulation (tDCS) on the acquisition and extinction of conditioned eyeblink responses

Cerebellar transcranial direct current stimulation (tDCS) has been reported to enhance the acquisition of conditioned eyeblink responses (CR), a form of associative motor learning. The aim of the present study was to determine possible long-term effects of cerebellar tDCS on the acquisition and extinction of CRs. Delay eyeblink conditioning was performed in 40 young and healthy human participants. On day 1, 100 paired CS (conditioned stimulus)–US (unconditioned stimulus) trials were applied. During the first 50 paired CS–US trials, 20 participants received anodal cerebellar tDCS, and 20 participants received sham stimulation. On days 2, 8 and 29, 50 paired CS–US trials were applied, followed by 30 CS-only extinction trials on day 29. CR acquisition was not significantly different between anodal and sham groups. During extinction, CR incidences were significantly reduced in the anodal group compared to sham, indicating reduced retention. In the anodal group, learning related increase of CR magnitude tended to be reduced, and timing of CRs tended to be delayed. The present data do not confirm previous findings of enhanced acquisition of CRs induced by anodal cerebellar tDCS. Rather, the present findings suggest a detrimental effect of anodal cerebellar tDCS on CR retention and possibly CR performance.

The Cerebellar Nuclei and Dexterous Limb Movements

Dexterous forelimb movements like reaching, grasping, and manipulating objects are fundamental building blocks of the mammalian motor repertoire. These behaviors are essential to everyday activities, and their elaboration underlies incredible accomplishments by human beings in art and sport. Moreover, the susceptibility of these behaviors to damage and disease of the nervous system can lead to debilitating deficits, highlighting a need for a better understanding of function and dysfunction in sensorimotor control. The cerebellum is central to coordinating limb movements, as defined in large part by Joseph Babinski and Gordon Holmes describing motor impairment in patients with cerebellar lesions over 100 years ago (Babinski, 1902; Holmes, 1917), and supported by many important human and animal studies that have been conducted since. Here, with a focus on output pathways of the cerebellar nuclei across mammalian species, we describe forelimb movement deficits observed when cerebellar circuits are perturbed, the mechanisms through which these circuits influence motor output, and key challenges in defining how the cerebellum refines limb movement.

Population coding in the cerebellum: a machine learning perspective

The cere resembles a feedforward, three-layer network of neurons in which the "hidden layer" consists of Purkinje cells (P-cells) and the output layer consists of deep cerebellar nucleus (DCN) neurons. In this analogy, the output of each DCN neuron is a prediction that is compared with the actual observation, resulting in an error signal that originates in the inferior olive. Efficient learning requires that the error signal reach the DCN neurons, as well as the P-cells that project onto them. However, this basic rule of learning is violated in the cerebellum: the olivary projections to the DCN are weak, particularly in adulthood. Instead, an extraordinarily strong signal is sent from the olive to the P-cells, producing complex spikes. Curiously, P-cells are grouped into small populations that converge onto single DCN neurons. Why are the P-cells organized in this way, and what is the membership criterion of each population? Here, I apply elementary mathematics from machine learning and consider the fact that P-cells that form a population exhibit a special property: they can synchronize their complex spikes, which in turn suppress activity of DCN neuron they project to. Thus complex spikes cannot only act as a teaching signal for a P-cell, but through complex spike synchrony, a P-cell population may act as a surrogate teacher for the DCN neuron that produced the erroneous output. It appears that grouping of P-cells into small populations that share a preference for error satisfies a critical requirement of efficient learning: providing error information to the output layer neuron (DCN) that was responsible for the error, as well as the hidden layer neurons (P-cells) that contributed to it. This population coding may account for several remarkable features of behavior during learning, including multiple timescales, protection from erasure, and spontaneous recovery of memory.

The Rules of Cerebellar Learning: Around the Ito Hypothesis

As a tribute to Masao Ito, we propose a model of cerebellar learning that incorporates and extends his original model. We suggest four principles that align well with conclusions from multiple cerebellar learning systems. (1) Climbing fiber inputs to the cerebellum drive early, fast, poorly-retained learning in the parallel fiber to Purkinje cell synapse. (2) Learned Purkinje cell outputs drive late, slow, well-retained learning in non-Purkinje cell inputs to neurons in the cerebellar nucleus, transferring learning from the cortex to the nucleus. (3) Recurrent feedback from Purkinje cells to the inferior olive, through interneurons in the cerebellar nucleus, limits the magnitude of fast, early learning in the cerebellar cortex. (4) Functionally different inputs are subjected to plasticity in the cerebellar cortex versus the cerebellar nucleus. A computational neural circuit model that is based on these principles mimics a large amount of neural and behavioral data obtained from the smooth pursuit eye movements of monkeys.