Spike-timing-dependent Plasticity Model Research Articles

Learning with filopodia and spines: Complementary strong and weak competition lead to specialized, graded, and protected receptive fields.

Filopodia are thin synaptic protrusions that have been long known to play an important role in early development. Recently, they have been found to be more abundant in the adult cortex than previously thought, and more plastic than spines (button-shaped mature synapses). Inspired by these findings, we introduce a new model of synaptic plasticity that jointly describes learning of filopodia and spines. The model assumes that filopodia exhibit strongly competitive learning dynamics -similarly to additive spike-timing-dependent plasticity (STDP). At the same time it proposes that, if filopodia undergo sufficient potentiation, they consolidate into spines. Spines follow weakly competitive learning, classically associated with multiplicative, soft-bounded models of STDP. This makes spines more stable and sensitive to the fine structure of input correlations. We show that our learning rule has a selectivity comparable to additive STDP and captures input correlations as well as multiplicative models of STDP. We also show how it can protect previously formed memories and perform synaptic consolidation. Overall, our results can be seen as a phenomenological description of how filopodia and spines could cooperate to overcome the individual difficulties faced by strong and weak competition mechanisms.

Stability against fluctuations: a two-dimensional study of scaling, bifurcations and spontaneous symmetry breaking in stochastic models of synaptic plasticity

Stochastic models of synaptic plasticity must confront the corrosive influence of fluctuations in synaptic strength on patterns of synaptic connectivity. To solve this problem, we have proposed that synapses act as filters, integrating plasticity induction signals and expressing changes in synaptic strength only upon reaching filter threshold. Our earlier analytical study calculated the lifetimes of quasi-stable patterns of synaptic connectivity with synaptic filtering. We showed that the plasticity step size in a stochastic model of spike-timing-dependent plasticity (STDP) acts as a temperature-like parameter, exhibiting a critical value below which neuronal structure formation occurs. The filter threshold scales this temperature-like parameter downwards, cooling the dynamics and enhancing stability. A key step in this calculation was a resetting approximation, essentially reducing the dynamics to one-dimensional processes. Here, we revisit our earlier study to examine this resetting approximation, with the aim of understanding in detail why it works so well by comparing it, and a simpler approximation, to the system’s full dynamics consisting of various embedded two-dimensional processes without resetting. Comparing the full system to the simpler approximation, to our original resetting approximation, and to a one-afferent system, we show that their equilibrium distributions of synaptic strengths and critical plasticity step sizes are all qualitatively similar, and increasingly quantitatively similar as the filter threshold increases. This increasing similarity is due to the decorrelation in changes in synaptic strength between different afferents caused by our STDP model, and the amplification of this decorrelation with larger synaptic filters.

Learning what matters: Synaptic plasticity with invariance to second-order input correlations.

Cortical populations of neurons develop sparse representations adapted to the statistics of the environment. To learn efficient population codes, synaptic plasticity mechanisms must differentiate relevant latent features from spurious input correlations, which are omnipresent in cortical networks. Here, we develop a theory for sparse coding and synaptic plasticity that is invariant to second-order correlations in the input. Going beyond classical Hebbian learning, our learning objective explains the functional form of observed excitatory plasticity mechanisms, showing how Hebbian long-term depression (LTD) cancels the sensitivity to second-order correlations so that receptive fields become aligned with features hidden in higher-order statistics. Invariance to second-order correlations enhances the versatility of biologically realistic learning models, supporting optimal decoding from noisy inputs and sparse population coding from spatially correlated stimuli. In a spiking model with triplet spike-timing-dependent plasticity (STDP), we show that individual neurons can learn localized oriented receptive fields, circumventing the need for input preprocessing, such as whitening, or population-level lateral inhibition. The theory advances our understanding of local unsupervised learning in cortical circuits, offers new interpretations of the Bienenstock-Cooper-Munro and triplet STDP models, and assigns a specific functional role to synaptic LTD mechanisms in pyramidal neurons.

TiN/Ti/HfO2/TiN memristive devices for neuromorphic computing: from synaptic plasticity to stochastic resonance.

We characterize TiN/Ti/HfO2/TiN memristive devices for neuromorphic computing. We analyze different features that allow the devices to mimic biological synapses and present the models to reproduce analytically some of the data measured. In particular, we have measured the spike timing dependent plasticity behavior in our devices and later on we have modeled it. The spike timing dependent plasticity model was implemented as the learning rule of a spiking neural network that was trained to recognize the MNIST dataset. Variability is implemented and its influence on the network recognition accuracy is considered accounting for the number of neurons in the network and the number of training epochs. Finally, stochastic resonance is studied as another synaptic feature. It is shown that this effect is important and greatly depends on the noise statistical characteristics.

Control of Network Bursting in a Model Spiking Network Supplied with Memristor—Implemented Plasticity

We consider an unstructured neuron network model composed of excitatory and inhibitory neurons. The synaptic connections are supplied with spike timing-dependent plasticity (STDP). We take the STDP model implemented using a memristor. In normal conditions, the network forms so-called bursting discharges typical of unstructured living networks in dissociated neuronal cultures. Incorporating a biologically inspired model, we demonstrate how memristive plasticity emulates spike timing-dependent plasticity, which is crucial for regulating synchronous brain activity. We have found that, when the memristor-based STDP for inhibitory connections is activated, the bursting dynamics are suppressed and the network turns to a random spiking mode. The dependence of bursting properties on the degree of the memristor-based STDP plasticity is analyzed. These findings hold implications for advancing invasive neurointerfaces and for the identification and management of epileptiform activity.

Characterization of Generalizability of Spike Timing Dependent Plasticity Trained Spiking Neural Networks.

A Spiking Neural Network (SNN) is trained with Spike Timing Dependent Plasticity (STDP), which is a neuro-inspired unsupervised learning method for various machine learning applications. This paper studies the generalizability properties of the STDP learning processes using the Hausdorff dimension of the trajectories of the learning algorithm. The paper analyzes the effects of STDP learning models and associated hyper-parameters on the generalizability properties of an SNN. The analysis is used to develop a Bayesian optimization approach to optimize the hyper-parameters for an STDP model for improving the generalizability properties of an SNN.

Analysis of Modification in Synaptic Plasticity STDP (Spike Timing Dependent Plasticity) Model by Changing Intracellular Calcium Concentration

Synapses are a junction between neurons that has a plastic property. Synaptic plasticity can be in the form of long-term potentiation (LTP) and long-term depression (LTD). The changes in intracellular calcium concentration can trigger LTP and LTD. Spike Timing Dependent Plasticity (STDP) is a modification of synapses that depend on the spike timing of pre-synapses and post-synapses neuron. In this study, we analyze the effects of intracellular calcium on the STDP phenomena based on Badoual’s model using mechanisms involving parameters such as calcium pumping, AMPA receptors, NMDA receptors, LTP enzymes, and LTD enzymes. In this model, a high calcium concentration will activate the LTP enzyme, while a low calcium concentration will activate the LTD enzyme, each of which will trigger the occurrence of LTP and LTD. The existence of LTP and LTD is the basis for the formation of the STDP. In this model, the parameters can be adjusted to obtain the STDP corresponding to experimental results where LTP is observed in the range between 0 < ∆t < 50ms, while LTD is observed at wider intervals between −150ms < ∆t <0. These parameters are related to the decay time of the NMDA receptor.

STDP-Based Pruning of Connections and Weight Quantization in Spiking Neural Networks for Energy-Efficient Recognition

Spiking neural networks (SNNs) with a large number of weights and varied weight distribution can be difficult to implement in emerging in-memory computing hardware due to the limitations on crossbar size (implementing dot product), the constrained number of conductance states in non-CMOS devices and the power budget. We present a sparse SNN topology where noncritical connections are pruned to reduce the network size, and the remaining critical synapses are weight quantized to accommodate for limited conductance states. Pruning is based on the power law weight-dependent spike timing dependent plasticity model; synapses between pre- and post-neuron with high spike correlation are retained, whereas synapses with low correlation or uncorrelated spiking activity are pruned. The weights of the retained connections are quantized to the available number of conductance states. The process of pruning noncritical connections and quantizing the weights of critical synapses is performed at regular intervals during training. We evaluated our sparse and quantized network on MNIST dataset and on a subset of images from Caltech-101 dataset. The compressed topology achieved a classification accuracy of 90.1% (91.6%) on the MNIST (Caltech-101) dataset with 3.1X (2.2X) and 4X (2.6X) improvement in energy and area, respectively. The compressed topology is energy and area efficient while maintaining the same classification accuracy of a 2-layer fully connected SNN topology.

Dendritic and Axonal Propagation Delays May Shape Neuronal Networks With Plastic Synapses.

Biological neuronal networks are highly adaptive and plastic. For instance, spike-timing-dependent plasticity (STDP) is a core mechanism which adapts the synaptic strengths based on the relative timing of pre- and postsynaptic spikes. In various fields of physiology, time delays cause a plethora of biologically relevant dynamical phenomena. However, time delays increase the complexity of model systems together with the computational and theoretical analysis burden. Accordingly, in computational neuronal network studies propagation delays were often neglected. As a downside, a classic STDP rule in oscillatory neurons without propagation delays is unable to give rise to bidirectional synaptic couplings, i.e., loops or uncoupled states. This is at variance with basic experimental results. In this mini review, we focus on recent theoretical studies focusing on how things change in the presence of propagation delays. Realistic propagation delays may lead to the emergence of neuronal activity and synaptic connectivity patterns, which cannot be captured by classic STDP models. In fact, propagation delays determine the inventory of attractor states and shape their basins of attractions. The results reviewed here enable to overcome fundamental discrepancies between theory and experiments. Furthermore, these findings are relevant for the development of therapeutic brain stimulation techniques aiming at shifting the diseased brain to more favorable attractor states.

Numerical Implementation of Wavelength-Dependent Photonic Spike Timing Dependent Plasticity Based on VCSOA

We propose to realize photonic spike timing dependent plasticity (STDP) by using a vertical-cavity semiconductor optical amplifier (VCSOA) subject to dual optical pulse injections. The computational model of the photonic STDP is presented for the first time based on the well-known Fabry–Perot approach. Through numerical simulations, the dependences of photonic STDP on the bias current of VCSOA and the input powers are analyzed carefully. Besides, the effect of the initial wavelength detuning on the photonic STDP is also explored. It is found that, the current scheme requires much lower bias current and input power to obtain controllable STDP curve when compared with the previously reported photonic STDP circuits; the initial wavelength detuning is an effectively controllable parameter to realize wavelength-dependent photonic STDP. The computational model of the photonic STDP based on a VCSOA is interesting and valuable for numerically simulating of large-scale photonic spiking neural network, and provides a guideline to design low power consumption photonic neuromorphic systems.

Neuromodulated Synaptic Plasticity on the SpiNNaker Neuromorphic System.

SpiNNaker is a digital neuromorphic architecture, designed specifically for the low power simulation of large-scale spiking neural networks at speeds close to biological real-time. Unlike other neuromorphic systems, SpiNNaker allows users to develop their own neuron and synapse models as well as specify arbitrary connectivity. As a result SpiNNaker has proved to be a powerful tool for studying different neuron models as well as synaptic plasticity—believed to be one of the main mechanisms behind learning and memory in the brain. A number of Spike-Timing-Dependent-Plasticity(STDP) rules have already been implemented on SpiNNaker and have been shown to be capable of solving various learning tasks in real-time. However, while STDP is an important biological theory of learning, it is a form of Hebbian or unsupervised learning and therefore does not explain behaviors that depend on feedback from the environment. Instead, learning rules based on neuromodulated STDP (three-factor learning rules) have been shown to be capable of solving reinforcement learning tasks in a biologically plausible manner. In this paper we demonstrate for the first time how a model of three-factor STDP, with the third-factor representing spikes from dopaminergic neurons, can be implemented on the SpiNNaker neuromorphic system. Using this learning rule we first show how reward and punishment signals can be delivered to a single synapse before going on to demonstrate it in a larger network which solves the credit assignment problem in a Pavlovian conditioning experiment. Because of its extra complexity, we find that our three-factor learning rule requires approximately 2× as much processing time as the existing SpiNNaker STDP learning rules. However, we show that it is still possible to run our Pavlovian conditioning model with up to 1 × 104 neurons in real-time, opening up new research opportunities for modeling behavioral learning on SpiNNaker.

Identification of Stable Spike-Timing-Dependent Plasticity from Spiking Activity with Generalized Multilinear Modeling.

Characterization of long-term activity-dependent plasticity from behaviorally driven spiking activity is important for understanding the underlying mechanisms of learning and memory. In this letter, we present a computational framework for quantifying spike-timing-dependent plasticity (STDP) during behavior by identifying a functional plasticity rule solely from spiking activity. First, we formulate a flexible point-process spiking neuron model structure with STDP, which includes functions that characterize the stationary and plastic properties of the neuron. The STDP model includes a novel function for prolonged plasticity induction, as well as a more typical function for synaptic weight change based on the relative timing of input-output spike pairs. Consideration for system stability is incorporated with weight-dependent synaptic modification. Next, we formalize an estimation technique using a generalized multilinear model (GMLM) structure with basis function expansion. The weight-dependent synaptic modification adds a nonlinearity to the model, which is addressed with an iterative unconstrained optimization approach. Finally, we demonstrate successful model estimation on simulated spiking data and show that all model functions can be estimated accurately with this method across a variety of simulation parameters, such as number of inputs, output firing rate, input firing type, and simulation time. Since this approach requires only naturally generated spikes, it can be readily applied to behaving animal studies to characterize the underlying mechanisms of learning and memory.

Modified STDP Triplet Rule Significantly Increases Neuron Training Stability in the Learning of Spatial Patterns

Spike-timing-dependent plasticity (STDP) is a set of Hebbian learning rules which are based firmly on biological evidence. STDP learning is capable of detecting spatiotemporal patterns highly obscured by noise. This feature appears attractive from the point of view of machine learning. In this paper three different additive STDP models of spike interactions were compared in respect to training performance when the neuron is exposed to a recurrent spatial pattern injected into Poisson noise. The STDP models compared were all-to-all interaction, nearest-neighbor interaction, and the nearest-neighbor triplet interaction. The parameters of the neuron model and STDP training rules were optimized for a range of spatial patterns of different sizes by the means of heuristic algorithm. The size of the pattern, that is, the number of synapses containing the pattern, was gradually decreased from what amounted to a relatively easy task down to a single synapse. Optimization was performed for each size of the pattern. The parameters were allowed to evolve freely. The triplet rule, in most cases, performed better by far than the other two rules, while the evolutionary algorithm immediately switched the polarity of the triplet update. The all-to-all rule achieved moderate results.

Stability and Competition in Multi-spike Models of Spike-Timing Dependent Plasticity.

Spike-timing dependent plasticity (STDP) is a widespread plasticity mechanism in the nervous system. The simplest description of STDP only takes into account pairs of pre- and postsynaptic spikes, with potentiation of the synapse when a presynaptic spike precedes a postsynaptic spike and depression otherwise. In light of experiments that explored a variety of spike patterns, the pair-based STDP model has been augmented to account for multiple pre- and postsynaptic spike interactions. As a result, a number of different “multi-spike” STDP models have been proposed based on different experimental observations. The behavior of these models at the population level is crucial for understanding mechanisms of learning and memory. The challenging balance between the stability of a population of synapses and their competitive modification is well studied for pair-based models, but it has not yet been fully analyzed for multi-spike models. Here, we address this issue through numerical simulations of an integrate-and-fire model neuron with excitatory synapses subject to STDP described by three different proposed multi-spike models. We also analytically calculate average synaptic changes and fluctuations about these averages. Our results indicate that the different multi-spike models behave quite differently at the population level. Although each model can produce synaptic competition in certain parameter regions, none of them induces synaptic competition with its originally fitted parameters. The dichotomy between synaptic stability and Hebbian competition, which is well characterized for pair-based STDP models, persists in multi-spike models. However, anti-Hebbian competition can coexist with synaptic stability in some models. We propose that the collective behavior of synaptic plasticity models at the population level should be used as an additional guideline in applying phenomenological models based on observations of single synapses.

What must come down goes up - the effect of noise on weights in spike-timing-dependent plasticity

In large-scale spiking neural models that learn with spike-timing-dependent plasticity (STDP), it is a crucial, but difficult problem to balance synaptic potentiation (necessary to learn a task) and synaptic depression (necessary to counteract accidental weight increase and to balance overall firing rates). Adding random noise and choosing parameters such that inhibition slightly dominates excitation [1,2] is considered one way of accomplishing this. With the learning rule being standard STDP [2], the parameter that determines whether inhibition or excitation dominates is the so-called α-parameter, defined as the ratio between parameters that determine amount of depression and those that determine amount of potentiation [3]. If the α-parameter is set to a value greater than 1, the weights are assumed to go down. However, using numerical simulations, we demonstrate that this is not the case. Using standard leaky integrate-and-fire neurons, we ran 10 simulations per parameter set (250s each), with α-parameters A = {0.5, 0.9, 1.0, 1.1, 1.25, 1.5} and noise frequencies F = {5, 10, 20, 40, 80, 160}. We also varied the maximum weight and the initial weight of the synapse from 0 to 1 in small intervals. In contrast to our assumptions, we find a weight increase with α-parameters greater than 1 (see Figure ​Figure1).1). The complex weight dynamics observed can be explained by the interplay of 3 factors. 1. The α-parameter: if it is greater than 1 it tends to drive the weights down, given that firing is uncorrelated. 2. The impact of the pre-synaptic spike on the post-synaptic potential (determined by synaptic weight, capacitance of the neuron, or time constant of the synapse): if the impact is strong enough pre-synaptic spikes will cause post-synaptic spikes and firing will no longer be uncorrelated. Hence, weights will tend to go up (for example, if the initial values of the weights are too high). 3. Noise frequency: There is a positive interaction between noise frequency and α-parameter in driving weights down. If the frequency is high enough, the α-parameter can be low. If the frequency is low the α-parameter needs to be very high. High frequency drives the weights down, because the post-synaptic neuron operates in input averaging mode, firing more regular than the pre-synaptic spikes that evoked it, and, therefore, being decorrelated from it [2]. These findings give insights in how to set parameters (in particular α-parameter, initial weights and noise frequency) to achieve a desired weight dynamics in large-scale STDP models. Figure 1 A plot of the weight strength after training for different frequencies with an initial weight of 0.5. As expected, the weight increases for α-parameters smaller than 1. However, the weight also increases for α-parameters larger than 1 ...

Survey and evaluation of neural computation models for bio-integrated systems

Integrating neurobiological cultures with computer systems presents an opportunity to enhance computational energy efficiency. These Bio-Integrated Systems (BISs) require knowledge about structure and behavior of neural components and their interfacing. In the early design phases, modeling neurons offers cost, failure-free and retrial benefits compared to laboratory grown neural networks. The usefulness of these models lays in characteristics of being realistic but also computationally efficient.This survey reviews computational models of spiking neurons and their changes in connections, known as plasticity. The review studies models that are faithful to real neural cultures, and are computational efficient for real-time BISs. Also, criteria and methods for comparing models with ‘in-vitro’ experiments are reviewed to conclude on the level of realism of models in comparison with biological setups. Izhikevich’s model of spiking neurons is recommended due to its accuracy in reproducing real neural firing patterns, computational efficiency, and ease of parameter adjustment. The model of Spike-timing dependent plasticity is recommended as current basis for representing neuron changes in connections. For the analysis of network connectivity and connectivity changes in BIS, the Cox method is recommended because it evaluates connections based on activities from all recorded neurons as opposed to pair-wise approaches.

A 2-transistor/1-resistor artificial synapse capable of communication and stochastic learning in neuromorphic systems.

Resistive (or memristive) switching devices based on metal oxides find applications in memory, logic and neuromorphic computing systems. Their small area, low power operation, and high functionality meet the challenges of brain-inspired computing aiming at achieving a huge density of active connections (synapses) with low operation power. This work presents a new artificial synapse scheme, consisting of a memristive switch connected to 2 transistors responsible for gating the communication and learning operations. Spike timing dependent plasticity (STDP) is achieved through appropriate shaping of the pre-synaptic and the post synaptic spikes. Experiments with integrated artificial synapses demonstrate STDP with stochastic behavior due to (i) the natural variability of set/reset processes in the nanoscale switch, and (ii) the different response of the switch to a given stimulus depending on the initial state. Experimental results are confirmed by model-based simulations of the memristive switching. Finally, system-level simulations of a 2-layer neural network and a simplified STDP model show random learning and recognition of patterns.

Shaping Synaptic Learning by the Duration of Postsynaptic Action Potential in a New STDP Model

Single spikes and their timing matter in changing synaptic efficacy, which is known as spike-timing-dependent plasticity (STDP). Most previous studies treated spikes as all-or-none events, and considered their duration and magnitude as negligible. Here we explore the effects of action potential (AP) duration on synaptic plasticity in a simplified model neuron using computer simulations. We propose a novel STDP model that depresses synapses using an AP duration dependent LTD window and induces potentiation of synaptic strength when presynaptic spikes arrive before and during a postsynaptic AP (dSTDP). We demonstrate that AP duration is another key factor for insensitizing the postsynaptic neural firing and for controlling the shape of synaptic weight distribution. Extended AP durations produce a wide unimodal weight distribution that resembles the ones reported experimentally and make the postsynaptic neuron tranquil when disturbed by poisson noise spike trains, while equivalently sensitive to the synchronized. Our results suggest that the impact of AP duration, modeled here as an AP-dependent STDP window, on synaptic plasticity can be dramatic and should motivate future STDP studies.

Microcircuit mechanisms involved in paired associative stimulation‐induced depression of corticospinal excitability

Synaptic weight changes induced by temporal correlations between the spikes of pre- and postsynaptic neurons are referred to as spike-timing-dependent plasticity (STDP). Transcranial magnetic stimulation (TMS) induces long-lasting effects on corticospinal excitability, if it is repetitively paired with stimulation of afferents from a corresponding contralateral hand region at short intervals (paired associative stimulation, PAS). PAS-induced plasticity has been linked with synaptic STDP. We aimed to investigate which elements of the cortical microcircuitry sustain and govern PAS-induced depression of corticospinal excitability in the target muscle representation (and enhancement of excitability in its functional surround). We show that the time window during which the interaction between both stimulus-induced cortical events leads to immediate post-interventional depression is short (<4.5 ms). The depressant PAS effects at the target representation were completely blocked by applying a subthreshold magnetic pulse 3 ms before the principal TMS pulse, even when the strength of the latter was adjusted to generate a motor-evoked potential of similar amplitude to that with the unconditioned magnetic pulse. Epidural recordings from the cervical cord of a patient showed that under this condition late TMS-evoked I-waves remain suppressed. When the intensity of the TMS component during PAS was lowered - sufficient to allow activation of inhibitory neurons, but insufficient to activate corticospinal neurons - excitability of short-latency intracortical inhibition remained unchanged. PAS-induced facilitation in the functional surround followed the same pattern as the centre-depressant effects. These findings may suggest that excitability-depressant PAS-induced effects are due to weakening of excitatory synapses between upper cortical layer principal neurons, but not those located on the corticospinal neuron, or inhibitory synapses. Inhibitory interneurons involved in short-latency intracortical inhibition are gate-keepers to producing centre-depressant/surround-facilitatory PAS effects. Based on these and earlier findings we propose a model specifying the composition and laminar location of the involved microcircuit of PAS-induced plasticity that may enhance its utility as a model of STDP in humans.

A Calcium-Based Simple Model of Multiple Spike Interactions in Spike-Timing-Dependent Plasticity

Spike-timing-dependent plasticity (STDP) is a form of synaptic modification that depends on the relative timings of presynaptic and postsynaptic spikes. In this letter, we proposed a calcium-based simple STDP model, described by an ordinary differential equation having only three state variables: one represents the density of intracellular calcium, one represents a fraction of open state NMDARs, and one represents the synaptic weight. We shown that in spite of its simplicity, the model can reproduce the properties of the plasticity that have been experimentally measured in various brain areas (e.g., layer 2/3 and 5 visual cortical slices, hippocampal cultures, and layer 2/3 somatosensory cortical slices) with respect to various patterns of presynaptic and postsynaptic spikes. In addition, comparisons with other STDP models are made, and the significance and advantages of the proposed model are discussed.