Timing Of Postsynaptic Spikes Research Articles

Tunable spike-timing-dependent plasticity in magnetic skyrmion manipulation chambers

Magnetic skyrmions, as scalable and nonvolatile spin textures, can dynamically interact with fields and currents, making them promising for unconventional computing. This paper presents a neuromorphic device based on skyrmion manipulation chambers to implement spike-timing-dependent plasticity (STDP), a mechanism for unsupervised learning in brain-inspired computing. STDP adjusts synaptic weights based on the timing of pre-synaptic and post-synaptic spikes. The proposed three-chamber design encodes synaptic weight in the number of skyrmions in the center chamber, with left and right chambers for pre- and post-synaptic spikes, respectively. Micromagnetic simulations demonstrate that the timing between applied currents across the chambers controls the final skyrmion count (weight). The device exhibits adaptability and learning capabilities by manipulating chamber parameters, mimicking Hebbian and dendritic location-based plasticity. The device's ability to maintain state post-write highlights its potential for advancing adaptable neuromorphic devices.

A Physical Framework to Study the Effect of Magnetic Fields on the Spike-Time Coding.

A temporal neural code reliant on the pattern of spike times rather than spike rates offers a feasible mechanism for encoding information from weak periodic external stimuli, such as static or extremely low-frequency electromagnetic fields. Our model focuses on the influence of magnetic fields on neurotransmitter dynamics near the neuron membrane. Neurotransmitter binding to specific receptor sites on membrane proteins can regulate biochemical reactions. The duration a neurotransmitter spends in the bonded state serves as a metric for the magnetic field's capacity as a chemical regulator. By initiating a physical analysis of ligand-receptor binding, utilizing the alpha function for synaptic conductance, and employing a modified version of Bell's law, we quantified the impact of magnetic fields on the bond half-life time and, consequently, on postsynaptic spike timing.

Supervised Learning in Multilayer Spiking Neural Networks With Spike Temporal Error Backpropagation.

The brain-inspired spiking neural networks (SNNs) hold the advantages of lower power consumption and powerful computing capability. However, the lack of effective learning algorithms has obstructed the theoretical advance and applications of SNNs. The majority of the existing learning algorithms for SNNs are based on the synaptic weight adjustment. However, neuroscience findings confirm that synaptic delays can also be modulated to play an important role in the learning process. Here, we propose a gradient descent-based learning algorithm for synaptic delays to enhance the sequential learning performance of single spiking neuron. Moreover, we extend the proposed method to multilayer SNNs with spike temporal-based error backpropagation. In the proposed multilayer learning algorithm, information is encoded in the relative timing of individual neuronal spikes, and learning is performed based on the exact derivatives of the postsynaptic spike times with respect to presynaptic spike times. Experimental results on both synthetic and realistic datasets show significant improvements in learning efficiency and accuracy over the existing spike temporal-based learning algorithms. We also evaluate the proposed learning method in an SNN-based multimodal computational model for audiovisual pattern recognition, and it achieves better performance compared with its counterparts.

Temporal Coding in Spiking Neural Networks With Alpha Synaptic Function: Learning With Backpropagation.

The timing of individual neuronal spikes is essential for biological brains to make fast responses to sensory stimuli. However, conventional artificial neural networks lack the intrinsic temporal coding ability present in biological networks. We propose a spiking neural network model that encodes information in the relative timing of individual spikes. In classification tasks, the output of the network is indicated by the first neuron to spike in the output layer. This temporal coding scheme allows the supervised training of the network with backpropagation, using locally exact derivatives of the postsynaptic spike times with respect to presynaptic spike times. The network operates using a biologically plausible synaptic transfer function. In addition, we use trainable pulses that provide bias, add flexibility during training, and exploit the decayed part of the synaptic function. We show that such networks can be successfully trained on multiple data sets encoded in time, including MNIST. Our model outperforms comparable spiking models on MNIST and achieves similar quality to fully connected conventional networks with the same architecture. The spiking network spontaneously discovers two operating modes, mirroring the accuracy-speed tradeoff observed in human decision-making: a highly accurate but slow regime, and a fast but slightly lower accuracy regime. These results demonstrate the computational power of spiking networks with biological characteristics that encode information in the timing of individual neurons. By studying temporal coding in spiking networks, we aim to create building blocks toward energy-efficient, state-based biologically inspired neural architectures. We provide open-source code for the model.

Event-Based Update of Synapses in Voltage-Based Learning Rules.

Due to the point-like nature of neuronal spiking, efficient neural network simulators often employ event-based simulation schemes for synapses. Yet many types of synaptic plasticity rely on the membrane potential of the postsynaptic cell as a third factor in addition to pre- and postsynaptic spike times. In some learning rules membrane potentials not only influence synaptic weight changes at the time points of spike events but in a continuous manner. In these cases, synapses therefore require information on the full time course of membrane potentials to update their strength which a priori suggests a continuous update in a time-driven manner. The latter hinders scaling of simulations to realistic cortical network sizes and relevant time scales for learning. Here, we derive two efficient algorithms for archiving postsynaptic membrane potentials, both compatible with modern simulation engines based on event-based synapse updates. We theoretically contrast the two algorithms with a time-driven synapse update scheme to analyze advantages in terms of memory and computations. We further present a reference implementation in the spiking neural network simulator NEST for two prototypical voltage-based plasticity rules: the Clopath rule and the Urbanczik-Senn rule. For both rules, the two event-based algorithms significantly outperform the time-driven scheme. Depending on the amount of data to be stored for plasticity, which heavily differs between the rules, a strong performance increase can be achieved by compressing or sampling of information on membrane potentials. Our results on computational efficiency related to archiving of information provide guidelines for the design of learning rules in order to make them practically usable in large-scale networks.

Multicoding in neural information transfer suggested by mathematical analysis of the frequency-dependent synaptic plasticity in vivo

Two elements of neural information processing have primarily been proposed: firing rate and spike timing of neurons. In the case of synaptic plasticity, although spike-timing-dependent plasticity (STDP) depending on presynaptic and postsynaptic spike times had been considered the most common rule, recent studies have shown the inhibitory nature of the brain in vivo for precise spike timing, which is key to the STDP. Thus, the importance of the firing frequency in synaptic plasticity in vivo has been recognized again. However, little is understood about how the frequency-dependent synaptic plasticity (FDP) is regulated in vivo. Here, we focused on the presynaptic input pattern, the intracellular calcium decay time constants, and the background synaptic activity, which vary depending on neuron types and the anatomical and physiological environment in the brain. By analyzing a calcium-based model, we found that the synaptic weight differs depending on these factors characteristic in vivo, even if neurons receive the same input rate. This finding suggests the involvement of multifaceted factors other than input frequency in FDP and even neural coding in vivo.

Effect of interpopulation spike-timing-dependent plasticity on synchronized rhythms in neuronal networks with inhibitory and excitatory populations.

We consider a two-population network consisting of both inhibitory (I) interneurons and excitatory (E) pyramidal cells. This I-E neuronal network has adaptive dynamic I to E and E to I interpopulation synaptic strengths, governed by interpopulation spike-timing-dependent plasticity (STDP). In previous works without STDPs, fast sparsely synchronized rhythms, related to diverse cognitive functions, were found to appear in a range of noise intensity D for static synaptic strengths. Here, by varying D, we investigate the effect of interpopulation STDPs on fast sparsely synchronized rhythms that emerge in both the I- and the E-populations. Depending on values of D, long-term potentiation (LTP) and long-term depression (LTD) for population-averaged values of saturated interpopulation synaptic strengths are found to occur. Then, the degree of fast sparse synchronization varies due to effects of LTP and LTD. In a broad region of intermediate D, the degree of good synchronization (with higher synchronization degree) becomes decreased, while in a region of large D, the degree of bad synchronization (with lower synchronization degree) gets increased. Consequently, in each I- or E-population, the synchronization degree becomes nearly the same in a wide range of D (including both the intermediate and the large D regions). This kind of "equalization effect" is found to occur via cooperative interplay between the average occupation and pacing degrees of spikes (i.e., the average fraction of firing neurons and the average degree of phase coherence between spikes in each synchronized stripe of spikes in the raster plot of spikes) in fast sparsely synchronized rhythms. Finally, emergences of LTP and LTD of interpopulation synaptic strengths (leading to occurrence of equalization effect) are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic spike times.

STDP-Based Unsupervised Spike Pattern Learning in a Photonic Spiking Neural Network With VCSELs and VCSOAs

We propose a photonic spiking neural network (SNN) consisting of photonic spiking neurons based on vertical-cavity surface-emitting lasers (VCSELs). The photonic spike timing dependent plasticity (STDP) is implemented in a vertical-cavity semiconductor optical amplifier (VCSOA). A versatile computational model of the photonic SNN is presented based on the rate equation models. Through numerical simulation, a spike pattern learning and recognition task is performed based on the photonic STDP. The results show that the post-synaptic spike timing (PST) is eventually converged iteratively to the first spike timing of the input spike pattern via unsupervised learning. Additionally, the convergence rate of the PST can be accelerated for a photonic SNN with more pre-synaptic neurons. The effects of VCSOA parameters on the convergence performance of the unsupervised spike learning are also considered. To the best of our knowledge, such a versatile computational model of photonic SNN for unsupervised learning and recognition of arbitrary spike pattern has not yet been reported, which would contribute one step forward toward numerical implementation of a large-scale energy-efficient photonic SNN, and hence is interesting for neuromorphic photonic systems and spiking information processing.

Effect of inhibitory spike-timing-dependent plasticity on fast sparsely synchronized rhythms in a small-world neuronal network

We consider the Watts–Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity D. We employ an asymmetric anti-Hebbian time window for the iSTDP update rule [which is in contrast to the Hebbian time window for the excitatory STDP (eSTDP)]. Depending on values of D, population-averaged values of saturated synaptic inhibition strengths are potentiated [long-term potentiation (LTP)] or depressed [long-term depression (LTD)] in comparison with the initial mean value, and dispersions from the mean values of LTP/LTD are much increased when compared with the initial dispersion, independently of D. In most cases of LTD where the effect of mean LTD is dominant in comparison with the effect of dispersion, good synchronization (with higher spiking measure) is found to get better via LTD, while bad synchronization (with lower spiking measure) is found to get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, we also investigate the effects of network architecture on FSS by changing the rewiring probability p of the SWN in the presence of iSTDP.

Stochastic spike synchronization in a small-world neural network with spike-timing-dependent plasticity

We consider the Watts–Strogatz small-world network (SWN) consisting of subthreshold neurons which exhibit noise-induced spikings. This neuronal network has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In previous works without STDP, stochastic spike synchronization (SSS) between noise-induced spikings of subthreshold neurons was found to occur in a range of intermediate noise intensities. Here, we investigate the effect of additive STDP on the SSS by varying the noise intensity. Occurrence of a “Matthew” effect in synaptic plasticity is found due to a positive feedback process. As a result, good synchronization gets better via long-term potentiation of synaptic strengths, while bad synchronization gets worse via long-term depression. Emergences of long-term potentiation and long-term depression of synaptic strengths are intensively investigated via microscopic studies based on the pair-correlations between the pre- and the post-synaptic IISRs (instantaneous individual spike rates) as well as the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, the effects of multiplicative STDP (which depends on states) on the SSS are studied and discussed in comparison with the case of additive STDP (independent of states). These effects of STDP on the SSS in the SWN are also compared with those in the regular lattice and the random graph.

P.1.j.001 - Hormone and menstrual cycle effects on sleep spindle parameters in oral contraceptive users and controls

We consider the Watts–Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity D. We employ an asymmetric anti-Hebbian time window for the iSTDP update rule [which is in contrast to the Hebbian time window for the excitatory STDP (eSTDP)]. Depending on values of D, population-averaged values of saturated synaptic inhibition strengths are potentiated [long-term potentiation (LTP)] or depressed [long-term depression (LTD)] in comparison with the initial mean value, and dispersions from the mean values of LTP/LTD are much increased when compared with the initial dispersion, independently of D. In most cases of LTD where the effect of mean LTD is dominant in comparison with the effect of dispersion, good synchronization (with higher spiking measure) is found to get better via LTD, while bad synchronization (with lower spiking measure) is found to get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, we also investigate the effects of network architecture on FSS by changing the rewiring probability p of the SWN in the presence of iSTDP.

Learning of Precise Spike Times with Homeostatic Membrane Potential Dependent Synaptic Plasticity.

Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that they can reliably generate spikes at specific points in time. Existing activity-dependent plasticity rules like Spike-Timing-Dependent Plasticity are agnostic to the goal of learning spike times. On the other hand, the existing formal and supervised learning algorithms perform a temporally precise comparison of projected activity with the target, but there is no known biologically plausible implementation of this comparison. Here, we propose a simple and local unsupervised synaptic plasticity mechanism that is derived from the requirement of a balanced membrane potential. Since the relevant signal for synaptic change is the postsynaptic voltage rather than spike times, we call the plasticity rule Membrane Potential Dependent Plasticity (MPDP). Combining our plasticity mechanism with spike after-hyperpolarization causes a sensitivity of synaptic change to pre- and postsynaptic spike times which can reproduce Hebbian spike timing dependent plasticity for inhibitory synapses as was found in experiments. In addition, the sensitivity of MPDP to the time course of the voltage when generating a spike allows MPDP to distinguish between weak (spurious) and strong (teacher) spikes, which therefore provides a neuronal basis for the comparison of actual and target activity. For spatio-temporal input spike patterns our conceptually simple plasticity rule achieves a surprisingly high storage capacity for spike associations. The sensitivity of the MPDP to the subthreshold membrane potential during training allows robust memory retrieval after learning even in the presence of activity corrupted by noise. We propose that MPDP represents a biophysically plausible mechanism to learn temporal target activity patterns.

Modulation of motoneuron firing by recurrent inhibition in the adult rat in vivo.

Recent reports show that synaptic inhibition can modulate postsynaptic spike timing without having strong effects on firing rate. Thus synaptic inhibition can achieve multiplicity in neural circuit operation through variable modulation of postsynaptic firing rate vs. timing. We tested this possibility for recurrent inhibition (RI) of spinal motoneurons. In in vivo electrophysiological studies of adult Wistar rats anesthetized by isoflurane, we examined repetitive firing of individual lumbosacral motoneurons recorded in current clamp and modulated by synchronous antidromic electrical stimulation of multiple motor axons and their centrally projecting collateral branches. Antidromic stimulation produced recurrent inhibitory postsynaptic potentials (RIPSPs) having properties similar to those detailed in the cat. Although synchronous RI produced marked short-term modulation of motoneuron spike timing and instantaneous firing rate, there was little or no suppression of average firing rate. The bias in firing modulation of timing over average rate was observed even for high-frequency RI stimulation (100 Hz), perhaps because of the brevity of RIPSPs, which were more than twofold shorter during motoneuron firing compared with rest. These findings demonstrate that RI in the mammalian spinal cord has the capacity to support and not impede heightened motor pool activity, possibly during rapid, forceful movements.

Supervised learning with complex spikes and spike-timing-dependent plasticity.

One distinctive feature of Purkinje cells is that they have two types of discharge: in addition to simple spikes they fire complex spikes in response to input from the climbing fibers. These complex spikes have an initial rapid burst of spikes and spikelets followed by a sustained depolarization; in some models of cerebellar function this climbing fiber input supervises learning in Purkinje cells. On the other hand, synaptic plasticity is often thought to rely on the timing of pre-synaptic and post-synaptic spikes. It is suggested here that the period of depolarization following a complex spike, combined with a simple spike-timing-dependent plasticity rule, gives a mechanism for the climbing fiber to supervise learning in the Purkinje cell. This proposal is illustrated using a simple simulation in which it is seen that the climbing fiber succeeds in supervising the learning.

Natural firing patterns reduce sensitivity of synaptic plasticity to spike-timing

Synaptic plasticity is sensitive to both the rate and the timing of preand postsynaptic spikes. In experimental protocols used to induce plasticity, the imposed spike trains are regular and the relative timing between every preand postsynaptic spike is fixed. This is at odds with natural firing patterns observed in the cortex of intact animals, where cells fire irregularly and the timing between preand post-synaptic spikes varies. To investigate synaptic changes elicited by in vivo-like irregularly firing neurons at different rates and realistic correlations between preand post-synaptic spikes, we use numerical simulations and mathematical analysis of synaptic plasticity models. We concentrate on a calcium-based model [1], and further consider a voltagebased model [2] and a spike-timing based model [3]. To allow for comparison, all models are fitted to plasticity results obtained in vitro [4]. We show that standard stimulation protocols overestimate the influence of spike-timing on synaptic plasticity. Using a simple modification of regular spike-pair protocols, we allow for neurons to fire irregularly. Such irregular spike-pairs reduce the amplitude of potentiation and depression obtained by varying the time difference between preand postsynaptic spikes. This protocol allows us to quantify the relative effects of firing rate and timing in natural firing patterns, and to predict changes induced by an arbitrary correlation function between preand post-synaptic spikes. We show that spike correlations change synaptic plasticity at low firing rates in all models; whereas their influence becomes negligible at high firing rates for the calcium-based model but remains significant for the other two models. Our findings yield predictions for novel experiments and help bridge the gap between existing results on synaptic plasticity and plasticity occurring under natural conditions.

A Neuromorphic Architecture for Object Recognition and Motion Anticipation Using Burst-STDP

In this work we investigate the possibilities offered by a minimal framework of artificial spiking neurons to be deployed in silico. Here we introduce a hierarchical network architecture of spiking neurons which learns to recognize moving objects in a visual environment and determine the correct motor output for each object. These tasks are learned through both supervised and unsupervised spike timing dependent plasticity (STDP). STDP is responsible for the strengthening (or weakening) of synapses in relation to pre- and post-synaptic spike times and has been described as a Hebbian paradigm taking place both in vitro and in vivo. We utilize a variation of STDP learning, called burst-STDP, which is based on the notion that, since spikes are expensive in terms of energy consumption, then strong bursting activity carries more information than single (sparse) spikes. Furthermore, this learning algorithm takes advantage of homeostatic renormalization, which has been hypothesized to promote memory consolidation during NREM sleep. Using this learning rule, we design a spiking neural network architecture capable of object recognition, motion detection, attention towards important objects, and motor control outputs. We demonstrate the abilities of our design in a simple environment with distractor objects, multiple objects moving concurrently, and in the presence of noise. Most importantly, we show how this neural network is capable of performing these tasks using a simple leaky-integrate-and-fire (LIF) neuron model with binary synapses, making it fully compatible with state-of-the-art digital neuromorphic hardware designs. As such, the building blocks and learning rules presented in this paper appear promising for scalable fully neuromorphic systems to be implemented in hardware chips.

A triplet spike-timing–dependent plasticity model generalizes the Bienenstock–Cooper–Munro rule to higher-order spatiotemporal correlations

Synaptic strength depresses for low and potentiates for high activation of the postsynaptic neuron. This feature is a key property of the Bienenstock-Cooper-Munro (BCM) synaptic learning rule, which has been shown to maximize the selectivity of the postsynaptic neuron, and thereby offers a possible explanation for experience-dependent cortical plasticity such as orientation selectivity. However, the BCM framework is rate-based and a significant amount of recent work has shown that synaptic plasticity also depends on the precise timing of presynaptic and postsynaptic spikes. Here we consider a triplet model of spike-timing-dependent plasticity (STDP) that depends on the interactions of three precisely timed spikes. Triplet STDP has been shown to describe plasticity experiments that the classical STDP rule, based on pairs of spikes, has failed to capture. In the case of rate-based patterns, we show a tight correspondence between the triplet STDP rule and the BCM rule. We analytically demonstrate the selectivity property of the triplet STDP rule for orthogonal inputs and perform numerical simulations for nonorthogonal inputs. Moreover, in contrast to BCM, we show that triplet STDP can also induce selectivity for input patterns consisting of higher-order spatiotemporal correlations, which exist in natural stimuli and have been measured in the brain. We show that this sensitivity to higher-order correlations can be used to develop direction and speed selectivity.

Floating Gate Synapses With Spike-Time-Dependent Plasticity

This paper describes a single transistor floating-gate synapse device that can be used to store a weight in a nonvolatile manner, compute a biological EPSP, and demonstrate biological learning rules such as Long-Term Potentiation, LTD, and spike-time dependent plasticity. We also describe a highly scalable architecture of a matrix of synapses to implement the described learning rules. Parameters for weight update in the 0.35 um process have been extracted and can be used to predict the change in weight based on time difference between pre- and post-synaptic spike times.

Cooperative structural plasticity based on pre- and postsynaptic spike timing

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Assortment of GABAergic plasticity in the cortical interneuron melting pot.

Cortical structures of the adult mammalian brain are characterized by a spectacular diversity of inhibitory interneurons, which use GABA as neurotransmitter. GABAergic neurotransmission is fundamental for integrating and filtering incoming information and dictating postsynaptic neuronal spike timing, therefore providing a tight temporal code used by each neuron, or ensemble of neurons, to perform sophisticated computational operations. However, the heterogeneity of cortical GABAergic cells is associated to equally diverse properties governing intrinsic excitability as well as strength, dynamic range, spatial extent, anatomical localization, and molecular components of inhibitory synaptic connections that they form with pyramidal neurons. Recent studies showed that similarly to their excitatory (glutamatergic) counterparts, also inhibitory synapses can undergo activity-dependent changes in their strength. Here, some aspects related to plasticity and modulation of adult cortical and hippocampal GABAergic synaptic transmission will be reviewed, aiming at providing a fresh perspective towards the elucidation of the role played by specific cellular elements of cortical microcircuits during both physiological and pathological operations.