Spectral analysis of input spike trains by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) has been observed in many brain areas such as sensory cortices, where it is hypothesized to structure synaptic connections between neurons. Previous studies have demonstrated how STDP can capture spiking information at short timescales using specific input configurations, such as coincident spiking, spike patterns and oscillatory spike trains. However, the corresponding computation in the case of arbitrary input signals is still unclear. This paper provides an overarching picture of the algorithm inherent to STDP, tying together many previous results for commonly used models of pairwise STDP. For a single neuron with plastic excitatory synapses, we show how STDP performs a spectral analysis on the temporal cross-correlograms between its afferent spike trains. The postsynaptic responses and STDP learning window determine kernel functions that specify how the neuron "sees" the input correlations. We thus denote this unsupervised learning scheme as 'kernel spectral component analysis' (kSCA). In particular, the whole input correlation structure must be considered since all plastic synapses compete with each other. We find that kSCA is enhanced when weight-dependent STDP induces gradual synaptic competition. For a spiking neuron with a "linear" response and pairwise STDP alone, we find that kSCA resembles principal component analysis (PCA). However, plain STDP does not isolate correlation sources in general, e.g., when they are mixed among the input spike trains. In other words, it does not perform independent component analysis (ICA). Tuning the neuron to a single correlation source can be achieved when STDP is paired with a homeostatic mechanism that reinforces the competition between synaptic inputs. Our results suggest that neuronal networks equipped with STDP can process signals encoded in the transient spiking activity at the timescales of tens of milliseconds for usual STDP.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks V: self-organization schemes and weight dependence

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity on a (much) slower time scale. This paper examines the effect of STDP in a recurrently connected network stimulated by external pools of input spike trains, where both input and recurrent synapses are plastic. Our previously developed theoretical framework is extended to incorporate weight-dependent STDP and dendritic delays. The weight dynamics is determined by an interplay between the neuronal activation mechanisms, the input spike-time correlations, and the learning parameters. For the case of two external input pools, the resulting learning scheme can exhibit a symmetry breaking of the input connections such that two neuronal groups emerge, each specialized to one input pool only. In addition, we show how the recurrent connections within each neuronal group can be strengthened by STDP at the expense of those between the two groups. This neuronal self-organization can be seen as a basic dynamical ingredient for the emergence of neuronal maps induced by activity-dependent plasticity.     

LTD windows of the STDP learning rule and synaptic connections having a large transmission delay enable robust sequence learning amid background noise

Spike-timing-dependent synaptic plasticity (STDP) is a simple and effective learning rule for sequence learning. However, synapses being subject to STDP rules are readily influenced in noisy circumstances because synaptic conductances are modified by pre- and postsynaptic spikes elicited within a few tens of milliseconds, regardless of whether those spikes convey information or not. Noisy firing existing everywhere in the brain may induce irrelevant enhancement of synaptic connections through STDP rules and would result in uncertain memory encoding and obscure memory patterns. We will here show that the LTD windows of the STDP rules enable robust sequence learning amid background noise in cooperation with a large signal transmission delay between neurons and a theta rhythm, using a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections. The important element of the present model for robust sequence learning amid background noise is the symmetric STDP rule having LTD windows on both sides of the LTP window, in addition to the loop connections having a large signal transmission delay and the theta rhythm pacing activities of stellate cells. Above all, the LTD window in the range of positive spike-timing is important to prevent influences of noise with the progress of sequence learning.     

STDP Installs in Winner-Take-All Circuits an Online Approximation to Hidden Markov Model Learning

In order to cross a street without being run over, we need to be able to extract very fast hidden causes of dynamically changing multi-modal sensory stimuli, and to predict their future evolution. We show here that a generic cortical microcircuit motif, pyramidal cells with lateral excitation and inhibition, provides the basis for this difficult but all-important information processing capability. This capability emerges in the presence of noise automatically through effects of STDP on connections between pyramidal cells in Winner-Take-All circuits with lateral excitation. In fact, one can show that these motifs endow cortical microcircuits with functional properties of a hidden Markov model, a generic model for solving such tasks through probabilistic inference. Whereas in engineering applications this model is adapted to specific tasks through offline learning, we show here that a major portion of the functionality of hidden Markov models arises already from online applications of STDP, without any supervision or rewards. We demonstrate the emergent computing capabilities of the model through several computer simulations. The full power of hidden Markov model learning can be attained through reward-gated STDP. This is due to the fact that these mechanisms enable a rejection sampling approximation to theoretically optimal learning. We investigate the possible performance gain that can be achieved with this more accurate learning method for an artificial grammar task.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV

In neuronal networks, the changes of synaptic strength (or weight) performed by spike-timing-dependent plasticity (STDP) are hypothesized to give rise to functional network structure. This article investigates how this phenomenon occurs for the excitatory recurrent connections of a network with fixed input weights that is stimulated by external spike trains. We develop a theoretical framework based on the Poisson neuron model to analyze the interplay between the neuronal activity (firing rates and the spike-time correlations) and the learning dynamics, when the network is stimulated by correlated pools of homogeneous Poisson spike trains. STDP can lead to both a stabilization of all the neuron firing rates (homeostatic equilibrium) and a robust weight specialization. The pattern of specialization for the recurrent weights is determined by a relationship between the input firing-rate and correlation structures, the network topology, the STDP parameters and the synaptic response properties. We find conditions for feed-forward pathways or areas with strengthened self-feedback to emerge in an initially homogeneous recurrent network.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II. Input selectivity—symmetry breaking

Spike-timing-dependent plasticity (STDP) is believed to structure neuronal networks by slowly changing the strengths (or weights) of the synaptic connections between neurons depending upon their spiking activity, which in turn modifies the neuronal firing dynamics. In this paper, we investigate the change in synaptic weights induced by STDP in a recurrently connected network in which the input weights are plastic but the recurrent weights are fixed. The inputs are divided into two pools with identical constant firing rates and equal within-pool spike-time correlations, but with no between-pool correlations. Our analysis uses the Poisson neuron model in order to predict the evolution of the input synaptic weights and focuses on the asymptotic weight distribution that emerges due to STDP. The learning dynamics induces a symmetry breaking for the individual neurons, namely for sufficiently strong within-pool spike-time correlation each neuron specializes to one of the input pools. We show that the presence of fixed excitatory recurrent connections between neurons induces a group symmetry-breaking effect, in which neurons tend to specialize to the same input pool. Consequently STDP generates a functional structure on the input connections of the network.     

Parallel processing by a homogeneous group of coupled model neurons can enhance, reduce and generate signal correlations

 Correlated activities have been proposed as correlates of flexible association and assembly coding. We addressed the basic question of how signal correlations on parallel pathways are enhanced, reduced and generated by homogeneous groups of coupled neurons, and how this depends on the input activities and their interactions with internal coupling processes. For this we simulated a fully connected group of identical impulse-coded neurons with dynamic input and threshold processes and additive or multiplicative lateral coupling. Input signals were Gaussian white noise (GWN), completely independent or partially correlated on a subgroup of the parallel inputs. We show that in states of high average spike rates input-output correlations were weak while the network could generate correlated activities of stochastic, oscillatory and rhythmic bursting types depending exclusively on lateral coupling strength. In states of low average spike rates input-output correlations were high and the network could effectively enhance or reduce differences in spatial correlation applied to its parallel inputs. The correlation differences were more pronounced with multiplicative lateral coupling than with the additive interactions commonly used. As the different modes of correlation processing emerged already by global changes in the average spike rate and lateral coupling strength, we assume that in real cortical circuits changes in correlational processing may also be induced by unspecific modulations of activation and lateral coupling. Received: 11 December 1995 / Accepted in revised form: 29 November 1996     

Lateral spike conduction velocity in the visual cortex affects spatial range of synchronization and receptive field size without visual experience: a learning model with spiking neurons

Classical receptive fields (cRF) increase in size from the retina to higher visual centers. The present work shows how temporal properties, in particular lateral spike velocity and spike input correlation, can affect cRF size and position without visual experience. We demonstrate how these properties are related to the spatial range of cortical synchronization if Hebbian learning dominates early development. For this, a largely reduced model of two successive levels of the visual cortex is developed (e.g., areas V1 and V2). It consists of retinotopic networks of spiking neurons with constant spike velocity in lateral connections. Feedforward connections between level 1 and 2 are additive and determine cRF size and shape, while lateral connections within level 1 are modulatory and affect the cortical range of synchronization. Input during development is mimicked by spike trains with spatially homogeneous properties and a confined temporal correlation width. During learning, the homogeneous lateral coupling shrinks to limited coupling structures defining synchronization and related association fields (AF). The size of level-1 synchronization fields determines the lateral coupling range of developing level-1-to-2 connections and, thus, the size of level-2 cRFs, even if the feedforward connections have distance-independent delays. AFs and cRFs increase with spike velocity in the lateral network and temporal correlation width of the input. Our results suggest that AF size of V1 and cRF size of V2 neurons are confined during learning by the temporal width of input correlations and the spike velocity in lateral connections without the need of visual experience. During learning from visual experience, a similar influence of AF size on the cRF size may be operative at successive levels of processing, including other parts of the visual system.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity–strengthening correlated input pathways

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity. In this paper, we extend previous studies of input selectivity induced by (STDP) for single neurons to the biologically interesting case of a neuronal network with fixed recurrent connections and plastic connections from external pools of input neurons. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of “steady” inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. The (STDP) model extends rate-based learning in that it can implement, at the same time, both a stabilization of the individual neuron firing rates and a slower weight specialization depending on the input spike-time correlations. When one input pathway has stronger within-pool correlations, the resulting synaptic dynamics induced by (STDP) are shown to be similar to those arising in the case of a purely feed-forward network: the weights from the more correlated inputs are potentiated at the expense of the remaining input connections.     

Mirrored STDP Implements Autoencoder Learning in a Network of Spiking Neurons

The autoencoder algorithm is a simple but powerful unsupervised method for training neural networks. Autoencoder networks can learn sparse distributed codes similar to those seen in cortical sensory areas such as visual area V1, but they can also be stacked to learn increasingly abstract representations. Several computational neuroscience models of sensory areas, including Olshausen & Field’s Sparse Coding algorithm, can be seen as autoencoder variants, and autoencoders have seen extensive use in the machine learning community. Despite their power and versatility, autoencoders have been difficult to implement in a biologically realistic fashion. The challenges include their need to calculate differences between two neuronal activities and their requirement for learning rules which lead to identical changes at feedforward and feedback connections. Here, we study a biologically realistic network of integrate-and-fire neurons with anatomical connectivity and synaptic plasticity that closely matches that observed in cortical sensory areas. Our choice of synaptic plasticity rules is inspired by recent experimental and theoretical results suggesting that learning at feedback connections may have a different form from learning at feedforward connections, and our results depend critically on this novel choice of plasticity rules. Specifically, we propose that plasticity rules at feedforward versus feedback connections are temporally opposed versions of spike-timing dependent plasticity (STDP), leading to a symmetric combined rule we call Mirrored STDP (mSTDP). We show that with mSTDP, our network follows a learning rule that approximately minimizes an autoencoder loss function. When trained with whitened natural image patches, the learned synaptic weights resemble the receptive fields seen in V1. Our results use realistic synaptic plasticity rules to show that the powerful autoencoder learning algorithm could be within the reach of real biological networks.     

Slowness: an objective for spike-timing-dependent plasticity?

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this "temporal stability" or "slowness" approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing-dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the "trace rule." The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.     

Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) with asymmetric learning windows is commonly found in the brain and useful for a variety of spike-based computations such as input filtering and associative memory. A natural consequence of STDP is establishment of causality in the sense that a neuron learns to fire with a lag after specific presynaptic neurons have fired. The effect of STDP on synchrony is elusive because spike synchrony implies unitary spike events of different neurons rather than a causal delayed relationship between neurons. We explore how synchrony can be facilitated by STDP in oscillator networks with a pacemaker. We show that STDP with asymmetric learning windows leads to self-organization of feedforward networks starting from the pacemaker. As a result, STDP drastically facilitates frequency synchrony. Even though differences in spike times are lessened as a result of synaptic plasticity, the finite time lag remains so that perfect spike synchrony is not realized. In contrast to traditional mechanisms of large-scale synchrony based on mutual interaction of coupled neurons, the route to synchrony discovered here is enslavement of downstream neurons by upstream ones. Facilitation of such feedforward synchrony does not occur for STDP with symmetric learning windows. Action Editor: Wulfram Gerstner     

Slowness: An Objective for Spike-Timing–Dependent Plasticity?

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this “temporal stability” or “slowness” approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing–dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the “trace rule.” The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.     

Noise propagation and signaling sensitivity in biological networks: a role for positive feedback

Interactions between genes and proteins are crucial for efficient processing of internal or external signals, but this connectivity also amplifies stochastic fluctuations by propagating noise between components. Linear (unbranched) cascades were shown to exhibit an interplay between the sensitivity to changes in input signals and the ability to buffer noise. We searched for biological circuits that can maintain signaling sensitivity while minimizing noise propagation, focusing on cases where the noise is characterized by rapid fluctuations. Negative feedback can buffer this type of noise, but this buffering comes at the expense of an even greater reduction in signaling sensitivity. By systematically analyzing three-component circuits, we identify positive feedback as a central motif allowing for the buffering of propagated noise while maintaining sensitivity to long-term changes in input signals. We show analytically that noise reduction in the presence of positive feedback results from improved averaging of rapid fluctuations over time, and discuss in detail a particular implementation in the control of nutrient homeostasis in yeast. As the design of biological networks optimizes for multiple constraints, positive feedback can be used to improve sensitivity without a compromise in the ability to buffer propagated noise.     

Network Self-Organization Explains the Statistics and Dynamics of Synaptic Connection Strengths in Cortex

The information processing abilities of neural circuits arise from their synaptic connection patterns. Understanding the laws governing these connectivity patterns is essential for understanding brain function. The overall distribution of synaptic strengths of local excitatory connections in cortex and hippocampus is long-tailed, exhibiting a small number of synaptic connections of very large efficacy. At the same time, new synaptic connections are constantly being created and individual synaptic connection strengths show substantial fluctuations across time. It remains unclear through what mechanisms these properties of neural circuits arise and how they contribute to learning and memory. In this study we show that fundamental characteristics of excitatory synaptic connections in cortex and hippocampus can be explained as a consequence of self-organization in a recurrent network combining spike-timing-dependent plasticity (STDP), structural plasticity and different forms of homeostatic plasticity. In the network, associative synaptic plasticity in the form of STDP induces a rich-get-richer dynamics among synapses, while homeostatic mechanisms induce competition. Under distinctly different initial conditions, the ensuing self-organization produces long-tailed synaptic strength distributions matching experimental findings. We show that this self-organization can take place with a purely additive STDP mechanism and that multiplicative weight dynamics emerge as a consequence of network interactions. The observed patterns of fluctuation of synaptic strengths, including elimination and generation of synaptic connections and long-term persistence of strong connections, are consistent with the dynamics of dendritic spines found in rat hippocampus. Beyond this, the model predicts an approximately power-law scaling of the lifetimes of newly established synaptic connection strengths during development. Our results suggest that the combined action of multiple forms of neuronal plasticity plays an essential role in the formation and maintenance of cortical circuits.     

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.     

Computational aspects of feedback in neural circuits

It has previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We investigate the computational capability of such circuits in the more realistic case where not only readout neurons, but in addition a few neurons within the circuit, have been trained for specific tasks. This is essentially equivalent to the case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any conceivable digital or analog computation on time-varying inputs. But even with noise, the resulting computational model can perform a large class of biologically relevant real-time computations that require a nonfading memory. We demonstrate these computational implications of feedback both theoretically, and through computer simulations of detailed cortical microcircuit models that are subject to noise and have complex inherent dynamics. We show that the application of simple learning procedures (such as linear regression or perceptron learning) to a few neurons enables such circuits to represent time over behaviorally relevant long time spans, to integrate evidence from incoming spike trains over longer periods of time, and to process new information contained in such spike trains in diverse ways according to the current internal state of the circuit. In particular we show that such generic cortical microcircuits with feedback provide a new model for working memory that is consistent with a large set of biological constraints. Although this article examines primarily the computational role of feedback in circuits of neurons, the mathematical principles on which its analysis is based apply to a variety of dynamical systems. Hence they may also throw new light on the computational role of feedback in other complex biological dynamical systems, such as, for example, genetic regulatory networks.     

Neural adaptation facilitates oscillatory responses to static inputs in a recurrent network of ON and OFF cells

We investigate the role of adaptation in a neural field model, composed of ON and OFF cells, with delayed all-to-all recurrent connections. As external spatially profiled inputs drive the network, ON cells receive inputs directly, while OFF cells receive an inverted image of the original signals. Via global and delayed inhibitory connections, these signals can cause the system to enter states of sustained oscillatory activity. We perform a bifurcation analysis of our model to elucidate how neural adaptation influences the ability of the network to exhibit oscillatory activity. We show that slow adaptation encourages input-induced rhythmic states by decreasing the Andronov–Hopf bifurcation threshold. We further determine how the feedback and adaptation together shape the resonant properties of the ON and OFF cell network and how this affects the response to time-periodic input. By introducing an additional frequency in the system, adaptation alters the resonance frequency by shifting the peaks where the response is maximal. We support these results with numerical experiments of the neural field model. Although developed in the context of the circuitry of the electric sense, these results are applicable to any network of spontaneously firing cells with global inhibitory feedback to themselves, in which a fraction of these cells receive external input directly, while the remaining ones receive an inverted version of this input via feedforward di-synaptic inhibition. Thus the results are relevant beyond the many sensory systems where ON and OFF cells are usually identified, and provide the backbone for understanding dynamical network effects of lateral connections and various forms of ON/OFF responses.     

The Effect of STDP Temporal Kernel Structure on the Learning Dynamics of Single Excitatory and Inhibitory Synapses

Spike-Timing Dependent Plasticity (STDP) is characterized by a wide range of temporal kernels. However, much of the theoretical work has focused on a specific kernel – the “temporally asymmetric Hebbian” learning rules. Previous studies linked excitatory STDP to positive feedback that can account for the emergence of response selectivity. Inhibitory plasticity was associated with negative feedback that can balance the excitatory and inhibitory inputs. Here we study the possible computational role of the temporal structure of the STDP. We represent the STDP as a superposition of two processes: potentiation and depression. This allows us to model a wide range of experimentally observed STDP kernels, from Hebbian to anti-Hebbian, by varying a single parameter. We investigate STDP dynamics of a single excitatory or inhibitory synapse in purely feed-forward architecture. We derive a mean-field-Fokker-Planck dynamics for the synaptic weight and analyze the effect of STDP structure on the fixed points of the mean field dynamics. We find a phase transition along the Hebbian to anti-Hebbian parameter from a phase that is characterized by a unimodal distribution of the synaptic weight, in which the STDP dynamics is governed by negative feedback, to a phase with positive feedback characterized by a bimodal distribution. The critical point of this transition depends on general properties of the STDP dynamics and not on the fine details. Namely, the dynamics is affected by the pre-post correlations only via a single number that quantifies its overlap with the STDP kernel. We find that by manipulating the STDP temporal kernel, negative feedback can be induced in excitatory synapses and positive feedback in inhibitory. Moreover, there is an exact symmetry between inhibitory and excitatory plasticity, i.e., for every STDP rule of inhibitory synapse there exists an STDP rule for excitatory synapse, such that their dynamics is identical.     

STDP allows fast rate-modulated coding with Poisson-like spike trains

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.