Temporal spike pattern learning

Sensory systems present environmental information to central nervous system as sequences of action potentials or spikes. How do animals recognize these sequences carrying information about their world? We present a biologically inspired neural circuit designed to enable spike pattern recognition. This circuit is capable of training itself on a given interspike interval (ISI) sequence and is then able to respond to presentations of the same sequence. The essential ingredients of the recognition circuit are (a) a tunable time delay circuit, (b) a spike selection unit, and (c) a tuning mechanism using spike timing dependent plasticity of inhibitory synapses. We have investigated this circuit using Hodgkin-Huxley neuron models connected by realistic excitatory and inhibitory synapses. It is robust in the presence of noise represented as jitter in the spike times of the ISI sequence.

A biologically plausible model of myelin plasticity demonstrates how oligodendrocytes can selectively adjust conduction delays in axon bundles to allow robust communication between brain regions through long-range synchronization.

Gamma rhythms have been the focus of significant research interest within the neuroscience community in recent years [1]. Earlier theoretical studies focused on the question: how can a network of GABA containing neurons generate gamma oscillations? The findings suggest that for non-instantaneous synaptic events, inhibition rather than excitation is a better synchronizing mechanism for the generation of gamma rhythms [2]. Synchrony in inhibitory neural networks however is extremely sensitive to intrinsic heterogeneity in the network [3]. Based on the evidence for spike timing dependent plasticity (STDP) in inhibitory neurons [4,5], we hypothesize that STDP of inhibitory synapses can promote robust neural synchrony in inhibitory neuronal networks in the presence of heterogeneity. We investigate our hypothesis in a computational (Figure ​(Figure1a)1a) and a hybrid (Figure ​(Figure1b)1b) uni-directionally coupled network (UCI) of two fast-spiking inhibitory neurons. In the computational model, each neuron is modeled using the Hodgkin-Huxley (HH) framework [4]. Heterogeneity (H) is modeled by the difference in the intrinsic firing activity of the coupled neurons resulting from different DC current input. In the presence of STDP, the strength of synaptic coupling between the coupled neurons is modeled using a linear additive rule as: gs(t) = gs(t – 1) + ΔgSTDP(Δt), where Δt = tA – tB is the time interval between successive spikes of the post-synaptic and the pre-synaptic neurons and ΔgSTDP is the STDP rule adapted from [4]. In Figure ​Figure1a,1a, we demonstrate the effect of STDP on synchrony between coupled neurons in the presence of and the absence of STDP for network heterogeneity H=12%. Theoretical analysis using the concept of spike time response curves and Arnold tongue revealed that STDP induced 1:1 synchrony in the UCI network is (i) robust against a large range of heterogeneity in the intrinsic firing activity of coupled neurons, and (ii) in-phase i.e., Δt ≈ 0. Furthermore, the time to in-phase synchronization increases with increasing heterogeneity. Figure 1 a) Theoretical model of UCI. Autaptic synapse is introduced to mimic spike frequency adaptation in neuronal firing activity. b) Hybrid UCI network. Dynamic clamp experimental results for experimental protocol with fixed static-synaptic strength gs(0)=0.5 ... We used the dynamic clamp technique to construct a hybrid UCI network consisting of an HH based model of a inhibitory neuron coupled to a living inhibitory neuron in the stratum oriens of area CA1 of the hippocampus. Whole cell patch clamp recordings were obtained from the live cell under the following experimental protocols: (i) Fix H, vary the static synapse coupling strength gs(0) and (ii) Fix static synapse coupling strength gs(0) and vary H. In Figure ​Figure1b,1b, we present results from the second experimental protocol. We see that as predicted by our theoretical model, the time to in phase neural synchrony in the hybrid UCI network increases with increasing heterogeneity. We conclude that STDP of inhibitory synapses is a putative mechanism for robust neural synchrony in inhibitory neuronal networks.

A perfect integrate-and-fire model driven by colored noise is studied by means of the interspike interval (ISI) density and the serial correlation coefficient. Exact and approximate expressions for these functions are derived for weak dichotomous or Gaussian noise, respectively. It is shown that correlations in the input result in positive correlations in the ISI sequence and in a reduction of ISI variability. The results also indicate that for weak noise, the noise distribution only shapes the ISI density but not the ISI correlations which are determined by the noise's correlation function.

The problem with training spiking neural networks (SNNs) is relevant due to the ultra-low power consumption these networks could exhibit when implemented in neuromorphic hardware. The ongoing progress in the fabrication of memristors, a prospective basis for analogue synapses, gives relevance to studying the possibility of SNN learning on the base of synaptic plasticity models, obtained by fitting the experimental measurements of the memristor conductance change. The dynamics of memristor conductances is (necessarily) nonlinear, because conductance changes depend on the spike timings, which neurons emit in an all-or-none fashion. The ability to solve classification tasks was previously shown for spiking network models based on the bio-inspired local learning mechanism of spike-timing-dependent plasticity (STDP), as well as with the plasticity that models the conductance change of nanocomposite (NC) memristors. Input data were presented to the network encoded into the intensities of Poisson input spike sequences. This work considers another approach for encoding input data into input spike sequences presented to the network: temporal encoding, in which an input vector is transformed into relative timing of individual input spikes. Since temporal encoding uses fewer input spikes, the processing of each input vector by the network can be faster and more energy-efficient. The aim of the current work is to show the applicability of temporal encoding to training spiking networks with three synaptic plasticity models: STDP, NC memristor approximation, and PPX memristor approximation. We assess the accuracy of the proposed approach on several benchmark classification tasks: Fisher’s Iris, Wisconsin breast cancer, and the pole balancing task (CartPole). The accuracies achieved by SNN with memristor plasticity and conventional STDP are comparable and are on par with classic machine learning approaches.

Spike timing dependent plasticity (STDP) learning rule is one of hot topics in neurobiology since it's been widely believed that synaptic plasticity mainly contribute to learning and memory in brain. Up to now, STDP has been observed in a wide variety of areas of brain, hippocampus, cortex and so on. Competition among synapses is an important behavior for this learning rule. In present study, we propose a single layer spiking neural network model using STDP learning rule in inhibitory synapses to investigate the competitive behavior. The experiments show that the synapses among neurons are both strengthened on the whole training process. Thus neurons inhibit the activities of one another, eventually the neuron with the highest input spike rate win the competition. We have found that the behavior is efficient when the differences of firing rates of input neurons without STDP are great than 5Hz, otherwise the winner neuron is random. In order to use the principle to artificial intelligent system, we use a mechanism of dynamic learning rate to let the neuron with the highest input to be selected by the competitive behavior as the winner. Therefore, a robust competitive spiking neural network is obtained.

Spike timing dependent plasticity (STDP) is a synaptic learning rule where the relative timing between the presynaptic and postsynaptic action potentials determines the sign and strength of synaptic plasticity. In its basic form STDP has an asymmetric form which incorporates both persistent increases and persistent decreases in synaptic strength. The basic form of STDP, however, is not a fixed property and depends on the dendritic location. An asymmetric curve is observed in the distal dendrites, whereas a symmetrical one is observed in the proximal ones. A recent computational study has shown that the transition from the asymmetry to symmetry is due to inhibition under certain conditions. Synapses have also been observed to be unreliable at generating plasticity when excitatory postsynaptic potentials and single spikes are paired at low frequencies. Bursts of spikes, however, are reliably signaled because transmitter release is facilitated. This article presents a two-compartment model of the CA1 pyramidal cell. The model is neurophysiologically plausible with its dynamics resulting from the interplay of many ionic and synaptic currents. Plasticity is measured by a deterministic Ca(2+) dynamics model which measures the instantaneous calcium level and its time course in the dendrite and change the strength of the synapse accordingly. The model is validated to match the asymmetrical form of STDP from the pairing of a presynaptic (dendritic) and postsynaptic (somatic) spikes as observed experimentally. With the parameter set unchanged the model investigates how pairing of bursts with single spikes and bursts in the presence or absence of inhibition shapes the STDP curve. The model predicts that inhibition strength and frequency are not the only factors of the asymmetry-to-symmetry switch of the STDP curve. Burst interspike interval is another factor. This study is an important first step towards understanding how STDP is affected under natural firing patterns in vivo.

Brain functions such as learning and memory rely on synaptic plasticity. Many studies have shown that synaptic plasticity can be driven by the timings between pre- and postsynaptic spikes, also known as spike-timing-dependent plasticity (STDP). In most of the modeling studies exploring STDP functions, presynaptic spikes have been postulated to be Poisson (random) spikes and postsynaptic neurons have been described using an integrate-and-fire model, for simplicity. However, experimental data suggest this is not necessarily true. In this study, we investigated how STDP worked in synaptic competition if more neurophysiologically realistic properties for pre- and postsynaptic dynamics were incorporated; presynaptic (input) spikes obeyed a gamma process and the postsynaptic neuron was a multi-timescale adaptive threshold model. Our results showed that STDP strengthened specific combinations of pre- and postsynaptic properties; regular spiking neurons favored regular input spikes whereas random spiking neurons did random ones, suggesting neural information coding utilizes both the properties.

Generalized Linear Models (GLMs) are stochastic models that have been successfully used to model neural activity of single cells and populations. Typically, this requires the spike train to be binned into a binary time series that is modeled as a Bernoulli-type GLM. Unless a loss in temporal precision is acceptable, the bin size has to be chosen on the order of milliseconds. This renders an application to long-term recordings infeasible for computational reasons. We propose a new, binning-free application of the GLM framework to model neural activity by noting that spike trains can equally be characterized by the sequence of continuous-valued inter-spike intervals (ISIs). It was shown that single-neuron spike trains can often be sufficiently modeled as a non-stationary renewal process. Here, we focus on the Gamma distribution for the inter-spike intervals as it allows the accommodation of a relative refractory period and includes the inhomogeneous Poisson process as a special case. We generalize the idea of a modulated Gamma process to the population level by including cross-couplings between the neurons in case of recordings from multiple neurons in parallel. In a Gamma-GLM, each observed inter-spike interval is modeled as a sample from a Gamma distribution whose mean can vary with time, e.g. through modulation by an external stimulus. Traditionally, ISIs are assumed to be independent. However, this renewal assumption can be relaxed by conditioning on the durations of previous intervals. An inter-neuron coupling is introduced by additionally conditioning on the times of spikes of the other neurons. The Gamma distribution and other canonical distributions for inter-spike intervals are part of the exponential family so that efficient maximum likelihood solutions for all model parameters can be obtained using the framework of Generalized Linear Models. Considering the ratio between bin sizes for time-discrete models and the typical length of cortical inter-spike intervals, the computational demand can be reduced by several orders of magnitude. Goodness-of-fit is assessed by adapting standard tests for point process models and evaluating spike prediction performance based on cross-validation. We demonstrate the versatility of the coupled Gamma model for estimating functional connectivity from multi-electrode recordings. With a data set obtained from multi-electrode recordings of the visual system of the awake monkey, we show that the test power of the Gamma-GLM for detecting functional connectivity links is comparable to the performance of a classical discrete-time GLM albeit requiring much less computational time and memory resources. Using the two models on the same data set, we are able to estimate the unknown, underlying connection density of the network. Finally, we discuss general limitations of coupled Gamma-GLMs on the type of interactions that can be faithfully represented and discuss similarities to other binning-free models, in particular Cox’s proportional hazards model.

Inverse stochastic resonance (ISR) is a counterintuitive phenomenon where noise reduces the oscillation frequency of an oscillator to a minimum occurring at an intermediate noise intensity, and sometimes even to the complete absence of oscillations. In neuroscience, ISR was first experimentally verified with cerebellar Purkinje neurons [Buchin et al., PLOS Comput. Biol. 12, e1005000 (2016)]. These experiments showed that ISR enables a locally optimal information transfer between the input and output spike train of neurons. Subsequent studies have further demonstrated the efficiency of information processing and transfer in neural networks with small-world network topology. We have conducted a numerical investigation into the impact of adaptivity on ISR in a small-world network of noisy FitzHugh-Nagumo (FHN) neurons, operating in a bi-metastable regime consisting of a metastable fixed point and a metastable limit cycle. Our results show that the degree of ISR is highly dependent on the value of the FHN model's timescale separation parameter ε. The network structure undergoes dynamic adaptation via mechanisms of either spike-time-dependent plasticity (STDP) with potentiation-/depression-domination parameter P or homeostatic structural plasticity (HSP) with rewiring frequency F. We demonstrate that both STDP and HSP amplify the effect of ISR when ε lies within the bi-stability region of FHN neurons. Specifically, at larger values of ε within the bi-stability regime, higher rewiring frequencies F are observed to enhance ISR at intermediate (weak) synaptic noise intensities, while values of P consistent with depression-domination (potentiation-domination) consistently enhance (deteriorate) ISR. Moreover, although STDP and HSP control parameters may jointly enhance ISR, P has a greater impact on improving ISR compared to F. Our findings inform future ISR enhancement strategies in noisy artificial neural circuits, aiming to optimize local information transfer between input and output spike trains in neuromorphic systems and prompt venues for experiments in neural networks.

A simple model of spike generation is described that gives rise to negative correlations in the interspike interval (ISI) sequence and leads to long-term spike train regularization. This regularization can be seen by examining the variance of the kth-order interval distribution for large k (the times between spike i and spike i + k). The variance is much smaller than would be expected if successive ISIs were uncorrelated. Such regularizing effects have been observed in the spike trains of electrosensory afferent nerve fibers and can lead to dramatic improvement in the detectability of weak signals encoded in the spike train data (Ratnam & Nelson, 2000). Here, we present a simple neural model in which negative ISI correlations and long-term spike train regularization arise from refractory effects associated with a dynamic spike threshold. Our model is derived from a more detailed model of electrosensory afferent dynamics developed recently by other investigators (Chacron, Longtin, St.-Hilaire, & Maler, 2000;Chacron, Longtin, & Maler, 2001). The core of this model is a dynamic spike threshold that is transiently elevated following a spike and subsequently decays until the next spike is generated. Here, we present a simplified version-the linear adaptive threshold model-that contains a single state variable and three free parameters that control the mean and coefficient of variation of the spontaneous ISI distribution and the frequency characteristics of the driven response. We show that refractory effects associated with the dynamic threshold lead to regularization of the spike train on long timescales. Furthermore, we show that this regularization enhances the detectability of weak signals encoded by the linear adaptive threshold model. Although inspired by properties of electrosensory afferent nerve fibers, such regularizing effects may play an important role in other neural systems where weak signals must be reliably detected in noisy spike trains. When modeling a neuronal system that exhibits this type of ISI correlation structure, the linear adaptive threshold model may provide a more appropriate starting point than conventional renewal process models that lack long-term regularizing effects.

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.

We describe a novel method for analyzing neural data that uses a combination of Markov transition matrices and Kullback-Leibler divergence to characterize spike history and spike patterns. For this method, the interspike intervals (ISIs) are divided into bins by quantiles, and a Markov transition matrix is computed for the ISI sequence. This Markov transition matrix is then compared to another Markov transition matrix constructed under the assumption of independent spiking. We then compute the Kullback-Leibler divergence between the distributions of ISI transition probabilities for each bin. The purpose of this method is to quantify the effects of spike history on neuron output and to help better characterize the flaws associated with assuming independent spiking. We test this method on both simulated data and experimental data from primary visual cortex of cats, publicly available through CRCNS [1-3]. Interspike intervals are simulated based on exponential and gamma distributions fit to the corresponding experimental ISI distributions.

Interspike intervals (ISIs) of dopamine (DA) neurons recorded in the substantia nigra are predicted partially by their immediate prior history. This study was designed to assess neuroanatomic origins of these sequential relationships. ISI data recorded from three groups of nigral DA neurons were studied: 1) 16 neurons recorded in unlesioned animals, 2) 14 neurons recorded after forebrain hemisection, 3) 12 neurons recorded after partial forebrain hemisection that reproduced nonspecific effects of the surgical lesion while leaving forebrain connections intact. As predicted, DA neurons recorded after full forebrain hemisection yielded statistically significant reductions in sequential predictability relative to control neurons and neurons recorded following partial hemisection. These data support the hypothesis that the sequence-dependent behavior of DA neurons arise in part from interactions with forebrain structures. ISI sequences recorded from unlesioned rats demonstrated maximum predictability when an average of 3.7 prior events were incorporated into the forecasting algorithm, thereby suggesting a physiological process whose "depth" of history-dependence is approximately 600-800 msec. Additional studies examining the functional significance of sequence-dependent ISI structure exhibited by nigral DA neurons are indicated.

Repeating spatiotemporal spike patterns exist and carry information. Here we investigated how a single spiking neuron can optimally respond to one given pattern (localist coding), or to either one of several patterns (distributed coding, i.e., the neuron's response is ambiguous but the identity of the pattern could be inferred from the response of multiple neurons), but not to random inputs. To do so, we extended a theory developed in a previous paper (Masquelier, 2017), which was limited to localist coding. More specifically, we computed analytically the signal-to-noise ratio (SNR) of a multi-pattern-detector neuron, using a threshold-free leaky integrate-and-fire (LIF) neuron model with non-plastic unitary synapses and homogeneous Poisson inputs. Surprisingly, when increasing the number of patterns, the SNR decreases slowly, and remains acceptable for several tens of independent patterns. In addition, we investigated whether spike-timing-dependent plasticity (STDP) could enable a neuron to reach the theoretical optimal SNR. To this aim, we simulated a LIF equipped with STDP, and repeatedly exposed it to multiple input spike patterns, embedded in equally dense Poisson spike trains. The LIF progressively became selective to every repeating pattern with no supervision, and stopped discharging during the Poisson spike trains. Furthermore, tuning certain STDP parameters, the resulting pattern detectors were optimal. Tens of independent patterns could be learned by a single neuron using a low adaptive threshold, in contrast with previous studies, in which higher thresholds led to localist coding only. Taken together these results suggest that coincidence detection and STDP are powerful mechanisms, fully compatible with distributed coding. Yet we acknowledge that our theory is limited to single neurons, and thus also applies to feed-forward networks, but not to recurrent ones.