A real-time spiking cerebellum model for learning robot control

Mesoscale simulations predict the role of synergistic cerebellar plasticity during classical eyeblink conditioning

According to the motor learning theory by Albus and Ito, synaptic depression at the parallel fibre to Purkinje cells synapse (pf-PC) is the main substrate responsible for learning sensorimotor contingencies under climbing fibre control. However, recent experimental evidence challenges this relatively monopolistic view of cerebellar learning. Bidirectional plasticity appears crucial for learning, in which different microzones can undergo opposite changes of synaptic strength (e.g. downbound microzones-more likely depression, upbound microzones-more likely potentiation), and multiple forms of plasticity have been identified, distributed over different cerebellar circuit synapses. Here, we have simulated classical eyeblink conditioning (CEBC) using an advanced spiking cerebellar model embedding downbound and upbound modules that are subject to multiple plasticity rules. Simulations indicate that synaptic plasticity regulates the cascade of precise spiking patterns spreading throughout the cerebellar cortex and cerebellar nuclei. CEBC was supported by plasticity at the pf-PC synapses as well as at the synapses of the molecular layer interneurons (MLIs), but only the combined switch-off of both sites of plasticity compromised learning significantly. By differentially engaging climbing fibre information and related forms of synaptic plasticity, both microzones contributed to generate a well-timed conditioned response, but it was the downbound module that played the major role in this process. The outcomes of our simulations closely align with the behavioural and electrophysiological phenotypes of mutant mice suffering from cell-specific mutations that affect processing of their PC and/or MLI synapses. Our data highlight that a synergy of bidirectional plasticity rules distributed across the cerebellum can facilitate finetuning of adaptive associative behaviours at a high spatiotemporal resolution.

CBMC: A Biomimetic Approach for Control of a 7-Degree of Freedom Robotic Arm

Many approaches inspired by brain science have been proposed for robotic control, specifically targeting situations where knowledge of the dynamic model is unavailable. This is crucial because dynamic model inaccuracies and variations can occur during the robot's operation. In this paper, inspired by the central nervous system (CNS), we present a CNS-based Biomimetic Motor Control (CBMC) approach consisting of four modules. The first module consists of a cerebellum-like spiking neural network that employs spiking timing-dependent plasticity to learn the dynamics mechanisms and adjust the synapses connecting the spiking neurons. The second module constructed using an artificial neural network, mimicking the regulation ability of the cerebral cortex to the cerebellum in the CNS, learns by reinforcement learning to supervise the cerebellum module with instructive input. The third and last modules are the cerebral sensory module and the spinal cord module, which deal with sensory input and provide modulation to torque commands, respectively. To validate our method, CBMC was applied to the trajectory tracking control of a 7-DoF robotic arm in simulation. Finally, experiments are conducted on the robotic arm using various payloads, and the results of these experiments clearly demonstrate the effectiveness of the proposed methodology.

The contribution of the basal ganglia and cerebellum to motor learning: A neuro-computational approach

Motor learning involves a widespread brain network including the basal ganglia, cerebellum, motor cortex, and brainstem. Despite its importance, little is known about how this network learns motor tasks and which role different parts of this network take. We designed a systems-level computational model of motor learning, including a cortex-basal ganglia motor loop and the cerebellum that both determine the response of central pattern generators in the brainstem. First, we demonstrate its ability to learn arm movements toward different motor goals. Second, we test the model in a motor adaptation task with cognitive control, where the model replicates human data. We conclude that the cortex-basal ganglia loop learns via a novelty-based motor prediction error to determine concrete actions given a desired outcome, and that the cerebellum minimizes the remaining aiming error.

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.

Dual STDP processes at Purkinje cells contribute to distinct improvements in accuracy and speed of saccadic eye movements

Saccadic eye-movements play a crucial role in visuo-motor control by allowing rapid foveation onto new targets. However, the neural processes governing saccades adaptation are not fully understood. Saccades, due to the short-time of execution (20-100 ms) and the absence of sensory information for online feedback control, must be controlled in a ballistic manner. Incomplete measurements of the movement trajectory, such as the visual endpoint error, are supposedly used to form internal predictions about the movement kinematics resulting in predictive control. In order to characterize the synaptic and neural circuit mechanisms underlying predictive saccadic control, we have reconstructed the saccadic system in a digital controller embedding a spiking neural network of the cerebellum with spike timing-dependent plasticity (STDP) rules driving parallel fiber-Purkinje cell long-term potentiation and depression (LTP and LTD). This model implements a control policy based on a dual plasticity mechanism, resulting in the identification of the roles of LTP and LTD in regulating the overall quality of saccade kinematics: it turns out that LTD increases the accuracy by decreasing visual error and LTP increases the peak speed. The control policy also required cerebellar PCs to be divided into two subpopulations, characterized by burst or pause responses. To our knowledge, this is the first model that explains in mechanistic terms the visual error and peak speed regulation of ballistic eye movements in forward mode exploiting spike-timing to regulate firing in different populations of the neuronal network. This elementary model of saccades could be extended and applied to other more complex cases in which single jerks are concatenated to compose articulated and coordinated movements.

CerebelluMorphic: Large-Scale Neuromorphic Model and Architecture for Supervised Motor Learning

The cerebellum plays a vital role in motor learning and control with supervised learning capability, while neuromorphic engineering devises diverse approaches to high-performance computation inspired by biological neural systems. This article presents a large-scale cerebellar network model for supervised learning, as well as a cerebellum-inspired neuromorphic architecture to map the cerebellar anatomical structure into the large-scale model. Our multinucleus model and its underpinning architecture contain approximately 3.5 million neurons, upscaling state-of-the-art neuromorphic designs by over 34 times. Besides, the proposed model and architecture incorporate 3411k granule cells, introducing a 284 times increase compared to a previous study including only 12k cells. This large scaling induces more biologically plausible cerebellar divergence/convergence ratios, which results in better mimicking biology. In order to verify the functionality of our proposed model and demonstrate its strong biomimicry, a reconfigurable neuromorphic system is used, on which our developed architecture is realized to replicate cerebellar dynamics during the optokinetic response. In addition, our neuromorphic architecture is used to analyze the dynamical synchronization within the Purkinje cells, revealing the effects of firing rates of mossy fibers on the resonance dynamics of Purkinje cells. Our experiments show that real-time operation can be realized, with a system throughput of up to 4.70 times larger than previous works with high synaptic event rate. These results suggest that the proposed work provides both a theoretical basis and a neuromorphic engineering perspective for brain-inspired computing and the further exploration of cerebellar learning.

A review of motor neural system robotic modeling approaches and instruments

In this review, we are considering an actively developing tool in neuroscience-robotic modeling. The new perspective and existing application fields, tools, and methods are discussed. We try to determine starting positions and approaches that are useful at the beginning of new research in this field. Among multiple directions of the research is robotic modeling on the level of muscles fibers and their afferents, skin surface sensors, muscles, and joints proprioceptors. Some examples of technical implementation for physical modeling are reviewed. They are software and hardware tools like event-related modeling algorithms, reduced neuron models, robotic drives constructions. We observe existing drives technologies and prospective electric motor types: switched reluctance and transverse flux motors. Next, we look at the existing examples and approaches for robotic modeling of the cerebellum and spinal cord neural networks. These examples show practical methods for the model neural network architecture and adaptation. Those methods allow the use of cortical and spinal cord reflexes for the network training and apply additional artificial blocks for data processing in other brain structures that transmit and receive data from biologically realistic models.

Cortico-Cerebellar Hyper-Connections and Reduced Purkinje Cells Behind Abnormal Eyeblink Conditioning in a Computational Model of Autism Spectrum Disorder

Empirical evidence suggests that children with autism spectrum disorder (ASD) show abnormal behavior during delay eyeblink conditioning. They show a higher conditioned response learning rate and earlier peak latency of the conditioned response signal. The neuronal mechanisms underlying this autistic behavioral phenotype are still unclear. Here, we use a physiologically constrained spiking neuron model of the cerebellar-cortical system to investigate which features are critical to explaining atypical learning in ASD. Significantly, the computer simulations run with the model suggest that the higher conditioned responses learning rate mainly depends on the reduced number of Purkinje cells. In contrast, the earlier peak latency mainly depends on the hyper-connections of the cerebellum with sensory and motor cortex. Notably, the model has been validated by reproducing the behavioral data collected from studies with real children. Overall, this article is a starting point to understanding the link between the behavioral and neurobiological basis in ASD learning. At the end of the paper, we discuss how this knowledge could be critical for devising new treatments.

Computational epidemiology study of homeostatic compensation during sensorimotor aging

The vestibulo-ocular reflex (VOR) stabilizes vision during head motion. Age-related changes of vestibular neuroanatomical properties predict a linear decay of VOR function. Nonetheless, human epidemiological data show a stable VOR function across the life span. In this study, we model cerebellum-dependent VOR adaptation to relate structural and functional changes throughout aging. We consider three neurosynaptic factors that may codetermine VOR adaptation during aging: the electrical coupling of inferior olive neurons, the long-term spike timing-dependent plasticity at parallel fiber - Purkinje cell synapses and mossy fiber - medial vestibular nuclei synapses, and the intrinsic plasticity of Purkinje cell synapses Our cross-sectional aging analyses suggest that long-term plasticity acts as a global homeostatic mechanism that underpins the stable temporal profile of VOR function. The results also suggest that the intrinsic plasticity of Purkinje cell synapses operates as a local homeostatic mechanism that further sustains the VOR at older ages. Importantly, the computational epidemiology approach presented in this study allows discrepancies among human cross-sectional studies to be understood in terms of interindividual variability in older individuals. Finally, our longitudinal aging simulations show that the amount of residual fibers coding for the peak and trough of the VOR cycle constitutes a predictive hallmark of VOR trajectories over a lifetime.

Towards a Bio-Inspired Real-Time Neuromorphic Cerebellum

This work presents the first simulation of a large-scale, bio-physically constrained cerebellum model performed on neuromorphic hardware. A model containing 97,000 neurons and 4.2 million synapses is simulated on the SpiNNaker neuromorphic system. Results are validated against a baseline simulation of the same model executed with NEST, a popular spiking neural network simulator using generic computational resources and double precision floating point arithmetic. Individual cell and network-level spiking activity is validated in terms of average spike rates, relative lead or lag of spike times, and membrane potential dynamics of individual neurons, and SpiNNaker is shown to produce results in agreement with NEST. Once validated, the model is used to investigate how to accelerate the simulation speed of the network on the SpiNNaker system, with the future goal of creating a real-time neuromorphic cerebellum. Through detailed communication profiling, peak network activity is identified as one of the main challenges for simulation speed-up. Propagation of spiking activity through the network is measured, and will inform the future development of accelerated execution strategies for cerebellum models on neuromorphic hardware. The large ratio of granule cells to other cell types in the model results in high levels of activity converging onto few cells, with those cells having relatively larger time costs associated with the processing of communication. Organizing cells on SpiNNaker in accordance with their spatial position is shown to reduce the peak communication load by 41%. It is hoped that these insights, together with alternative parallelization strategies, will pave the way for real-time execution of large-scale, bio-physically constrained cerebellum models on SpiNNaker. This in turn will enable exploration of cerebellum-inspired controllers for neurorobotic applications, and execution of extended duration simulations over timescales that would currently be prohibitive using conventional computational platforms.

On Robot Compliance: A Cerebellar Control Approach

The work presented here is a novel biological approach for the compliant control of a robotic arm in real time (RT). We integrate a spiking cerebellar network at the core of a feedback control loop performing torque-driven control. The spiking cerebellar controller provides torque commands allowing for accurate and coordinated arm movements. To compute these output motor commands, the spiking cerebellar controller receives the robot's sensorial signals, the robot's goal behavior, and an instructive signal. These input signals are translated into a set of evolving spiking patterns representing univocally a specific system state at every point of time. Spike-timing-dependent plasticity (STDP) is then supported, allowing for building adaptive control. The spiking cerebellar controller continuously adapts the torque commands provided to the robot from experience as STDP is deployed. Adaptive torque commands, in turn, help the spiking cerebellar controller to cope with built-in elastic elements within the robot's actuators mimicking human muscles (inherently elastic). We propose a natural integration of a bioinspired control scheme, based on the cerebellum, with a compliant robot. We prove that our compliant approach outperforms the accuracy of the default factory-installed position control in a set of tasks used for addressing cerebellar motor behavior: controlling six degrees of freedom (DoF) in smooth movements, fast ballistic movements, and unstructured scenario compliant movements.

A multizone cerebellar chip for bioinspired adaptive robot control and sensorimotor processing

The cerebellum is a neural structure essential for learning, which is connected via multiple zones to many different regions of the brain, and is thought to improve human performance in a large range of sensory, motor and even cognitive processing tasks. An intriguing possibility for the control of complex robotic systems would be to develop an artificial cerebellar chip with multiple zones that could be similarly connected to a variety of subsystems to optimize performance. The novel aim of this paper, therefore, is to propose and investigate a multizone cerebellar chip applied to a range of tasks in robot adaptive control and sensorimotor processing. The multizone cerebellar chip was evaluated using a custom robotic platform consisting of an array of tactile sensors driven by dielectric electroactive polymers mounted upon a standard industrial robot arm. The results demonstrate that the performance in each task was improved by the concurrent, stable learning in each cerebellar zone. This paper, therefore, provides the first empirical demonstration that a synthetic, multizone, cerebellar chip could be embodied within existing robotic systems to improve performance in a diverse range of tasks, much like the cerebellum in a biological system.

Cerebellar adaptive mechanisms explain the optimal control of saccadic eye movements

Cerebellar synaptic plasticity is vital for adaptability and fine tuning of goal-directed movements. The perceived sensory errors between desired and actual movement outcomes are commonly considered to induce plasticity in the cerebellar synapses, with an objective to improve desirability of the executed movements. In rapid goal-directed eye movements called saccades, the only available sensory feedback is the direction of reaching error information received only at end of the movement. Moreover, this sensory error dependent plasticity can only improve the accuracy of the movements, while ignoring other essential characteristics such as reaching in minimum-time. In this work we propose a rate based, cerebellum inspired adaptive filter model to address refinement of both accuracy and movement-time of saccades. We use optimal control approach in conjunction with information constraints posed by the cerebellum to derive bio-plausible supervised plasticity rules. We implement and validate this bio-inspired scheme on a humanoid robot. We found out that, separate plasticity mechanisms in the model cerebellum separately control accuracy and movement-time. These plasticity mechanisms ensure that optimal saccades are produced by just receiving the direction of end reaching error as an evaluative signal. Furthermore, the model emulates encoding in the cerebellum of movement kinematics as observed in biological experiments.

How the Cerebellum and Prefrontal Cortex Cooperate During Trace Eyeblinking Conditioning

Several data have demonstrated that during the widely used experimental paradigm for studying associative learning, trace eye blinking conditioning (TEBC), there is a strong interaction between cerebellum and medial prefrontal cortex (mPFC). Despite this evidence, the neural mechanisms underlying this interaction are still not clear. Here, we propose a neurophysiologically plausible computational model to address this issue. The model is constrained on the basis of two critical anatomo-physiological features: (i) the cerebello-cortical organization through two circuits, respectively, targeting M1 and mPFC; (ii) the different timing in the plasticity mechanisms of these parallel circuits produced by the granule cells time sensitivity according to which different subpopulations are active at different moments during conditioned stimuli. The computer simulations run with the model suggest that these features are critical to understand how the cooperation between cerebellum and mPFC supports motor areas during TEBC. In particular, a greater trace interval produces greater plasticity changes at the slow path synapses involving mPFC with respect to plasticity changes at the fast path involving M1. As a consequence, the greater is the trace interval, the stronger is the mPFC involvement. The model has been validated by reproducing data collected through recent real mice experiments.

A Cerebellum-Inspired Learning Approach for Adaptive and Anticipatory Control

The cerebellum, which is responsible for motor control and learning, has been suggested to act as a Smith predictor for compensation of time-delays by means of internal forward models. However, insights about how forward model predictions are integrated in the Smith predictor have not yet been unveiled. To fill this gap, a novel bio-inspired modular control architecture that merges a recurrent cerebellar-like loop for adaptive control and a Smith predictor controller is proposed. The goal is to provide accurate anticipatory corrections to the generation of the motor commands in spite of sensory delays and to validate the robustness of the proposed control method to input and physical dynamic changes. The outcome of the proposed architecture with other two control schemes that do not include the Smith control strategy or the cerebellar-like corrections are compared. The results obtained on four sets of experiments confirm that the cerebellum-like circuit provides more effective corrections when only the Smith strategy is adopted and that minor tuning in the parameters, fast adaptation and reproducible configuration are enabled.

Supervised Learning in SNN via Reward-Modulated Spike-Timing-Dependent Plasticity for a Target Reaching Vehicle

Spiking neural networks (SNNs) offer many advantages over traditional artificial neural networks (ANNs) such as biological plausibility, fast information processing, and energy efficiency. Although SNNs have been used to solve a variety of control tasks using the Spike-Timing-Dependent Plasticity (STDP) learning rule, existing solutions usually involve hard-coded network architectures solving specific tasks rather than solving different kinds of tasks generally. This results in neglecting one of the biggest advantages of ANNs, i.e., being general-purpose and easy-to-use due to their simple network architecture, which usually consists of an input layer, one or multiple hidden layers and an output layer. This paper addresses the problem by introducing an end-to-end learning approach of spiking neural networks constructed with one hidden layer and reward-modulated Spike-Timing-Dependent Plasticity (R-STDP) synapses in an all-to-all fashion. We use the supervised reward-modulated Spike-Timing-Dependent-Plasticity learning rule to train two different SNN-based sub-controllers to replicate a desired obstacle avoiding and goal approaching behavior, provided by pre-generated datasets. Together they make up a target-reaching controller, which is used to control a simulated mobile robot to reach a target area while avoiding obstacles in its path. We demonstrate the performance and effectiveness of our trained SNNs to achieve target reaching tasks in different unknown scenarios.

Spike burst-pause dynamics of Purkinje cells regulate sensorimotor adaptation

Cerebellar Purkinje cells mediate accurate eye movement coordination. However, it remains unclear how oculomotor adaptation depends on the interplay between the characteristic Purkinje cell response patterns, namely tonic, bursting, and spike pauses. Here, a spiking cerebellar model assesses the role of Purkinje cell firing patterns in vestibular ocular reflex (VOR) adaptation. The model captures the cerebellar microcircuit properties and it incorporates spike-based synaptic plasticity at multiple cerebellar sites. A detailed Purkinje cell model reproduces the three spike-firing patterns that are shown to regulate the cerebellar output. Our results suggest that pauses following Purkinje complex spikes (bursts) encode transient disinhibition of target medial vestibular nuclei, critically gating the vestibular signals conveyed by mossy fibres. This gating mechanism accounts for early and coarse VOR acquisition, prior to the late reflex consolidation. In addition, properly timed and sized Purkinje cell bursts allow the ratio between long-term depression and potentiation (LTD/LTP) to be finely shaped at mossy fibre-medial vestibular nuclei synapses, which optimises VOR consolidation. Tonic Purkinje cell firing maintains the consolidated VOR through time. Importantly, pauses are crucial to facilitate VOR phase-reversal learning, by reshaping previously learnt synaptic weight distributions. Altogether, these results predict that Purkinje spike burst-pause dynamics are instrumental to VOR learning and reversal adaptation.

Cerebellar Purkinje cells regulate accurate eye movement coordination. However, it remains unclear how cerebellar-dependent oculomotor adaptation depends on the interplay between Purkinje cell characteristic response patterns: tonic, high frequency bursting, and post-complex spike pauses. We explore the role of Purkinje spike burst-pause dynamics in VOR adaptation. A biophysical model of Purkinje cell is at the core of a spiking network model, which captures the cerebellar microcircuit properties and incorporates spike-based synaptic plasticity mechanisms at different cerebellar sites. We show that Purkinje spike burst-pause dynamics are critical for (1) gating the vestibular-motor response association during VOR acquisition; (2) mediating the LTD/LTP balance for VOR consolidation; (3) reshaping synaptic efficacy distributions for VOR phase-reversal adaptation; (4) explaining the reversal VOR gain discontinuities during sleeping.

VOR Adaptation on a Humanoid iCub Robot Using a Spiking Cerebellar Model

We embed a spiking cerebellar model within an adaptive real-time (RT) control loop that is able to operate a real robotic body (iCub) when performing different vestibulo-ocular reflex (VOR) tasks. The spiking neural network computation, including event- and time-driven neural dynamics, neural activity, and spike-timing dependent plasticity (STDP) mechanisms, leads to a nondeterministic computation time caused by the neural activity volleys encountered during cerebellar simulation. This nondeterministic computation time motivates the integration of an RT supervisor module that is able to ensure a well-orchestrated neural computation time and robot operation. Actually, our neurorobotic experimental setup (VOR) benefits from the biological sensory motor delay between the cerebellum and the body to buffer the computational overloads as well as providing flexibility in adjusting the neural computation time and RT operation. The RT supervisor module provides for incremental countermeasures that dynamically slow down or speed up the cerebellar simulation by either halting the simulation or disabling certain neural computation features (i.e., STDP mechanisms, spike propagation, and neural updates) to cope with the RT constraints imposed by the real robot operation. This neurorobotic experimental setup is applied to different horizontal and vertical VOR adaptive tasks that are widely used by the neuroscientific community to address cerebellar functioning. We aim to elucidate the manner in which the combination of the cerebellar neural substrate and the distributed plasticity shapes the cerebellar neural activity to mediate motor adaptation. This paper underlies the need for a two-stage learning process to facilitate VOR acquisition.

A Metric for Evaluating Neural Input Representation in Supervised Learning Networks

Supervised learning has long been attributed to several feed-forward neural circuits within the brain, with particular attention being paid to the cerebellar granular layer. The focus of this study is to evaluate the input activity representation of these feed-forward neural networks. The activity of cerebellar granule cells is conveyed by parallel fibers and translated into Purkinje cell activity, which constitutes the sole output of the cerebellar cortex. The learning process at this parallel-fiber-to-Purkinje-cell connection makes each Purkinje cell sensitive to a set of specific cerebellar states, which are roughly determined by the granule-cell activity during a certain time window. A Purkinje cell becomes sensitive to each neural input state and, consequently, the network operates as a function able to generate a desired output for each provided input by means of supervised learning. However, not all sets of Purkinje cell responses can be assigned to any set of input states due to the network's own limitations (inherent to the network neurobiological substrate), that is, not all input-output mapping can be learned. A key limiting factor is the representation of the input states through granule-cell activity. The quality of this representation (e.g., in terms of heterogeneity) will determine the capacity of the network to learn a varied set of outputs. Assessing the quality of this representation is interesting when developing and studying models of these networks to identify those neuron or network characteristics that enhance this representation. In this study we present an algorithm for evaluating quantitatively the level of compatibility/interference amongst a set of given cerebellar states according to their representation (granule-cell activation patterns) without the need for actually conducting simulations and network training. The algorithm input consists of a real-number matrix that codifies the activity level of every considered granule-cell in each state. The capability of this representation to generate a varied set of outputs is evaluated geometrically, thus resulting in a real number that assesses the goodness of the representation.

CABots and Other Neural Agents

The best way to develop a Turing test passing AI is to follow the human model: an embodied agent that functions over a wide range of domains, is a human cognitive model, follows human neural functioning and learns. These properties will endow the agent with the deep semantics required to pass the test. An embodied agent functioning over a wide range of domains is needed to be exposed to and learn the semantics of those domains. Following human cognitive and neural functioning simplifies the search for sufficiently sophisticated mechanisms by reusing mechanisms that are already known to be sufficient. This is a difficult task, but initial steps have been taken, including the development of CABots, neural agents embodied in virtual environments. Several different CABots run in response to natural language commands, performing a cognitive mapping task. These initial agents are quite some distance from passing the test, and to develop an agent that passes will require broad collaboration. Several next steps are proposed, and these could be integrated using, for instance, the Platforms from the Human Brain Project as a foundation for this collaboration.

A Survey of Robotics Control Based on Learning-Inspired Spiking Neural Networks

Biological intelligence processes information using impulses or spikes, which makes those living creatures able to perceive and act in the real world exceptionally well and outperform state-of-the-art robots in almost every aspect of life. To make up the deficit, emerging hardware technologies and software knowledge in the fields of neuroscience, electronics, and computer science have made it possible to design biologically realistic robots controlled by spiking neural networks (SNNs), inspired by the mechanism of brains. However, a comprehensive review on controlling robots based on SNNs is still missing. In this paper, we survey the developments of the past decade in the field of spiking neural networks for control tasks, with particular focus on the fast emerging robotics-related applications. We first highlight the primary impetuses of SNN-based robotics tasks in terms of speed, energy efficiency, and computation capabilities. We then classify those SNN-based robotic applications according to different learning rules and explicate those learning rules with their corresponding robotic applications. We also briefly present some existing platforms that offer an interaction between SNNs and robotics simulations for exploration and exploitation. Finally, we conclude our survey with a forecast of future challenges and some associated potential research topics in terms of controlling robots based on SNNs.

Bio-inspired spiking neural network for nonlinear systems control

Spiking neural networks (SNN) are the third generation of artificial neural networks. SNN are the closest approximation to biological neural networks. SNNs make use of temporal spike trains to command inputs and outputs, allowing a faster and more complex computation. As demonstrated by biological organisms, they are a potentially good approach to designing controllers for highly nonlinear dynamic systems in which the performance of controllers developed by conventional techniques is not satisfactory or difficult to implement. SNN-based controllers exploit their ability for online learning and self-adaptation to evolve when transferred from simulations to the real world. SNN's inherent binary and temporary way of information codification facilitates their hardware implementation compared to analog neurons. Biological neural networks often require a lower number of neurons compared to other controllers based on artificial neural networks. In this work, these neuronal systems are imitated to perform the control of non-linear dynamic systems. For this purpose, a control structure based on spiking neural networks has been designed. Particular attention has been paid to optimizing the structure and size of the neural network. The proposed structure is able to control dynamic systems with a reduced number of neurons and connections. A supervised learning process using evolutionary algorithms has been carried out to perform controller training. The efficiency of the proposed network has been verified in two examples of dynamic systems control. Simulations show that the proposed control based on SNN exhibits superior performance compared to other approaches based on Neural Networks and SNNs.

Dynamic Redistribution of Plasticity in a Cerebellar Spiking Neural Network Reproducing an Associative Learning Task Perturbed by TMS

During natural learning, synaptic plasticity is thought to evolve dynamically and redistribute within and among subcircuits. This process should emerge in plastic neural networks evolving under behavioral feedback and should involve changes distributed across multiple synaptic sites. In eyeblink classical conditioning (EBCC), the cerebellum learns to predict the precise timing between two stimuli, hence EBCC represents an elementary yet meaningful paradigm to investigate the cerebellar network functioning. We have simulated EBCC mechanisms by reconstructing a realistic cerebellar microcircuit model and embedding multiple plasticity rules imitating those revealed experimentally. The model was tuned to fit experimental EBCC human data, estimating the underlying learning time-constants. Learning started rapidly with plastic changes in the cerebellar cortex followed by slower changes in the deep cerebellar nuclei. This process was characterized by differential development of long-term potentiation and depression at individual synapses, with a progressive accumulation of plasticity distributed over the whole network. The experimental data included two EBCC sessions interleaved by a trans-cranial magnetic stimulation (TMS). The experimental and the model response data were not significantly different in each learning phase, and the model goodness-of-fit was [Formula: see text] for all the experimental conditions. The models fitted on TMS data revealed a slowed down re-acquisition (sessions-2) compared to the control condition ([Formula: see text]). The plasticity parameters characterizing each model significantly differ among conditions, and thus mechanistically explain these response changes. Importantly, the model was able to capture the alteration in EBCC consolidation caused by TMS and showed that TMS affected plasticity at cortical synapses thereby altering the fast learning phase. This, secondarily, also affected plasticity in deep cerebellar nuclei altering learning dynamics in the entire sensory-motor loop. This observation reveals dynamic redistribution of changes over the entire network and suggests how TMS affects local circuit computation and memory processing in the cerebellum.

A Multiple-Plasticity Spiking Neural Network Embedded in a Closed-Loop Control System to Model Cerebellar Pathologies

The cerebellum plays a crucial role in sensorimotor control and cerebellar disorders compromise adaptation and learning of motor responses. However, the link between alterations at network level and cerebellar dysfunction is still unclear. In principle, this understanding would benefit of the development of an artificial system embedding the salient neuronal and plastic properties of the cerebellum and operating in closed-loop. To this aim, we have exploited a realistic spiking computational model of the cerebellum to analyze the network correlates of cerebellar impairment. The model was modified to reproduce three different damages of the cerebellar cortex: (i) a loss of the main output neurons (Purkinje Cells), (ii) a lesion to the main cerebellar afferents (Mossy Fibers), and (iii) a damage to a major mechanism of synaptic plasticity (Long Term Depression). The modified network models were challenged with an Eye-Blink Classical Conditioning test, a standard learning paradigm used to evaluate cerebellar impairment, in which the outcome was compared to reference results obtained in human or animal experiments. In all cases, the model reproduced the partial and delayed conditioning typical of the pathologies, indicating that an intact cerebellar cortex functionality is required to accelerate learning by transferring acquired information to the cerebellar nuclei. Interestingly, depending on the type of lesion, the redistribution of synaptic plasticity and response timing varied greatly generating specific adaptation patterns. Thus, not only the present work extends the generalization capabilities of the cerebellar spiking model to pathological cases, but also predicts how changes at the neuronal level are distributed across the network, making it usable to infer cerebellar circuit alterations occurring in cerebellar pathologies.

Model-Driven Analysis of Eyeblink Classical Conditioning Reveals the Underlying Structure of Cerebellar Plasticity and Neuronal Activity

The cerebellum plays a critical role in sensorimotor control. However, how the specific circuits and plastic mechanisms of the cerebellum are engaged in closed-loop processing is still unclear. We developed an artificial sensorimotor control system embedding a detailed spiking cerebellar microcircuit with three bidirectional plasticity sites. This proved able to reproduce a cerebellar-driven associative paradigm, the eyeblink classical conditioning (EBCC), in which a precise time relationship between an unconditioned stimulus (US) and a conditioned stimulus (CS) is established. We challenged the spiking model to fit an experimental data set from human subjects. Two subsequent sessions of EBCC acquisition and extinction were recorded and transcranial magnetic stimulation (TMS) was applied on the cerebellum to alter circuit function and plasticity. Evolutionary algorithms were used to find the near-optimal model parameters to reproduce the behaviors of subjects in the different sessions of the protocol. The main finding is that the optimized cerebellar model was able to learn to anticipate (predict) conditioned responses with accurate timing and success rate, demonstrating fast acquisition, memory stabilization, rapid extinction, and faster reacquisition as in EBCC in humans. The firing of Purkinje cells (PCs) and deep cerebellar nuclei (DCN) changed during learning under the control of synaptic plasticity, which evolved at different rates, with a faster acquisition in the cerebellar cortex than in DCN synapses. Eventually, a reduced PC activity released DCN discharge just after the CS, precisely anticipating the US and causing the eyeblink. Moreover, a specific alteration in cortical plasticity explained the EBCC changes induced by cerebellar TMS in humans. In this paper, for the first time, it is shown how closed-loop simulations, using detailed cerebellar microcircuit models, can be successfully used to fit real experimental data sets. Thus, the changes of the model parameters in the different sessions of the protocol unveil how implicit microcircuit mechanisms can generate normal and altered associative behaviors.The cerebellum plays a critical role in sensorimotor control. However, how the specific circuits and plastic mechanisms of the cerebellum are engaged in closed-loop processing is still unclear. We developed an artificial sensorimotor control system embedding a detailed spiking cerebellar microcircuit with three bidirectional plasticity sites. This proved able to reproduce a cerebellar-driven associative paradigm, the eyeblink classical conditioning (EBCC), in which a precise time relationship between an unconditioned stimulus (US) and a conditioned stimulus (CS) is established. We challenged the spiking model to fit an experimental data set from human subjects. Two subsequent sessions of EBCC acquisition and extinction were recorded and transcranial magnetic stimulation (TMS) was applied on the cerebellum to alter circuit function and plasticity. Evolutionary algorithms were used to find the near-optimal model parameters to reproduce the behaviors of subjects in the different sessions of the protocol. The main finding is that the optimized cerebellar model was able to learn to anticipate (predict) conditioned responses with accurate timing and success rate, demonstrating fast acquisition, memory stabilization, rapid extinction, and faster reacquisition as in EBCC in humans. The firing of Purkinje cells (PCs) and deep cerebellar nuclei (DCN) changed during learning under the control of synaptic plasticity, which evolved at different rates, with a faster acquisition in the cerebellar cortex than in DCN synapses. Eventually, a reduced PC activity released DCN discharge just after the CS, precisely anticipating the US and causing the eyeblink. Moreover, a specific alteration in cortical plasticity explained the EBCC changes induced by cerebellar TMS in humans. In this paper, for the first time, it is shown how closed-loop simulations, using detailed cerebellar microcircuit models, can be successfully used to fit real experimental data sets. Thus, the changes of the model parameters in the different sessions of the protocol unveil how implicit microcircuit mechanisms can generate normal and altered associative behaviors.

Event- and Time-Driven Techniques Using Parallel CPU-GPU Co-processing for Spiking Neural Networks

Modeling and simulating the neural structures which make up our central neural system is instrumental for deciphering the computational neural cues beneath. Higher levels of biological plausibility usually impose higher levels of complexity in mathematical modeling, from neural to behavioral levels. This paper focuses on overcoming the simulation problems (accuracy and performance) derived from using higher levels of mathematical complexity at a neural level. This study proposes different techniques for simulating neural models that hold incremental levels of mathematical complexity: leaky integrate-and-fire (LIF), adaptive exponential integrate-and-fire (AdEx), and Hodgkin-Huxley (HH) neural models (ranged from low to high neural complexity). The studied techniques are classified into two main families depending on how the neural-model dynamic evaluation is computed: the event-driven or the time-driven families. Whilst event-driven techniques pre-compile and store the neural dynamics within look-up tables, time-driven techniques compute the neural dynamics iteratively during the simulation time. We propose two modifications for the event-driven family: a look-up table recombination to better cope with the incremental neural complexity together with a better handling of the synchronous input activity. Regarding the time-driven family, we propose a modification in computing the neural dynamics: the bi-fixed-step integration method. This method automatically adjusts the simulation step size to better cope with the stiffness of the neural model dynamics running in CPU platforms. One version of this method is also implemented for hybrid CPU-GPU platforms. Finally, we analyze how the performance and accuracy of these modifications evolve with increasing levels of neural complexity. We also demonstrate how the proposed modifications which constitute the main contribution of this study systematically outperform the traditional event- and time-driven techniques under increasing levels of neural complexity.

Evaluation of Teaching Signals for Motor Control in the Cerebellum during Real-World Robot Application

Motor learning in the cerebellum is believed to entail plastic changes at synapses between parallel fibers and Purkinje cells, induced by the teaching signal conveyed in the climbing fiber (CF) input. Despite the abundant research on the cerebellum, the nature of this signal is still a matter of debate. Two types of movement error information have been proposed to be plausible teaching signals: sensory error (SE) and motor command error (ME); however, their plausibility has not been tested in the real world. Here, we conducted a comparison of different types of CF teaching signals in real-world engineering applications by using a realistic neuronal network model of the cerebellum. We employed a direct current motor (simple task) and a two-wheeled balancing robot (difficult task). We demonstrate that SE, ME or a linear combination of the two is sufficient to yield comparable performance in a simple task. When the task is more difficult, although SE slightly outperformed ME, these types of error information are all able to adequately control the robot. We categorize granular cells according to their inputs and the error signal revealing that different granule cells are preferably engaged for SE, ME or their combination. Thus, unlike previous theoretical and simulation studies that support either SE or ME, it is demonstrated for the first time in a real-world engineering application that both SE and ME are adequate as the CF teaching signal in a realistic computational cerebellar model, even when the control task is as difficult as stabilizing a two-wheeled balancing robot.

Distributed Cerebellar Motor Learning: A Spike-Timing-Dependent Plasticity Model

Deep cerebellar nuclei neurons receive both inhibitory (GABAergic) synaptic currents from Purkinje cells (within the cerebellar cortex) and excitatory (glutamatergic) synaptic currents from mossy fibers. Those two deep cerebellar nucleus inputs are thought to be also adaptive, embedding interesting properties in the framework of accurate movements. We show that distributed spike-timing-dependent plasticity mechanisms (STDP) located at different cerebellar sites (parallel fibers to Purkinje cells, mossy fibers to deep cerebellar nucleus cells, and Purkinje cells to deep cerebellar nucleus cells) in close-loop simulations provide an explanation for the complex learning properties of the cerebellum in motor learning. Concretely, we propose a new mechanistic cerebellar spiking model. In this new model, deep cerebellar nuclei embed a dual functionality: deep cerebellar nuclei acting as a gain adaptation mechanism and as a facilitator for the slow memory consolidation at mossy fibers to deep cerebellar nucleus synapses. Equipping the cerebellum with excitatory (e-STDP) and inhibitory (i-STDP) mechanisms at deep cerebellar nuclei afferents allows the accommodation of synaptic memories that were formed at parallel fibers to Purkinje cells synapses and then transferred to mossy fibers to deep cerebellar nucleus synapses. These adaptive mechanisms also contribute to modulate the deep-cerebellar-nucleus-output firing rate (output gain modulation toward optimizing its working range).

Cortical Spiking Network Interfaced with Virtual Musculoskeletal Arm and Robotic Arm

Embedding computational models in the physical world is a critical step towards constraining their behavior and building practical applications. Here we aim to drive a realistic musculoskeletal arm model using a biomimetic cortical spiking model, and make a robot arm reproduce the same trajectories in real time. Our cortical model consisted of a 3-layered cortex, composed of several hundred spiking model-neurons, which display physiologically realistic dynamics. We interconnected the cortical model to a two-joint musculoskeletal model of a human arm, with realistic anatomical and biomechanical properties. The virtual arm received muscle excitations from the neuronal model, and fed back proprioceptive information, forming a closed-loop system. The cortical model was trained using spike timing-dependent reinforcement learning to drive the virtual arm in a 2D reaching task. Limb position was used to simultaneously control a robot arm using an improved network interface. Virtual arm muscle activations responded to motoneuron firing rates, with virtual arm muscles lengths encoded via population coding in the proprioceptive population. After training, the virtual arm performed reaching movements which were smoother and more realistic than those obtained using a simplistic arm model. This system provided access to both spiking network properties and to arm biophysical properties, including muscle forces. The use of a musculoskeletal virtual arm and the improved control system allowed the robot arm to perform movements which were smoother than those reported in our previous paper using a simplistic arm. This work provides a novel approach consisting of bidirectionally connecting a cortical model to a realistic virtual arm, and using the system output to drive a robotic arm in real time. Our techniques are applicable to the future development of brain neuroprosthetic control systems, and may enable enhanced brain-machine interfaces with the possibility for finer control of limb prosthetics.

The 40-year history of modeling active dendrites in cerebellar Purkinje cells: emergence of the first single cell "community model"

The subject of the effects of the active properties of the Purkinje cell dendrite on neuronal function has been an active subject of study for more than 40 years. Somewhat unusually, some of these investigations, from the outset have involved an interacting combination of experimental and model-based techniques. This article recounts that 40-year history, and the view of the functional significance of the active properties of the Purkinje cell dendrite that has emerged. It specifically considers the emergence from these efforts of what is arguably the first single cell "community" model in neuroscience. The article also considers the implications of the development of this model for future studies of the complex properties of neuronal dendrites.

Biohybrid Control of General Linear Systems Using the Adaptive Filter Model of Cerebellum

The adaptive filter model of the cerebellar microcircuit has been successfully applied to biological motor control problems, such as the vestibulo-ocular reflex (VOR), and to sensory processing problems, such as the adaptive cancelation of reafferent noise. It has also been successfully applied to problems in robotics, such as adaptive camera stabilization and sensor noise cancelation. In previous applications to inverse control problems, the algorithm was applied to the velocity control of a plant dominated by viscous and elastic elements. Naive application of the adaptive filter model to the displacement (as opposed to velocity) control of this plant results in unstable learning and control. To be more generally useful in engineering problems, it is essential to remove this restriction to enable the stable control of plants of any order. We address this problem here by developing a biohybrid model reference adaptive control (MRAC) scheme, which stabilizes the control algorithm for strictly proper plants. We evaluate the performance of this novel cerebellar-inspired algorithm with MRAC scheme in the experimental control of a dielectric electroactive polymer, a class of artificial muscle. The results show that the augmented cerebellar algorithm is able to accurately control the displacement response of the artificial muscle. The proposed solution not only greatly extends the practical applicability of the cerebellar-inspired algorithm, but may also shed light on cerebellar involvement in a wider range of biological control tasks.

A Spiking Neural Simulator Integrating Event-Driven and Time-Driven Computation Schemes Using Parallel CPU-GPU Co-Processing: A Case Study

Time-driven simulation methods in traditional CPU architectures perform well and precisely when simulating small-scale spiking neural networks. Nevertheless, they still have drawbacks when simulating large-scale systems. Conversely, event-driven simulation methods in CPUs and time-driven simulation methods in graphic processing units (GPUs) can outperform CPU time-driven methods under certain conditions. With this performance improvement in mind, we have developed an event-and-time-driven spiking neural network simulator suitable for a hybrid CPU-GPU platform. Our neural simulator is able to efficiently simulate bio-inspired spiking neural networks consisting of different neural models, which can be distributed heterogeneously in both small layers and large layers or subsystems. For the sake of efficiency, the low-activity parts of the neural network can be simulated in CPU using event-driven methods while the high-activity subsystems can be simulated in either CPU (a few neurons) or GPU (thousands or millions of neurons) using time-driven methods. In this brief, we have undertaken a comparative study of these different simulation methods. For benchmarking the different simulation methods and platforms, we have used a cerebellar-inspired neural-network model consisting of a very dense granular layer and a Purkinje layer with a smaller number of cells (according to biological ratios). Thus, this cerebellar-like network includes a dense diverging neural layer (increasing the dimensionality of its internal representation and sparse coding) and a converging neural layer (integration) similar to many other biologically inspired and also artificial neural networks.

A realistic bi-hemispheric model of the cerebellum uncovers the purpose of the abundant granule cells during motor control

The cerebellar granule cells (GCs) have been proposed to perform lossless, adaptive spatio-temporal coding of incoming sensory/motor information required by downstream cerebellar circuits to support motor learning, motor coordination, and cognition. Here we use a physio-anatomically inspired bi-hemispheric cerebellar neuronal network (biCNN) to selectively enable/disable the output of GCs and evaluate the behavioral and neural consequences during three different control scenarios. The control scenarios are a simple direct current motor (1 degree of freedom: DOF), an unstable two-wheel balancing robot (2 DOFs), and a simulation model of a quadcopter (6 DOFs). Results showed that adequate control was maintained with a relatively small number of GCs (< 200) in all the control scenarios. However, the minimum number of GCs required to successfully govern each control plant increased with their complexity (i.e., DOFs). It was also shown that increasing the number of GCs resulted in higher robustness against changes in the initialization parameters of the biCNN model (i.e., synaptic connections and synaptic weights). Therefore, we suggest that the abundant GCs in the cerebellar cortex provide the computational power during the large repertoire of motor activities and motor plants the cerebellum is involved with, and bring robustness against changes in the cerebellar microcircuit (e.g., neuronal connections).

How the credit assignment problems in motor control could be solved after the cerebellum predicts increases in error

We present a cerebellar architecture with two main characteristics. The first one is that complex spikes respond to increases in sensory errors. The second one is that cerebellar modules associate particular contexts where errors have increased in the past with corrective commands that stop the increase in error. We analyze our architecture formally and computationally for the case of reaching in a 3D environment. In the case of motor control, we show that there are synergies of this architecture with the Equilibrium-Point hypothesis, leading to novel ways to solve the motor error and distal learning problems. In particular, the presence of desired equilibrium lengths for muscles provides a way to know when the error is increasing, and which corrections to apply. In the context of Threshold Control Theory and Perceptual Control Theory we show how to extend our model so it implements anticipative corrections in cascade control systems that span from muscle contractions to cognitive operations.

Adaptive robotic control driven by a versatile spiking cerebellar network

The cerebellum is involved in a large number of different neural processes, especially in associative learning and in fine motor control. To develop a comprehensive theory of sensorimotor learning and control, it is crucial to determine the neural basis of coding and plasticity embedded into the cerebellar neural circuit and how they are translated into behavioral outcomes in learning paradigms. Learning has to be inferred from the interaction of an embodied system with its real environment, and the same cerebellar principles derived from cell physiology have to be able to drive a variety of tasks of different nature, calling for complex timing and movement patterns. We have coupled a realistic cerebellar spiking neural network (SNN) with a real robot and challenged it in multiple diverse sensorimotor tasks. Encoding and decoding strategies based on neuronal firing rates were applied. Adaptive motor control protocols with acquisition and extinction phases have been designed and tested, including an associative Pavlovian task (Eye blinking classical conditioning), a vestibulo-ocular task and a perturbed arm reaching task operating in closed-loop. The SNN processed in real-time mossy fiber inputs as arbitrary contextual signals, irrespective of whether they conveyed a tone, a vestibular stimulus or the position of a limb. A bidirectional long-term plasticity rule implemented at parallel fibers-Purkinje cell synapses modulated the output activity in the deep cerebellar nuclei. In all tasks, the neurorobot learned to adjust timing and gain of the motor responses by tuning its output discharge. It succeeded in reproducing how human biological systems acquire, extinguish and express knowledge of a noisy and changing world. By varying stimuli and perturbations patterns, real-time control robustness and generalizability were validated. The implicit spiking dynamics of the cerebellar model fulfill timing, prediction and learning functions.

Online and post-trial feedback differentially affect implicit adaptation to a visuomotor rotation

Multiple motor learning processes can be discriminated in visuomotor rotation paradigms. At least four processes have been proposed: Implicit adaptation updates an internal model based on prediction errors. Model-free reinforcement reinforces actions that achieve task success. Use-dependent learning favors repetition of prior movements, and strategic learning uses explicit knowledge about the task. The current experiment tested whether the processes involved in motor learning differ when visual feedback is altered. Specifically, we hypothesized that online and post-trial feedback would cause different amounts of implicit adaptation. Twenty subjects performed drawing movements to targets under a 45° counterclockwise visuomotor rotation while aiming at a clockwise adjacent target. Subjects received visual feedback via a cursor on a screen. One group saw the cursor throughout the movement (online feedback), while the other only saw the final position after movement execution (post-trial feedback). Both groups initially hit the target by applying the strategy. After 80 trials, subjects with online feedback had drifted in clockwise direction [mean direction error: 15.1° (SD 11.2°)], thus overcompensating the rotation. Subjects with post-trial feedback remained accurate [mean: 0.7° (SD 2.0°), TIME ×

GROUP

F = 3.926, p = 0.003]. We interpret this overcompensation to reflect implicit adaptation isolated from other mechanisms, because it is driven by prediction error rather than task success (model-free reinforcement) or repetition (use-dependent learning). The current findings extend previous work (e.g., Mazzoni and Krakauer in J Neurosci 26:3642-3645, 2006; Hinder et al. in Exp Brain Res 201:191-207, 2010) and suggest that online feedback promotes more implicit adaptation than does post-trial feedback.

Spike-timing-dependent construction

Spike-timing-dependent construction (STDC) is the production of new spiking neurons and connections in a simulated neural network in response to neuron activity. Following the discovery of spike-timing-dependent plasticity (STDP), significant effort has gone into the modeling and simulation of adaptation in spiking neural networks (SNNs). Limitations in computational power imposed by network topology, however, constrain learning capabilities through connection weight modification alone. Constructive algorithms produce new neurons and connections, allowing automatic structural responses for applications of unknown complexity and nonstationary solutions. A conceptual analogy is developed and extended to theoretical conditions for modeling synaptic plasticity as network construction. Generalizing past constructive algorithms, we propose a framework for the design of novel constructive SNNs and demonstrate its application in the development of simulations for the validation of developed theory. Potential directions of future research and applications of STDC for biological modeling and machine learning are also discussed.

Realtime cerebellum: a large-scale spiking network model of the cerebellum that runs in realtime using a graphics processing unit

The cerebellum plays an essential role in adaptive motor control. Once we are able to build a cerebellar model that runs in realtime, which means that a computer simulation of 1 s in the simulated world completes within 1 s in the real world, the cerebellar model could be used as a realtime adaptive neural controller for physical hardware such as humanoid robots. In this paper, we introduce "Realtime Cerebellum (RC)", a new implementation of our large-scale spiking network model of the cerebellum, which was originally built to study cerebellar mechanisms for simultaneous gain and timing control and acted as a general-purpose supervised learning machine of spatiotemporal information known as reservoir computing, on a graphics processing unit (GPU). Owing to the massive parallel computing capability of a GPU, RC runs in realtime, while reproducing qualitatively the same simulation results of the Pavlovian delay eyeblink conditioning with the previous version. RC is adopted as a realtime adaptive controller of a humanoid robot, which is instructed to learn a proper timing to swing a bat to hit a flying ball online. These results suggest that RC provides a means to apply the computational power of the cerebellum as a versatile supervised learning machine towards engineering applications.

Bio-inspired adaptive feedback error learning architecture for motor control

This study proposes an adaptive control architecture based on an accurate regression method called Locally Weighted Projection Regression (LWPR) and on a bio-inspired module, such as a cerebellar-like engine. This hybrid architecture takes full advantage of the machine learning module (LWPR kernel) to abstract an optimized representation of the sensorimotor space while the cerebellar component integrates this to generate corrective terms in the framework of a control task. Furthermore, we illustrate how the use of a simple adaptive error feedback term allows to use the proposed architecture even in the absence of an accurate analytic reference model. The presented approach achieves an accurate control with low gain corrective terms (for compliant control schemes). We evaluate the contribution of the different components of the proposed scheme comparing the obtained performance with alternative approaches. Then, we show that the presented architecture can be used for accurate manipulation of different objects when their physical properties are not directly known by the controller. We evaluate how the scheme scales for simulated plants of high Degrees of Freedom (7-DOFs).

FROM SENSORS TO SPIKES: EVOLVING RECEPTIVE FIELDS TO ENHANCE SENSORIMOTOR INFORMATION IN A ROBOT-ARM

In biological systems, instead of actual encoders at different joints, proprioception signals are acquired through distributed receptive fields. In robotics, a single and accurate sensor output per link (encoder) is commonly used to track the position and the velocity. Interfacing bio-inspired control systems with spiking neural networks emulating the cerebellum with conventional robots is not a straight forward task. Therefore, it is necessary to adapt this one-dimensional measure (encoder output) into a multidimensional space (inputs for a spiking neural network) to connect, for instance, the spiking cerebellar architecture; i.e. a translation from an analog space into a distributed population coding in terms of spikes. This paper analyzes how evolved receptive fields (optimized towards information transmission) can efficiently generate a sensorimotor representation that facilitates its discrimination from other "sensorimotor states". This can be seen as an abstraction of the Cuneate Nucleus (CN) functionality in a robot-arm scenario. We model the CN as a spiking neuron population coding in time according to the response of mechanoreceptors during a multi-joint movement in a robot joint space. An encoding scheme that takes into account the relative spiking time of the signals propagating from peripheral nerve fibers to second-order somatosensory neurons is proposed. Due to the enormous number of possible encodings, we have applied an evolutionary algorithm to evolve the sensory receptive field representation from random to optimized encoding. Following the nature-inspired analogy, evolved configurations have shown to outperform simple hand-tuned configurations and other homogenized configurations based on the solution provided by the optimization engine (evolutionary algorithm). We have used artificial evolutionary engines as the optimization tool to circumvent nonlinearity responses in receptive fields.

ADAPTIVE CEREBELLAR SPIKING MODEL EMBEDDED IN THE CONTROL LOOP: CONTEXT SWITCHING AND ROBUSTNESS AGAINST NOISE

This work evaluates the capability of a spiking cerebellar model embedded in different loop architectures (recurrent, forward, and forward&recurrent) to control a robotic arm (three degrees of freedom) using a biologically-inspired approach. The implemented spiking network relies on synaptic plasticity (long-term potentiation and long-term depression) to adapt and cope with perturbations in the manipulation scenario: changes in dynamics and kinematics of the simulated robot. Furthermore, the effect of several degrees of noise in the cerebellar input pathway (mossy fibers) was assessed depending on the employed control architecture. The implemented cerebellar model managed to adapt in the three control architectures to different dynamics and kinematics providing corrective actions for more accurate movements. According to the obtained results, coupling both control architectures (forward&recurrent) provides benefits of the two of them and leads to a higher robustness against noise.

Cerebellar input configuration toward object model abstraction in manipulation tasks

It is widely assumed that the cerebellum is one of the main nervous centers involved in correcting and refining planned movement and accounting for disturbances occurring during movement, for instance, due to the manipulation of objects which affect the kinematics and dynamics of the robot-arm plant model. In this brief, we evaluate a way in which a cerebellar-like structure can store a model in the granular and molecular layers. Furthermore, we study how its microstructure and input representations (context labels and sensorimotor signals) can efficiently support model abstraction toward delivering accurate corrective torque values for increasing precision during different-object manipulation. We also describe how the explicit (object-related input labels) and implicit state input representations (sensorimotor signals) complement each other to better handle different models and allow interpolation between two already stored models. This facilitates accurate corrections during manipulations of new objects taking advantage of already stored models.

Cerebellarlike corrective model inference engine for manipulation tasks

This paper presents how a simple cerebellumlike architecture can infer corrective models in the framework of a control task when manipulating objects that significantly affect the dynamics model of the system. The main motivation of this paper is to evaluate a simplified bio-mimetic approach in the framework of a manipulation task. More concretely, the paper focuses on how the model inference process takes place within a feedforward control loop based on the cerebellar structure and on how these internal models are built up by means of biologically plausible synaptic adaptation mechanisms. This kind of investigation may provide clues on how biology achieves accurate control of non-stiff-joint robot with low-power actuators which involve controlling systems with high inertial components. This paper studies how a basic temporal-correlation kernel including long-term depression (LTD) and a constant long-term potentiation (LTP) at parallel fiber-Purkinje cell synapses can effectively infer corrective models. We evaluate how this spike-timing-dependent plasticity correlates sensorimotor activity arriving through the parallel fibers with teaching signals (dependent on error estimates) arriving through the climbing fibers from the inferior olive. This paper addresses the study of how these LTD and LTP components need to be well balanced with each other to achieve accurate learning. This is of interest to evaluate the relevant role of homeostatic mechanisms in biological systems where adaptation occurs in a distributed manner. Furthermore, we illustrate how the temporal-correlation kernel can also work in the presence of transmission delays in sensorimotor pathways. We use a cerebellumlike spiking neural network which stores the corrective models as well-structured weight patterns distributed among the parallel fibers to Purkinje cell connections.

Model-founded explorations of the roles of molecular layer inhibition in regulating purkinje cell responses in cerebellar cortex: more trouble for the beam hypothesis

For most of the last 50 years, the functional interpretation for inhibition in cerebellar cortical circuitry has been dominated by the relatively simple notion that excitatory and inhibitory dendritic inputs sum, and if that sum crosses threshold at the soma the Purkinje cell generates an action potential. Thus, inhibition has traditionally been relegated to a role of sculpting, restricting, or blocking excitation. At the level of networks, this relatively simply notion is manifest in mechanisms like "surround inhibition" which is purported to "shape" or "tune" excitatory neuronal responses. In the cerebellum, where all cell types except one (the granule cell) are inhibitory, these assumptions regarding the role of inhibition continue to dominate. Based on our recent series of modeling and experimental studies, we now suspect that inhibition may play a much more complex, subtle, and central role in the physiological and functional organization of cerebellar cortex. This paper outlines how model-based studies are changing our thinking about the role of feed-forward molecular layer inhibition in the cerebellar cortex. The results not only have important implications for continuing efforts to understand what the cerebellum computes, but might also reveal important features of the evolution of this large and quintessentially vertebrate brain structure.