Search

The final version of this paper has been published in IEEEXplore available at http://ieeexplore.ieee.org/document/7727213. Please cite this paper as: Amirhossein Tavanaei, Timothee Masquelier, and Anthony Maida, Acquisition of visual features through probabilistic spike-timing-dependent plasticity. IEEE International Joint Conference on Neural Networks. pp. 307-314, IJCNN 2016. This paper explores modifications to a feedforward five-layer spiking convolutional network (SCN) of the ventral visual stream [Masquelier, T., Thorpe, S., Unsupervised learning of visual features through spike timing dependent plasticity. PLoS Computational Biology, 3(2), 247-257]. The original model showed that a spike-timing-dependent plasticity (STDP) learning algorithm embedded in an appropriately selected SCN could perform unsupervised feature discovery. The discovered features where interpretable and could effectively be used to perform rapid binary decisions in a classifier. In order to study the robustness of the previous results, the present research examines the effects of modifying some of the components of the original model. For improved biological realism, we replace the original non-leaky integrate-and-fire neurons with Izhikevich-like neurons. We also replace the original STDP rule with a novel rule that has a probabilistic interpretation. The probabilistic STDP slightly but significantly improves the performance for both types of model neurons. Use of the Izhikevich-like neuron was not found to improve performance although performance was still comparable to the IF neuron. This shows that the model is robust enough to handle more biologically realistic neurons. We also conclude that the underlying reasons for stable performance in the model are preserved despite the overt changes to the explicit components of the model., Comment: IEEE-IJCNN 2016

Retinal image of surrounding objects varies tremendously due to the changes in position, size, pose, illumination condition, background context, occlusion, noise, and non-rigid deformations. But despite these huge variations, our visual system is able to invariantly recognize any object in just a fraction of a second. To date, various computational models have been proposed to mimic the hierarchical processing of the ventral visual pathway, with limited success. Here, we show that the association of both biologically inspired network architecture and learning rule significantly improves the models' performance when facing challenging invariant object recognition problems. Our model is an asynchronous feedforward spiking neural network. When the network is presented with natural images, the neurons in the entry layers detect edges, and the most activated ones fire first, while neurons in higher layers are equipped with spike timing-dependent plasticity. These neurons progressively become selective to intermediate complexity visual features appropriate for object categorization. The model is evaluated on 3D-Object and ETH-80 datasets which are two benchmarks for invariant object recognition, and is shown to outperform state-of-the-art models, including DeepConvNet and HMAX. This demonstrates its ability to accurately recognize different instances of multiple object classes even under various appearance conditions (different views, scales, tilts, and backgrounds). Several statistical analysis techniques are used to show that our model extracts class specific and highly informative features.

Visual Abstract, How a population of retinal ganglion cells (RGCs) encodes the visual scene remains an open question. Going beyond individual RGC coding strategies, results in salamander suggest that the relative latencies of a RGC pair encode spatial information. Thus, a population code based on this concerted spiking could be a powerful mechanism to transmit visual information rapidly and efficiently., How a population of retinal ganglion cells (RGCs) encodes the visual scene remains an open question. Going beyond individual RGC coding strategies, results in salamander suggest that the relative latencies of a RGC pair encode spatial information. Thus, a population code based on this concerted spiking could be a powerful mechanism to transmit visual information rapidly and efficiently. Here, we tested this hypothesis in mouse by recording simultaneous light-evoked responses from hundreds of RGCs, at pan-retinal level, using a new generation of large-scale, high-density multielectrode array consisting of 4096 electrodes. Interestingly, we did not find any RGCs exhibiting a clear latency tuning to the stimuli, suggesting that in mouse, individual RGC pairs may not provide sufficient information. We show that a significant amount of information is encoded synergistically in the concerted spiking of large RGC populations. Thus, the RGC population response described with relative activities, or ranks, provides more relevant information than classical independent spike count- or latency- based codes. In particular, we report for the first time that when considering the relative activities across the whole population, the wave of first stimulus-evoked spikes is an accurate indicator of stimulus content. We show that this coding strategy coexists with classical neural codes, and that it is more efficient and faster. Overall, these novel observations suggest that already at the level of the retina, concerted spiking provides a reliable and fast strategy to rapidly transmit new visual scenes.

Deep convolutional neural networks (DCNNs) have attracted much attention recently, and have shown to be able to recognize thousands of object categories in natural image databases. Their architecture is somewhat similar to that of the human visual system: both use restricted receptive fields, and a hierarchy of layers which progressively extract more and more abstracted features. Yet it is unknown whether DCNNs match human performance at the task of view-invariant object recognition, whether they make similar errors and use similar representations for this task, and whether the answers depend on the magnitude of the viewpoint variations. To investigate these issues, we benchmarked eight state-of-the-art DCNNs, the HMAX model, and a baseline shallow model and compared their results to those of humans with backward masking. Unlike in all previous DCNN studies, we carefully controlled the magnitude of the viewpoint variations to demonstrate that shallow nets can outperform deep nets and humans when variations are weak. When facing larger variations, however, more layers were needed to match human performance and error distributions, and to have representations that are consistent with human behavior. A very deep net with 18 layers even outperformed humans at the highest variation level, using the most human-like representations.

Increasing evidence suggests that sensory stimulation not only changes the level of cortical activity with respect to baseline but also its structure. Despite having been reported in a multitude of conditions and preparations (for instance, as a quenching of intertrial variability, Churchland et al., 2010), such changes remain relatively poorly characterized. Here, we used optical imaging of voltage-sensitive dyes to explore, in V4 of an awake macaque, the spatiotemporal characteristics of both visually evoked and spontaneously ongoing neuronal activity and their difference. With respect to the spontaneous case, we detected a reduction in large-scale activity (cortical extent>1 mm) in the alpha range (5 to 12.5 Hz) during sensory inflow accompanied by a decrease in pairwise correlations. Moreover, the spatial patterns of correlation obtained during the different visual stimuli were on the average more similar one to another than they were to that obtained in the absence of stimulation. Finally, these observed changes in activity dynamics approached saturation already at very low stimulus contrasts, unlike the progressive, near-linear increase of the mean raw evoked responses over a wide range of contrast values, which could indicate a specific switching in the presence of a sensory inflow. This work was supported by the European Union (Integrated Project BrainScales), Award No. IST-FET-2010-269921; a French-Hungarian International ANR grant MULTISCALEFUNIM; and recurrent funding by CNRS and Aix-Marseille Université.

Fixational eye movements are common across vertebrates, yet their functional roles, if any, are debated [1]. To investigate this issue, we exposed the Virtual Retina simulator [2] to natural images, generated realistic drifts and microsaccades using the model of ref. [3], and analyzed the output spike trains of the parvocellular retinal ganglion cells (RGC). We first computed cross-correlograms between pairs of RGC that are strongly excited by the image corresponding to the mean eye position. Not surprisingly, in the absence of eye movements, that is when analyzing the tonic (sustained) response to a static image, these cross-correlograms are flat. Adding some slow drift (~20 min/s, self-avoiding random walk) creates long timescale (>1s) correlations because both cells tend to have high firing rates for central positions. Adding microsaccades (~0.5° in 25ms, that is ~20°/s) creates short timescale (tens of ms) correlations: cells that are strongly excited at a particular landing location tend to spike synchronously shortly after the landing. What do the patterns of synchronous spikes represent? To investigate this issue, we fed the RGC spike trains to neurons equipped with spike timing-dependent plasticity (STDP) and lateral inhibitory connections, as in ref. [4]. Neurons self-organized, and each one selected a set of afferents that consistently fired synchronously. We then reconstructed the corresponding visual stimuli by convolving the synaptic weight matrices with the RGC receptive fields. In most cases, we could easily recognize what was learned (e.g. a face), and the neuron was selective (e.g. only responded for microsaccades that landed on a face). Without eye movements, or with only the drift, the STDP-based learning failed, because it needs correlations at a timescale roughly matching the STDP time constants [5]. Microsaccades are thus necessary to generate a synchrony-based coding scheme. More specifically, after each microsaccade landing, cells that are strongly excited by the image corresponding to the landing location tend to fire their first spikes synchronously. Patterns of synchronous spikes can be decoded rapidly – as soon as the first spikes are received – by downstream “coincidence detector” neurons, which do not need to know the landing times. Finally, the required connectivity to do so can spontaneously emerge with STDP. As a whole, these results suggest a new role for microsaccades – to enable efficient visual feature learning and detection thanks to synchronization – that differs from other proposals such as time-to-first spike coding with respect to microsaccade landing times.

Oscillatory brain activity has been widely reported experimentally, yet its functional roles, if any, are still under debate. In this review we argue two things: firstly, thanks to oscillations, even slowly changing stimuli can be encoded in precise relative spike times, decodable by downstream "coincidence detector" neurons in a feedforward manner. Secondly, the required connectivity to do so can spontaneously emerge with spike timing-dependent plasticity (STDP), in an unsupervised manner. The key here is that a common oscillatory drive enables neurons to remain under a fluctuation-driven regime. In this regime spike time jitter does not accumulate and can thus be lower than the intrinsic timescales of stimulus fluctuations, which leads to so-called "temporal encoding". Furthermore, the oscillatory drive formats the spikes in discrete oversampling volleys, and the relative spike times between neurons indicate the eventual differences in their activation levels. The oversampling accelerates the STDP-based learning for downstream neurons. After learning, readout only takes one oscillatory cycle. Finally, we also discuss experimental evidence, and the question of how the theory is complementary to the so-called "communication through coherence" theory.

(This chapter is reprints material from Zamarreno-Ramos et al. in Front. Neurosci. 5:26, 2011 and Serrano-Gotarredona et al. in Front. Neurosci. 7:02, 2013, with permission.) Here we present a very exciting overlap between emergent nano technology and neuroscience, which has been discovered by neuromorphic engineers. Specifically, we are linking one type of memristor nano technology devices to the biological synaptic update rule known as Spike-Time-Dependent-Plasticity found in real biological synapses. Understanding this link allows neuromorphic engineers to develop circuit architectures that use this type of memristors to artificially emulate parts of the visual cortex. We focus on the type of memristors referred to as voltage or flux driven memristors and focus our discussions on behavioral macro models for such devices. The implementations result in fully asynchronous architectures with neurons sending their action potentials not only forwards but also backwards. One critical aspect is to use neurons that generate spikes of specific shapes. We will see how by changing the shapes of the neuron action potential spikes we can tune and manipulate the STDP learning rules for both excitatory and inhibitory synapses. We will see how neurons and memristors can be interconnected to achieve large scale spiking learning systems, that follow a type of multiplicative STDP learning rule. We will briefly extend the architectures to use three-terminal transistors with similar memristive behavior. We will illustrate how a V1 visual cortex layer can be assembled and how it is capable of learning to extract orientations from visual data coming from a real artificial CMOS spiking retina observing real life scenes. Finally, we will discuss limitations of currently available memristors. The results presented are based on behavioral simulations and do not take into account non-idealities of devices and interconnects. The aim here is to present, in a tutorial manner, an initial framework for the possible development of fully asynchronous STDP learning neuromorphic architectures exploiting two or three terminal memristive type devices. (A Supplemental Material compressed zip file containing all files used for the simulations can be downloaded from http://www.frontiersin.org/neuromorphic_engineering/10.3389/fnins.2011.00026/abstract.)

International audience; We do not claim that the brain is completely deterministic, and we agree that noise may be beneficial in some cases. But we suggest that neuronal variability may be often overestimated, due to uncontrolled internal variables, and/or the use of inappropriate reference times. These ideas are not new, but should be reexamined in the light of recent experimental findings: trial-to-trial variability is often correlated across neurons, across trials, greater for higher-order neurons, and reduced by attention, suggesting that " intrinsic " sources of noise can only account for a minimal part of it. While it is obviously difficult to control for all internal variables, the problem of reference time can be largely avoided by recording multiple neurons at the same time, and looking at statistical structures in relative latencies. These relative latencies have another major advantage: they are insensitive to the variability that is shared across neurons, which is often a significant part of the total variability. Thus, we suggest that signal-to-noise ratios in the brain may be much higher than usually thought, leading to reactive systems, economic in terms of number of neurons, and energy efficient.

In this paper we review several ways of realizing asynchronous Spike-Timing-Dependent-Plasticity (STDP) using memristors as synapses. Our focus is on how to use individual memristors to implement synaptic weight multiplications, in a way such that it is not necessary to (a) introduce global synchronization and (b) to separate memristor learning phases from memristor performing phases. In the approaches described, neurons fire spikes asynchronously when they wish and memristive synapses perform computation and learn at their own pace, as it happens in biological neural systems. We distinguish between two different memristor physics, depending on whether they respond to the original "moving wall" or to the "filament creation and annihilation" models. Independent of the memristor physics, we discuss two different types of STDP rules that can be implemented with memristors: either the pure timing-based rule that takes into account the arrival time of the spikes from the pre- and the post-synaptic neurons, or a hybrid rule that takes into account only the timing of pre-synaptic spikes and the membrane potential and other state variables of the post-synaptic neuron. We show how to implement these rules in cross-bar architectures that comprise massive arrays of memristors, and we discuss applications for artificial vision. © 2013 Serrano-Gotarredona, Masquelier, Prodromakis, Indiveri and Linares-Barranco., This work was supported by Spanish grants from the Ministry of Economy and Competitivity TEC200-106039-C04-01/02 (VULCANO) (with support from the European Regional Development Fund) and PRI-PIMCHI-2011-0768 (PNEUMA) coordinated with the European CHIST-ERA program, and Andalusian gran tTIC6091(NANONEURO). T. Masquelier was supported by the Europe an Union Seventh Framework Programme (FP7/2007-2013) under grant agreement 269459 (CORONET).

We have built a phenomenological spiking model of the cat early visual system comprising the retina, the Lateral Geniculate Nucleus (LGN) and V1's layer 4, and established four main results (1) When exposed to videos that reproduce with high fidelity what a cat experiences under natural conditions, adjacent Retinal Ganglion Cells (RGCs) have spike-time correlations at a short timescale (~30 ms), despite neuronal noise and possible jitter accumulation. (2) In accordance with recent experimental findings, the LGN filters out some noise. It thus increases the spike reliability and temporal precision, the sparsity, and, importantly, further decreases down to ~15 ms adjacent cells' correlation timescale. (3) Downstream simple cells in V1's layer 4, if equipped with Spike Timing-Dependent Plasticity (STDP), may detect these fine-scale cross-correlations, and thus connect principally to ON- and OFF-centre cells with Receptive Fields (RF) aligned in the visual space, and thereby become orientation selective, in accordance with Hubel and Wiesel (Journal of Physiology 160:106---154, 1962) classic model. Up to this point we dealt with continuous vision, and there was no absolute time reference such as a stimulus onset, yet information was encoded and decoded in the relative spike times. (4) We then simulated saccades to a static image and benchmarked relative spike time coding and time-to-first spike coding w.r.t. to saccade landing in the context of orientation representation. In both the retina and the LGN, relative spike times are more precise, less affected by pre-landing history and global contrast than absolute ones, and lead to robust contrast invariant orientation representations in V1.

Spike timing-dependent plasticity (STDP) has been shown to enable single neurons to detect repeatedly presented spatiotemporal spike patterns. This holds even when such patterns are embedded in equally dense random spiking activity, that is, in the absence of external reference times such as a stimulus onset. Here we demonstrate, both analytically and numerically, that STDP can also learn repeating rate-modulated patterns, which have received more experimental evidence, for example, through post-stimulus time histograms (PSTHs). Each input spike train is generated from a rate function using a stochastic sampling mechanism, chosen to be an inhomogeneous Poisson process here. Learning is feasible provided significant covarying rate modulations occur within the typical timescale of STDP (∼10–20 ms) for sufficiently many inputs (∼100 among 1000 in our simulations), a condition that is met by many experimental PSTHs. Repeated pattern presentations induce spike-time correlations that are captured by STDP. Despite imprecise input spike times and even variable spike counts, a single trained neuron robustly detects the pattern just a few milliseconds after its presentation. Therefore, temporal imprecision and Poisson-like firing variability are not an obstacle to fast temporal coding. STDP provides an appealing mechanism to learn such rate patterns, which, beyond sensory processing, may also be involved in many cognitive tasks., Author Summary In vivo neural responses to stimuli are known to have a lot of variability across trials. If the same number of spikes is emitted from trial to trial, the neuron is said to be reliable. If the timing of such spikes is roughly preserved across trials, the neuron is said to be precise. Here we demonstrate both analytically and numerically that the well-established Hebbian learning rule of spike-timing-dependent plasticity (STDP) can learn response patterns despite relatively low reliability (Poisson-like variability) and low temporal precision (10–20 ms). These features are in line with many experimental observations, in which a poststimulus time histogram (PSTH) is evaluated over multiple trials. In our model, however, information is extracted from the relative spike times between afferents without the need of an absolute reference time, such as a stimulus onset. Relevantly, recent experiments show that relative timing is often more informative than the absolute timing. Furthermore, the scope of application for our study is not restricted to sensory systems. Taken together, our results suggest a fine temporal resolution for the neural code, and that STDP is an appropriate candidate for encoding and decoding such activity.

In this paper we present a very exciting overlap between emergent nanotechnology and neuroscience, which has been discovered by neuromorphic engineers. Specifically, we are linking one type of memristor nanotechnology devices to the biological synaptic update rule known as spike-time-dependent-plasticity (STDP) found in real biological synapses. Understanding this link allows neuromorphic engineers to develop circuit architectures that use this type of memristors to artificially emulate parts of the visual cortex. We focus on the type of memristors referred to as voltage or flux driven memristors and focus our discussions on a behavioral macro-model for such devices. The implementations result in fully asynchronous architectures with neurons sending their action potentials not only forward but also backward. One critical aspect is to use neurons that generate spikes of specific shapes. We will see how by changing the shapes of the neuron action potential spikes we can tune and manipulate the STDP learning rules for both excitatory and inhibitory synapses. We will see how neurons and memristors can be interconnected to achieve large scale spiking learning systems, that follow a type of multiplicative STDP learning rule. We will briefly extend the architectures to use three-terminal transistors with similar memristive behavior. We will illustrate how a V1 visual cortex layer can assembled and how it is capable of learning to extract orientations from visual data coming from a real artificialCMOS spiking retina observing real life scenes. Finally, we will discuss limitations of currently available memristors. The results presented are based on behavioral simulations and do not take into account non-idealities of devices and interconnects. The aim of this paper is to present, in a tutorial manner, an initial framework for the possible development of fully asynchronous STDP learning neuromorphic architectures exploiting two or three-terminal memristive type devices. All files used for the simulations are made available through the journal web site., This work was supported by EU grant 216777 (NABAB), Spanish grants (with support from the European Regional Development Fund) TEC2006-11730-C03-01 (SAMANTA2), TEC2009-10639-C04-01 (VULCANO), and Andalusian grant P06TIC01417 (Brain System).

International audience; Recent experiments have established that information can be encoded in the spike times of neurons relative to the phase of a background oscillation in the local field potential-a phenomenon referred to as "phase-of-firing coding" (PoFC). These firing phase preferences could result from combining an oscillation in the input current with a stimulus-dependent static component that would produce the variations in preferred phase, but it remains unclear whether these phases are an epiphenomenon or really affect neuronal interactions-only then could they have a functional role. Here we show that PoFC has a major impact on downstream learning and decoding with the now well established spike timing-dependent plasticity (STDP). To be precise, we demonstrate with simulations how a single neuron equipped with STDP robustly detects a pattern of input currents automatically encoded in the phases of a subset of its afferents, and repeating at random intervals. Remarkably, learning is possible even when only a small fraction of the afferents ( approximately 10%) exhibits PoFC. The ability of STDP to detect repeating patterns had been noted before in continuous activity, but it turns out that oscillations greatly facilitate learning. A benchmark with more conventional rate-based codes demonstrates the superiority of oscillations and PoFC for both STDP-based learning and the speed of decoding: the oscillation partially formats the input spike times, so that they mainly depend on the current input currents, and can be efficiently learned by STDP and then recognized in just one oscillation cycle. This suggests a major functional role for oscillatory brain activity that has been widely reported experimentally.

Recently it has been shown that a repeating arbitrary spatiotemporal spike pattern hidden in equally dense distracter spike trains can be robustly detected and learned by a single neuron equipped with spike-timing-dependent plasticity (STDP) (Masquelier, Guyonneau, & Thorpe, 2008). To be precise, the neuron becomes selective to successive coincidences of the pattern. Here we extend this scheme to a more realistic scenario with multiple repeating patterns and multiple STDP neurons “listening” to the incoming spike trains. These “listening” neurons are in competition: as soon as one fires, it strongly inhibits the others through lateral connections (one-winner-take-all mechanism). This tends to prevent the neurons from learning the same (parts of the) repeating patterns, as shown in simulations. Instead, the population self-organizes, trying to cover the different patterns or coding one pattern by the successive firings of several neurons, and a powerful distributed coding scheme emerges. Taken together, these results illustrate how the brain could easily encode and decode information in the spike times, a theory referred to as temporal coding, and how STDP could play a key role by detecting repeating patterns and generating selective response to them.

One of the most striking features of the cortex is its ability to wire itself. Understanding how the visual cortex wires up through development and how visual experience refines connections into adulthood is a key question for Neuroscience. While computational models of the visual cortex are becoming increasingly detailed, the question of how such architecture could self-organize through visual experience is often overlooked. Here we focus on the class of hierarchical feed-forward models of the ventral stream of the visual cortex, which extend the classical simple-to-complex cells model by Hubel and Wiesel to extra-striate areas, and have been shown to account for a host of experimental data. Such models assume two functional classes of simple and complex cells with specific predictions about their respective wiring and resulting functionalities. In these networks, the issue of learning, especially for complex cells, is perhaps the least well understood. In fact, in most of these models, the connectivity between simple and complex cells is not learned but rather hard-wired. Several algorithms have been proposed for learning invariances at the complex cell level based on a trace rule to exploit the temporal continuity of sequences of natural images.

Using numerical simulations and analytical calculations, we have recently demonstrated that, thanks to the physiological learning mechanism referred to as Spike Timing-Dependent Plasticity (STDP), neurons can detect and learn repeating spike patterns, in an unsupervised manner, even when those patterns are embedded in noise[1-3] - a computationally difficult problem. Here, we show that the learning rule is optimal, in that it maximizes the response to the patterns, while minimizing the mean response to noise. Therefore, by thresholding the response, one can at the same time maximize the hit rate, and minimize the false alarm rate. More formally, if one considers a linear neuron, with n excitatory afferents, with synaptic weights w1 ... wn in 0[1], and one input spike pattern, the goal is to find a set of synaptic weights that maximizes the neuron's response to the pattern, while minimizing the mean response to Poisson input noise. We first show that, to find the optimal set, one should convolve the input spike pattern with the excitatory postsynaptic potential (EPSP) response kernel, and select the highest resulting peaks. For each peak p, only a subset of the afferents np contributed significantly to the response. One should select the highest peak with minimal np, choose w = 1 for the contributing afferents, and w = 0 for all the others (in order to minimize the mean response to Poisson noise). Then, we investigate the conditions under which STDP indeed reaches this optimum, using analytical calculations with a linear inhomogeneous Poisson model[3,4], as well as simulations with both leaky-integrate-and-fire (LIF) and Poisson neurons. Our results indicate that, in a number of cases, STDP indeed reaches this optimum, especially when coupled with homeostatic mechanisms. In other words, when faced with one repeating pattern to learn, STDP tends to chose the best "signature" of this pattern, that is a time window with as many (nearly) coincident spikes as possible from as few afferents as possible, and concentrates weights on these afferents only, thereby minimizing the probability of strong responses due to fortuitous spike coincidences. When faced with multiple repeating patterns, the ones with best signatures tend to be learned in priority.

Experimental studies have observed Long Term synaptic Potentiation (LTP) when a presynaptic neuron fires shortly before a postsynaptic neuron, and Long Term Depression (LTD) when the presynaptic neuron fires shortly after, a phenomenon known as Spike Timing Dependent Plasticity (STDP). When a neuron is presented successively with discrete volleys of input spikes STDP has been shown to learn 'early spike patterns', that is to concentrate synaptic weights on afferents that consistently fire early, with the result that the postsynaptic spike latency decreases, until it reaches a minimal and stable value. Here, we show that these results still stand in a continuous regime where afferents fire continuously with a constant population rate. As such, STDP is able to solve a very difficult computational problem: to localize a repeating spatio-temporal spike pattern embedded in equally dense 'distractor' spike trains. STDP thus enables some form of temporal coding, even in the absence of an explicit time reference. Given that the mechanism exposed here is simple and cheap it is hard to believe that the brain did not evolve to use it.

Recognition tasks performed by humans and animalsrequire the learning and storage of representations byneuronal networks of external sensory stimuli. Recentstudies have established the importance of timing withinspike trains for synaptic plasticity, which is hypothesisedto lead to learning at the behavioral level [1,2]. This spike-timing-dependent plasticity (STDP) was shown to bothstabilize the weights of the synapses on a neuron andinduce competition between them in order to generatenetwork structure [3]. For example, STDP can capturetemporal correlation or interaural time differences at thescale of milliseconds within spike trains [1,3].