Self-organization of spiking neural network that generates autonomous behavior in a real mobile robot

In this paper, we propose self-organization algorithm of spiking neural network (SNN) applicable to autonomous robot for generation of adoptive and goal-directed behavior. First, we formulated a SNN model whose inputs and outputs were analog and the hidden unites are interconnected each other. Next, we implemented it into a miniature mobile robot Khepera. In order to see whether or not a solution(s) for the given task(s) exists with the SNN, the robot was evolved with the genetic algorithm in the environment. The robot acquired the obstacle avoidance and navigation task successfully, exhibiting the presence of the solution. After that, a self-organization algorithm based on a use-dependent synaptic potentiation and depotentiation at synapses of input layer to hidden layer and of hidden layer to output layer was formulated and implemented into the robot. In the environment, the robot incrementally organized the network and the given tasks were successfully performed. The time needed to acquire the desired adoptive and goal-directed behavior using the proposed self-organization method was much less than that with the genetic evolution, approximately one fifth.     

Multisensory integration in the superior colliculus: a neural network model

Neurons in the superior colliculus (SC) are known to integrate stimuli of different modalities (e.g., visual and auditory) following specific properties. In this work, we present a mathematical model of the integrative response of SC neurons, in order to suggest a possible physiological mechanism underlying multisensory integration in SC. The model includes three distinct neural areas: two unimodal areas (auditory and visual) are devoted to a topological representation of external stimuli, and communicate via synaptic connections with a third downstream area (in the SC) responsible for multisensory integration. The present simulations show that the model, with a single set of parameters, can mimic various responses to different combinations of external stimuli including the inverse effectiveness, both in terms of multisensory enhancement and contrast, the existence of within- and cross-modality suppression between spatially disparate stimuli, a reduction of network settling time in response to cross-modal stimuli compared with individual stimuli. The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain several aspects of multisensory integration.     

A discrete time neural network model with spiking neurons

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in Soula et al. (Neural Comput. 18, 1, 2006). Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (“raster plots”). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.      

Hebbian mechanisms help explain development of multisensory integration in the superior colliculus: a neural network model

The superior colliculus (SC) integrates relevant sensory information (visual, auditory, somatosensory) from several cortical and subcortical structures, to program orientation responses to external events. However, this capacity is not present at birth, and it is acquired only through interactions with cross-modal events during maturation. Mathematical models provide a quantitative framework, valuable in helping to clarify the specific neural mechanisms underlying the maturation of the multisensory integration in the SC. We extended a neural network model of the adult SC (Cuppini et?al., Front Integr Neurosci 4:1?C15, 2010) to describe the development of this phenomenon starting from an immature state, based on known or suspected anatomy and physiology, in which: (1) AES afferents are present but weak, (2) Responses are driven from non-AES afferents, and (3) The visual inputs have a marginal spatial tuning. Sensory experience was modeled by repeatedly presenting modality-specific and cross-modal stimuli. Synapses in the network were modified by simple Hebbian learning rules. As a consequence of this exposure, (1) Receptive fields shrink and come into spatial register, and (2) SC neurons gained the adult characteristic integrative properties: enhancement, depression, and inverse effectiveness. Importantly, the unique architecture of the model guided the development so that integration became dependent on the relationship between the cortical input and the SC. Manipulations of the statistics of the experience during the development changed the integrative profiles of the neurons, and results matched well with the results of physiological studies.     

Linear ensemble-coding in midbrain superior colliculus specifies the saccade kinematics

Recently, we proposed an ensemble-coding scheme of the midbrain superior colliculus (SC) in which, during a saccade, each spike emitted by each recruited SC neuron contributes a fixed minivector to the gaze-control motor output. The size and direction of this 'spike vector' depend exclusively on a cell's location within the SC motor map (Goossens and Van Opstal, in J Neurophysiol 95: 2326-2341, 2006). According to this simple scheme, the planned saccade trajectory results from instantaneous linear summation of all spike vectors across the motor map. In our simulations with this model, the brainstem saccade generator was simplified by a linear feedback system, rendering the total model (which has only three free parameters) essentially linear. Interestingly, when this scheme was applied to actually recorded spike trains from 139 saccade-related SC neurons, measured during thousands of eye movements to single visual targets, straight saccades resulted with the correct velocity profiles and nonlinear kinematic relations ('main sequence properties' and 'component stretching'). Hence, we concluded that the kinematic nonlinearity of saccades resides in the spatial-temporal distribution of SC activity, rather than in the brainstem burst generator. The latter is generally assumed in models of the saccadic system. Here we analyze how this behaviour might emerge from this simple scheme. In addition, we will show new experimental evidence in support of the proposed mechanism.     

A neural network study of precollicular saccadic averaging

Saccadic averaging is the phenomenon that two simultaneously presented retinal inputs result in a saccade with an endpoint located on an intermediate position between the two stimuli. Recordings from neurons in the deeper layers of the superior colliculus have revealed neural correlates of saccade averaging, indicating that it takes place at this level or upstream. Recently, we proposed a neural network for internal feedback in saccades. This neural network model is different from other models in that it suggests the possibility that averaging takes place in a stage upstream of the colliculus. The network consists of output units representing the neural map of the deeper layers of the superior colliculus and hidden layers imitating areas in the posterior parietal cortex. The deeper layers of the superior colliculus represent the motor error of a desired saccade, e.g. an eye movement to a visual target. In this article we show that averaging is an emergent property of the proposed network. When two retinal targets with different intensities are simultaneously presented to the network, the activity in the output layer represents a single motor error with a weighted average value. Our goal is to understand the mechanism of weighted averaging in this neural network. It appears that averaging in the model is caused by the linear dependence of the net input, received by the hidden units, on retinal error, independent of its retinal coding format. For nonnormalized retinal error inputs, also the nonlinearity between the net input and the activity of the hidden units plays a role in the averaging process. The averaging properties of the model are in agreement with physiological experiments if the hypothetical retinal error input map is normalized. The neural network predicts that if this normalization is overruled by electrical stimulation, averaging still takes place. However, in this case – as a consequence of the feedback task – the location of the resulting saccade depends on the initial eye position and the total intensity/current applied at the two locations. This could be a way to verify the neural network model. If the assumptions for the model are valid, a physiological implication of this paper is that averaging of saccades takes place upstream of the superior colliculus. Received: 22 June 1997 / Accepted in revised form: 19 February 1998     

Directional operations in the motor cortex modeled by a neural network of spiking neurons

A neural network with realistically modeled, spiking neurons is proposed to model ensemble operations of directionally tuned neurons in the motor cortex. The model reproduces well directional operations previously identified experimentally, including the prediction of the direction of an upcoming movement in reaching tasks and the rotation of the neuronal population vector in a directional transformation task.     

Testing of information condensation in a model reverberating spiking neural network

Information about external world is delivered to the brain in the form of structured in time spike trains. During further processing in higher areas, information is subjected to a certain condensation process, which results in formation of abstract conceptual images of external world, apparently, represented as certain uniform spiking activity partially independent on the input spike trains details. Possible physical mechanism of condensation at the level of individual neuron was discussed recently. In a reverberating spiking neural network, due to this mechanism the dynamics should settle down to the same uniform/ periodic activity in response to a set of various inputs. Since the same periodic activity may correspond to different input spike trains, we interpret this as possible candidate for information condensation mechanism in a network. Our purpose is to test this possibility in a network model consisting of five fully connected neurons, particularly, the influence of geometric size of the network, on its ability to condense information. Dynamics of 20 spiking neural networks of different geometric sizes are modelled by means of computer simulation. Each network was propelled into reverberating dynamics by applying various initial input spike trains. We run the dynamics until it becomes periodic. The Shannon's formula is used to calculate the amount of information in any input spike train and in any periodic state found. As a result, we obtain explicit estimate of the degree of information condensation in the networks, and conclude that it depends strongly on the net's geometric size.     

Open-loop simulations of the primate saccadic system using burst cell discharge from the superior colliculus

 Saccade-related burst neurons (SRBNs) in the monkey superior colliculus (SC) have been hypothesized to provide the brainstem saccadic burst generator with the dynamic error signal and the movement initiating trigger signal. To test this claim, we performed two sets of open-loop simulations on a burst generator model with the local feedback disconnected using experimentally obtained SRBN activity as both the driving and trigger signal inputs to the model. First, using neural data obtained from cells located near the middle of the rostral to caudal extent of the SC, the internal parameters of the model were optimized by means of a stochastic hill-climbing algorithm to produce an intermediate-sized saccade. The parameter values obtained from the optimization were then fixed and additional simulations were done using the experimental data from rostral collicular neurons (small saccades) and from more caudal neurons (large saccades); the model generated realistic saccades, matching both position and velocity profiles of real saccades to the centers of the movement fields of all these cells. Second, the model was driven by SRBN activity affiliated with interrupted saccades, the resumed eye movements observed following electrical stimulation of the omnipause region. Once again, the model produced eye movements that closely resembled the interrupted saccades produced by such simulations, but minor readjustment of parameters reflecting the weight of the projection of the trigger signal was required. Our study demonstrates that a model of the burst generator produces reasonably realistic saccades when driven with actual samples of SRBN discharges. Received: 25 October 1994/Accepted in revised form: 20 June 1995     

A discrete time neural network model with spiking neurons: II: Dynamics with noise

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.     

A neural network model of the inferior colliculus with modifiable lateral inhibitory synapses for human echolocation

 We propose a neural network model of the inferior colliculus (IC) for human echolocation. Neuronal mechanisms for human echolocation were investigated by simulating the model. The model consists of the neural networks of the central nucleus (ICc) and external nucleus (ICx) of the inferior colliculus. The neurons of the ICc receive interaural sound stimuli via multiple contralateral delay lines and a single ipsilateral delay line. The neurons of the ICc send output signals to the neurons of the ICx in a convergent manner. We stimulated the ICc with pairs of a direct sound (a sonar sound) and an echo sound (the reflection from an object). Information about the distance between the model and the object is expressed by the delay time of the echo sound with respect to the direct sound. The results presented here show that neurons of the ICc responsive to interaural onset time differences contribute to the creation of an auditory distance map in the ICx. We trained the model with various pairs of direct-echo sounds and modified synaptic connection strengths of the networks according to the Hebbian rule. It is shown that self-organized long-term depression of lateral inhibitory synaptic connections plays an important role in enhancing echolocation skills. Received: 26 November 2000 / Accepted in revised form: 16 October 2001     

The three-loop model: a neural network for the generation of saccadic reaction times

This paper presents a computer simulation of the three-loop model for the temporal aspects of the generation of visually guided saccadic eye movements. The intention is to reproduce complex experimental reaction time distributions by a simple neural network. The operating elements are artificial but realistic neurones. Four modules are constructed, each consisting of 16 neural elements. Within each module, the elements are connected in an all-to-all manner. The modules are working parallel and serial according to the anatomically and physiologically identified visuomotor pathways including the superior colliculus, the frontal eye fields, and the parietal cortex. Two transient-sustained input lines drive the network: one represents the visual activity produced by the onset of the saccade target, the other represents a central activity controlling the preparation of saccades, e.g. the end of active fixation. The model works completely deterministically; its stochastic output is a consequence of the stochastic properties of the input only. Simulations show how multimodal distributions of saccadic reaction times are produced as a natural consequence of the model structure. The gap effect on saccadic reaction times is correctly produced by the model: depending only on the gap duration (all model parameters unchanged) express, fast-regular, and slow-regular saccades are obtained in different numbers. In agreement with the experiments, bi- or trimodal distributions are produced only for medium gap durations (around 200 ms), while for shorter or longer gaps the express mode disappears and the distributions turn bi- or even unimodal. The effect of varying the strength of the transient-sustained components and the ongoing activity driving the hierarchically highest module are considered to account for the interindividual variability of the latency distributions obtained from different subjects, effects of different instructions to the same subject, and the observation of express makers (subjects who produce exclusively express saccades). How the model can be extended to describe the spatial aspects of the saccade system will be discussed as well as the effects of training and/or rapid adaptation to experimental conditions.     

A neural network model of speech acquisition and motor equivalent speech production

This article describes a neural network model that addresses the acquisition of speaking skills by infants and subsequent motor equivalent production of speech sounds. The model learns two mappings during a babbling phase. A phonetic-to-orosensory mapping specifies a vocal tract target for each speech sound; these targets take the form of convex regions in orosensory coordinates defining the shape of the vocal tract. The babbling process wherein these convex region targets are formed explains how an infant can learn phoneme-specific and language-specific limits on acceptable variability of articulator movements. The model also learns an orosensory-to-articulatory mapping wherein cells coding desired movement directions in orosensory space learn articulator movements that achieve these orosensory movement directions. The resulting mapping provides a natural explanation for the formation of coordinative structures. This mapping also makes efficient use of redundancy in the articulator system, thereby providing the model with motor equivalent capabilities. Simulations verify the model's ability to compensate for constraints or perturbations applied to the articulators automatically and without new learning and to explain contextual variability seen in human speech production.Supported in part by AFOSR F49620-92-J-0499     

A case for spiking neural network simulation based on configurable multiple-FPGA systems

Recent neuropsychological research has begun to reveal that neurons encode information in the timing of spikes. Spiking neural network simulations are a flexible and powerful method for investigating the behaviour of neuronal systems. Simulation of the spiking neural networks in software is unable to rapidly generate output spikes in large-scale of neural network. An alternative approach, hardware implementation of such system, provides the possibility to generate independent spikes precisely and simultaneously output spike waves in real time, under the premise that spiking neural network can take full advantage of hardware inherent parallelism. We introduce a configurable FPGA-oriented hardware platform for spiking neural network simulation in this work. We aim to use this platform to combine the speed of dedicated hardware with the programmability of software so that it might allow neuroscientists to put together sophisticated computation experiments of their own model. A feed-forward hierarchy network is developed as a case study to describe the operation of biological neural systems (such as orientation selectivity of visual cortex) and computational models of such systems. This model demonstrates how a feed-forward neural network constructs the circuitry required for orientation selectivity and provides platform for reaching a deeper understanding of the primate visual system. In the future, larger scale models based on this framework can be used to replicate the actual architecture in visual cortex, leading to more detailed predictions and insights into visual perception phenomenon.     

Neural network simulations of the primate oculomotor system III. An one-dimensional, one-directional model of the superior colliculus

This report evaluates the performance of a biologically motivated neural network model of the primate superior colliculus (SC). Consistent with known anatomy and physiology, its major features include excitatory connections between its output elements, nigral gating mechanisms, and an eye displacement feedback of reticular origin to recalculate the metrics of saccades to memorized targets in retinotopic coordinates. Despite the fact that it makes no use of eye position or eye velocity information, the model can account for the accuracy of saccades in double step stimulation experiments. Further, the model accounts for the effects of focal SC lesions. Finally, it accounts for the properties of saccades evoked in response to the electrical stimulation of the SC. These include the approximate size constancy of evoked saccades despite increases of stimulus intensity, the fact that the size of evoked saccades depends on the time that has elapsed from a previous saccade, the fact that staircases of saccades are evoked in response to prolonged stimuli, and the fact that the size of saccades evoked in response to the simultaneous stimulation of two SC sites is the average of the saccades that are evoked when the two sites are separately stimulated. Received: 3 November 1997 / Accepted in revised form: 30 June 1998     

Decoding of a motor command vector from distributed activity in superior colliculus

 Several alternative methods for decoding the desired motor command vector from neural networks containing distributed, place-coded information have been suggested. The two most widely discussed candidate mechanisms are vector summation (VS) and a center-of-mass (CM) computation. The latter mechanism has also been called vector averaging. The present paper compares the operation of these two methods in a model of an experimentally well-studied neural structure, the superior colliculus (SC). The SC is one structure that has been shown to be responsible for generating saccadic command vectors in the form of distributed neural activity that is topologically arranged across its surface. It has been suggested that the pattern of eye-movement errors obtained following the placement of a collicular lesion can distinguish between these two mechanisms. As a result of this suggestion, the pattern of saccadic errors produced by lesions in the SC have been widely cited to support the CM hypothesis. In the present paper the placement of a discrete lesion is simulated in a recurrent (dynamic) neural network model of the SC. These dynamic connections in the model SC network produce a systematic shift of the locus of distributed activity away from the site of the lesion. The spatiotemporal shift in the location of SC activity then produces a pattern of saccadic errors that appear to support the CM hypothesis, even though ensemble activity in our model colliculus is decoded by VS. This result demonstrates that, when ensemble activity on the SC motor map is dynamically modulated over space and time by intrinsic collicular circuitry, an explicit CM computation is not needed to reproduce the pattern of physiological results that follow focal SC lesions. Received: 19 December 2000 / Accepted in revised form: 27 September 2001     

A model that integrates eye velocity commands to keep track of smooth eye displacements

Past results have reported conflicting findings on the oculomotor system’s ability to keep track of smooth eye movements in darkness. Whereas some results indicate that saccades cannot compensate for smooth eye displacements, others report that memory-guided saccades during smooth pursuit are spatially correct. Recently, it was shown that the amount of time before the saccade made a difference: short-latency saccades were retinotopically coded, whereas long-latency saccades were spatially coded. Here, we propose a model of the saccadic system that can explain the available experimental data. The novel part of this model consists of a delayed integration of efferent smooth eye velocity commands. Two alternative physiologically realistic neural mechanisms for this integration stage are proposed. Model simulations accurately reproduced prior findings. Thus, this model reconciles the earlier contradictory reports from the literature about compensation for smooth eye movements before saccades because it involves a slow integration process. Action Editor: Jonathan D. Victor