Timing Of Individual Spikes Research Articles

Algebraic approach to spike-time neural codes in the hippocampus.

Although temporal coding through spike-time patterns has long been of interest in neuroscience, the specific structures that could be useful for spike-time codes remain highly unclear. Here, we introduce an analytical approach, using techniques from discrete mathematics, to study spike-time codes. As an initial example, we focus on the phenomenon of "phase precession" in the rodent hippocampus. During navigation and learning on a physical track, specific cells in a rodent's brain form a highly structured pattern relative to the oscillation of population activity in this region. Studies of phase precession largely focus on its role in precisely ordering spike times for synaptic plasticity, as the role of phase precession in memory formation is well established. Comparatively less attention has been paid to the fact that phase precession represents one of the best candidates for a spike-time neural code. The precise nature of this code remains an open question. Here, we derive an analytical expression for a function mapping points in physical space to complex-valued spikes by representing individual spike times as complex numbers. The properties of this function make explicit a specific relationship between past and future in spike patterns of the hippocampus. Importantly, this mathematical approach generalizes beyond the specific phenomenon studied here, providing a technique to study the neural codes within precise spike-time sequences found during sensory coding and motor behavior. We then introduce a spike-based decoding algorithm, based on this function, that successfully decodes a simulated animal's trajectory using only the animal's initial position and a pattern of spike times. This decoder is robust to noise in spike times and works on a timescale almost an order of magnitude shorter than typically used with decoders that work on average firing rate. These results illustrate the utility of a discrete approach, based on the structure and symmetries in spike patterns across finite sets of cells, to provide insight into the structure and function of neural systems.

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

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

Latency correction in sparse neuronal spike trains

Background:In neurophysiological data, latency refers to a global shift of spikes from one spike train to the next, either caused by response onset fluctuations or by finite propagation speed. Such systematic shifts in spike timing lead to a spurious decrease in synchrony which needs to be corrected. New Method:We propose a new algorithm of multivariate latency correction suitable for sparse data for which the relevant information is not primarily in the rate but in the timing of each individual spike. The algorithm is designed to correct systematic delays while maintaining all other kinds of noisy disturbances. It consists of two steps, spike matching and distance minimization between the matched spikes using simulated annealing. Results:We show its effectiveness on simulated and real data: cortical propagation patterns recorded via calcium imaging from mice before and after stroke. Using simulations of these data we also establish criteria that can be evaluated beforehand in order to anticipate whether our algorithm is likely to yield a considerable improvement for a given dataset. Comparison with Existing Method(s):Existing methods of latency correction rely on adjusting peaks in rate profiles, an approach that is not feasible for spike trains with low firing in which the timing of individual spikes contains essential information. Conclusions:For any given dataset the criterion for applicability of the algorithm can be evaluated quickly and in case of a positive outcome the latency correction can be applied easily since the source codes of the algorithm are publicly available.

Rectified Linear Postsynaptic Potential Function for Backpropagation in Deep Spiking Neural Networks.

Spiking neural networks (SNNs) use spatiotemporal spike patterns to represent and transmit information, which are not only biologically realistic but also suitable for ultralow-power event-driven neuromorphic implementation. Just like other deep learning techniques, deep SNNs (DeepSNNs) benefit from the deep architecture. However, the training of DeepSNNs is not straightforward because the well-studied error backpropagation (BP) algorithm is not directly applicable. In this article, we first establish an understanding as to why error BP does not work well in DeepSNNs. We then propose a simple yet efficient rectified linear postsynaptic potential function (ReL-PSP) for spiking neurons and a spike-timing-dependent BP (STDBP) learning algorithm for DeepSNNs where the timing of individual spikes is used to convey information (temporal coding), and learning (BP) is performed based on spike timing in an event-driven manner. We show that DeepSNNs trained with the proposed single spike time-based learning algorithm can achieve the state-of-the-art classification accuracy. Furthermore, by utilizing the trained model parameters obtained from the proposed STDBP learning algorithm, we demonstrate ultralow-power inference operations on a recently proposed neuromorphic inference accelerator. The experimental results also show that the neuromorphic hardware consumes 0.751 mW of the total power consumption and achieves a low latency of 47.71 ms to classify an image from the Modified National Institute of Standards and Technology (MNIST) dataset. Overall, this work investigates the contribution of spike timing dynamics for information encoding, synaptic plasticity, and decision-making, providing a new perspective to the design of future DeepSNNs and neuromorphic hardware.

Information-Theoretic Approach and Fundamental Limits of Resolving Two Closely Timed Neuronal Spikes in Mouse Brain Calcium Imaging.

Although optical imaging of neurons using fluorescent genetically encoded calcium sensors has enabled large-scale in vivo experiments, the sensors' slow dynamics often blur closely timed action potentials into indistinguishable transients. While several previous approaches have been proposed to estimate the timing of individual spikes, they have overlooked the important and practical problem of estimating interspike interval (ISI) for overlapping transients. We use statistical detection theory to find the minimum detectable ISI under different levels of signal-to-noise ratio (SNR), model complexity, and recording speed. We also derive the Cramer-Rao lower bounds (CRBs) for the problem of ISI estimation. We use Monte-Carlo simulations with biologically derived parameters to numerically obtain the minimum detectable ISI and evaluate the performance of our estimators. Furthermore, we apply our detector to distinguish overlapping transients from experimentally obtained calcium imaging data. Experiments based on simulated and real data across different SNR levels and recording speeds show that our algorithms can accurately distinguish two fluorescence signals with ISI on the order of tens of milliseconds, shorter than the waveform's rise time. Our study shows that the statistically optimal ISI estimators closely approached the CRBs. Our work suggests that full analysis using recording speed, sensor kinetics, SNR, and the sensor's stochastically distributed response to action potentials can accurately resolve ISIs much smaller than the fluorescence waveform's rise time in modern calcium imaging experiments. Such analysis aids not only in future spike detection methods, but also in future experimental design when choosing sensors of neuronal activity.

Implementing Signature Neural Networks with Spiking Neurons.

Spiking Neural Networks constitute the most promising approach to develop realistic Artificial Neural Networks (ANNs). Unlike traditional firing rate-based paradigms, information coding in spiking models is based on the precise timing of individual spikes. It has been demonstrated that spiking ANNs can be successfully and efficiently applied to multiple realistic problems solvable with traditional strategies (e.g., data classification or pattern recognition). In recent years, major breakthroughs in neuroscience research have discovered new relevant computational principles in different living neural systems. Could ANNs benefit from some of these recent findings providing novel elements of inspiration? This is an intriguing question for the research community and the development of spiking ANNs including novel bio-inspired information coding and processing strategies is gaining attention. From this perspective, in this work, we adapt the core concepts of the recently proposed Signature Neural Network paradigm—i.e., neural signatures to identify each unit in the network, local information contextualization during the processing, and multicoding strategies for information propagation regarding the origin and the content of the data—to be employed in a spiking neural network. To the best of our knowledge, none of these mechanisms have been used yet in the context of ANNs of spiking neurons. This paper provides a proof-of-concept for their applicability in such networks. Computer simulations show that a simple network model like the discussed here exhibits complex self-organizing properties. The combination of multiple simultaneous encoding schemes allows the network to generate coexisting spatio-temporal patterns of activity encoding information in different spatio-temporal spaces. As a function of the network and/or intra-unit parameters shaping the corresponding encoding modality, different forms of competition among the evoked patterns can emerge even in the absence of inhibitory connections. These parameters also modulate the memory capabilities of the network. The dynamical modes observed in the different informational dimensions in a given moment are independent and they only depend on the parameters shaping the information processing in this dimension. In view of these results, we argue that plasticity mechanisms inside individual cells and multicoding strategies can provide additional computational properties to spiking neural networks, which could enhance their capacity and performance in a wide variety of real-world tasks.

Noisy Juxtacellular Stimulation In Vivo Leads to Reliable Spiking and Reveals High-Frequency Coding in Single Neurons.

Nanostimulation of single identified neurons in vivo can control spike frequency parametrically and, surprisingly, can even bias the animal's behavioral response. Here, we extend this stimulation protocol to time-dependent broadband noise stimulation in sensory and motor cortices of rat. In response to such stimuli, we found increased temporal spike-time reliability. The information transmission properties reveal, both experimentally and theoretically, that the neurons support high-frequency stimulation beyond the inverse membrane time. Generating a stimulus using the neuron's response properties, we could evoke prescribed spike times with high precision. Our work helps to establish a novel method for precise temporal control of single-cell spiking and provides a simplified biophysical description of single-neuron spiking under time-dependent in vivo-like stimulation.

Oxytocin Neurones: Intrinsic Mechanisms Governing the Regularity of Spiking Activity.

Oxytocin neurones of the rat supraoptic nucleus are osmoresponsive and, with all other things being equal, they fire at a mean rate that is proportional to the plasma sodium concentration. However, individual spike times are governed by highly stochastic events, namely the random occurrences of excitatory synaptic inputs, the probability of which is increased by increasing extracellular osmotic pressure. Accordingly, interspike intervals (ISIs) are very irregular. In the present study, we show, by statistical analyses of firing patterns in oxytocin neurones, that the mean firing rate as measured in bins of a few seconds is more regular than expected from the variability of ISIs. This is consistent with an intrinsic activity‐dependent negative‐feedback mechanism. To test this, we compared observed neuronal firing patterns with firing patterns generated by a leaky integrate‐and‐fire model neurone, modified to exhibit activity‐dependent mechanisms known to be present in oxytocin neurones. The presence of a prolonged afterhyperpolarisation (AHP) was critical for the ability to mimic the observed regularisation of mean firing rate, although we also had to add a depolarising afterpotential (DAP; sometimes called an afterdepolarisation) to the model to match the observed ISI distributions. We tested this model by comparing its behaviour with the behaviour of oxytocin neurones exposed to apamin, a blocker of the medium AHP. Good fits indicate that the medium AHP actively contributes to the firing patterns of oxytocin neurones during non‐bursting activity, and that oxytocin neurones generally express a DAP, even though this is usually masked by superposition of a larger AHP.

Learning Precise Spike Train-to-Spike Train Transformations in Multilayer Feedforward Neuronal Networks.

We derive a synaptic weight update rule for learning temporally precise spike train-to-spike train transformations in multilayer feedforward networks of spiking neurons. The framework, aimed at seamlessly generalizing error backpropagation to the deterministic spiking neuron setting, is based strictly on spike timing and avoids invoking concepts pertaining to spike rates or probabilistic models of spiking. The derivation is founded on two innovations. First, an error functional is proposed that compares the spike train emitted by the output neuron of the network to the desired spike train by way of their putative impact on a virtual postsynaptic neuron. This formulation sidesteps the need for spike alignment and leads to closed-form solutions for all quantities of interest. Second, virtual assignment of weights to spikes rather than synapses enables a perturbation analysis of individual spike times and synaptic weights of the output, as well as all intermediate neurons in the network, which yields the gradients of the error functional with respect to the said entities. Learning proceeds via a gradient descent mechanism that leverages these quantities. Simulation experiments demonstrate the efficacy of the proposed learning framework. The experiments also highlight asymmetries between synapses on excitatory and inhibitory neurons.

Spike count, spike timing and temporal information in the cortex of awake, freely moving rats

Objective. Sensory processing of peripheral information is not stationary but is, in general, a dynamic process related to the behavioral state of the animal. Yet the link between the state of the behavior and the encoding properties of neurons is unclear. This report investigates the impact of the behavioral state on the encoding mechanisms used by cortical neurons for both detection and discrimination of somatosensory stimuli in awake, freely moving, rats. Approach. Neuronal activity was recorded from the primary somatosensory cortex of five rats under two different behavioral states (quiet versus whisking) while electrical stimulation of increasing stimulus strength was delivered to the mystacial pad. Information theoretical measures were then used to measure the contribution of different encoding mechanisms to the information carried by neurons in response to the whisker stimulation. Main results. We found that the behavioral state of the animal modulated the total amount of information conveyed by neurons and that the timing of individual spikes increased the information compared to the total count of spikes alone. However, the temporal information, i.e. information exclusively related to when the spikes occur, was not modulated by behavioral state. Significance. We conclude that information about somatosensory stimuli is modulated by the behavior of the animal and this modulation is mainly expressed in the spike count while the temporal information is more robust to changes in behavioral state.

Variable-structure-systems based approach for online learning of spiking neural networks and its experimental evaluation

Raising the level of biological realism by utilizing the timing of individual spikes, spiking neural networks (SNNs) are considered to be the third generation of artificial neural networks. In this work, a novel variable-structure-systems based approach for online learning of SNN is developed and tested on the identification and speed control of a real-time servo system. In this approach, neurocontroller parameters are used to define a time-varying sliding surface to lead the control error signal to zero. To prove the convergence property of the developed algorithm, the Lyapunov stability method is utilized. The results of the real-time experiments on the laboratory servo system for a number of different load conditions including nonlinear and time-varying ones indicate that the control structure exhibits a highly robust behavior against disturbances and sudden changes in the command signal.

Neuronal Oscillations in Golgi Cells and Purkinje Cells are Accompanied by Decreases in Shannon Information Entropy

Neuronal oscillations have been shown to contribute to the function of the cerebral cortex by coordinating the neuronal activities of distant cortical regions via a temporal synchronization of neuronal discharge patterns. This can occur regardless whether these regions are linked by cortico-cortical pathways or not. Less is known concerning the role of neuronal oscillations in the cerebellum. Golgi cells and Purkinje cells are both principal cell types in the cerebellum. Purkinje cells are the sole output cells of the cerebellar cortex while Golgi cells contribute to information processing at the input stage of the cerebellar cortex. Both cell types have large cell bodies, as well as dendritic structures, that can generate large currents. The discharge patterns of both these cell types also exhibit oscillations. In view of the massive afferent information conveyed by the mossy fiber-granule cell system to different and distant areas of the cerebellar cortex, it is relevant to inquire the role of cerebellar neuronal oscillations in information processing. In this study, we compared the discharge patterns of Golgi cells and Purkinje cells in conscious rats and in rats anesthetized with urethane. We assessed neuronal oscillations by analyzing the regularity in the timing of individual spikes within a spike train by using autocorrelograms and fast-Fourier transform. We measured the differences in neuronal oscillations and the amount of information content in a spike train (defined by Shannon entropy processed per unit time) in rats under anesthesia and in conscious, awake rats. Our findings indicated that anesthesia caused more prominent neuronal oscillations in both Golgi cells and Purkinje cells accompanied by decreases in Shannon information entropy in their spike trains.

Microsecond precision of interaural time differences processing in the medial superior olive studied by a computational model

The medial superior olive (MSO) neural circuit in auditory brainstem computes sound azimuth from the interaural time difference (ITD) [1]. High spike timing precision in the order of tens of microseconds is necessary for this neural computation. This makes the MSO an ideal object to study spike time codes, as the relevant information is encoded by the spike timing relative to sound phase. In the MSO, spike timing precision deteriorates towards higher sound frequencies. Experimental recordings of Joris [4] demonstrate this by the vector strength (VS) function (see Figure ​Figure1A).1A). To explore the effects of the spike timing jitter on the MSO performance, we have introduced a model of the MSO circuit [2,3]. In our previous work, the model was explored using simulations, giving the value ranges of MSO circuit parameters which are necessary for proper functioning of the MSO in mammals [1]. In the present work we complement the simulations with several fits of smooth functions to the data and with analytical calculations. Figure. ​Figure.1A1A shows the shortest ITD detected by the model circuit, with its minimal value at sound frequency 1 kHz. Figure. 1B shows the MSO circuit precision in dependence on the spike timing jitter, which is defined as standard deviation of individual spike times relative to the sound phase. Figure ​Figure1B1B compares the simulated system, jagged line, and exponential curve fitted to the simulation with the analytical estimates of the just noticeable difference (JND) of ITD, line with circles. Figure 1 MSO precision in dependence on sound frequency and spike timing jitter. (A) Vector strength (VS), in units per cent shown together with the smallest detectable ITD in µs in dependence on sound frequency. Sound frequency 140 Hz used in [2] is shown ...

Modifying spiking precision in conductance-based neuronal models

The temporal precision of a neuron's spiking can be characterized by calculating its “jitter,” defined as the standard deviation of the timing of individual spikes in response to repeated presentations of a stimulus. Sub-millisecond jitters have been measured for neurons in a variety of experimental systems and appear to be functionally important in some instances. We have investigated how modifying a neuron's maximal conductances affects jitter using the leaky integrate-and-fire (LIF) model and an eight-conductance Hodgkin-Huxley type (HH8) model. We observed that jitter can be largely understood in the LIF model in terms of the neuron's filtering properties. In the HH8 model we found the role of individual conductances in determining jitter to be complicated and dependent on the model's spiking properties. Distinct behaviors were observed for populations with slow (<11.5 Hz) and fast (>11.5 Hz) spike rates and appear to be related to differences in a particular channel's activity at times just before spiking occurs.

Computing Complex Visual Features with Retinal Spike Times

Neurons in sensory systems can represent information not only by their firing rate, but also by the precise timing of individual spikes. For example, certain retinal ganglion cells, first identified in the salamander, encode the spatial structure of a new image by their first-spike latencies. Here we explore how this temporal code can be used by downstream neural circuits for computing complex features of the image that are not available from the signals of individual ganglion cells. To this end, we feed the experimentally observed spike trains from a population of retinal ganglion cells to an integrate-and-fire model of post-synaptic integration. The synaptic weights of this integration are tuned according to the recently introduced tempotron learning rule. We find that this model neuron can perform complex visual detection tasks in a single synaptic stage that would require multiple stages for neurons operating instead on neural spike counts. Furthermore, the model computes rapidly, using only a single spike per afferent, and can signal its decision in turn by just a single spike. Extending these analyses to large ensembles of simulated retinal signals, we show that the model can detect the orientation of a visual pattern independent of its phase, an operation thought to be one of the primitives in early visual processing. We analyze how these computations work and compare the performance of this model to other schemes for reading out spike-timing information. These results demonstrate that the retina formats spatial information into temporal spike sequences in a way that favors computation in the time domain. Moreover, complex image analysis can be achieved already by a simple integrate-and-fire model neuron, emphasizing the power and plausibility of rapid neural computing with spike times.

Improved SpikeProp for Using Particle Swarm Optimization

A spiking neurons network encodes information in the timing of individual spike times. A novel supervised learning rule for SpikeProp is derived to overcome the discontinuities introduced by the spiking thresholding. This algorithm is based on an error-backpropagation learning rule suited for supervised learning of spiking neurons that use exact spike time coding. The SpikeProp is able to demonstrate the spiking neurons that can perform complex nonlinear classification in fast temporal coding. This study proposes enhancements of SpikeProp learning algorithm for supervised training of spiking networks which can deal with complex patterns. The proposed methods include the SpikeProp particle swarm optimization (PSO) and angle driven dependency learning rate. These methods are presented to SpikeProp network for multilayer learning enhancement and weights optimization. Input and output patterns are encoded as spike trains of precisely timed spikes, and the network learns to transform the input trains into target output trains. With these enhancements, our proposed methods outperformed other conventional neural network architectures.

Information Recall Using Relative Spike Timing in a Spiking Neural Network

We present a neural network that is capable of completing and correcting a spiking pattern given only a partial, noisy version. It operates in continuous time and represents information using the relative timing of individual spikes. The network is capable of correcting and recalling multiple patterns simultaneously. We analyze the network's performance in terms of information recall. We explore two measures of the capacity of the network: one that values the accurate recall of individual spike times and another that values only the presence or absence of complete patterns. Both measures of information are found to scale linearly in both the number of neurons and the period of the patterns, suggesting these are natural measures of network information. We show a smooth transition from encodings that provide precise spike times to flexible encodings that can encode many scenes. This makes it plausible that many diverse tasks could be learned with such an encoding.

Does rhythmic entrainment represent a generalized mechanism for organizing computation in the brain?

Does rhythmic entrainment represent a generalized mechanism for organizing computation in the brain?

Predicting the Timing of Spikes Evoked by Tactile Stimulation of the Hand

What does the hand tell the brain? Tactile stimulation of the hand evokes remarkably precise patterns of neural activity, suggesting that the timing of individual spikes may convey information. However, many aspects of the transformation of mechanical deformations of the skin into spike trains remain unknown. Here we describe an integrate-and-fire model that accurately predicts the timing of individual spikes evoked by arbitrary mechanical vibrations in three types of mechanoreceptive afferent fibers that innervate the hand. The model accounts for most known properties of the three fiber types, including rectification, frequency-sensitivity, and patterns of spike entrainment as a function of stimulus frequency. These results not only shed light on the mechanisms of mechanotransduction but can be used to provide realistic tactile feedback in upper-limb neuroprostheses.

Selecting appropriate surrogate methods for spike correlation analysis

In the correlation analysis of experimentally recorded parallel spike trains one has to thoroughly consider the statistical features of the data in order to prevent false positive results [1]. Typically, the complexity of the data prevents us from using analytical expressions for evaluating the significance of observed correlations. Similarly, parametric tests presuppose models that are typically simplifications of the real neuronal data and thus may ignore important features. An alternative to these approaches is to use surrogate data, i.e. modified versions of the original data, to assess the significance [2]. The goal of this study is to develop selection criteria for suitable surrogate types. To study the applicability of surrogates we defined data sets exhibiting different statistical features found in typical experimental data (non-stationary firing rates, cross-trial non-stationary rates, deviation from Poisson) in combinations of increasing complexity. To demonstrate the impact of surrogate schemes on correlation analysis, we examine these with different surrogate generation methods commonly used in the literature [1]. Common to all these methods is that they in one way or the other destroy the precise temporal relation of the spiking activities between the neurons, by e.g. shuffling the trial ids (tr-shu) [3], randomizing the spike times (sp-rnd), randomly dithering the whole spike train against the other (tr-di) [4,5], dithering of individual spike times (sp-di) [6,7], dithering spike times under conservation of the joint-ISI distribution (jisi-di) [8], or by exchanging spikes across trials under local preservation of spike counts (sp-exg) [9,10]. To quantify the applicability of the various surrogates for significance estimation of spike correlation we concentrate on spike coincidences (allowed temporal precision: +/-1ms) and use their empirical count nemp as a test statistic. The p-value of nemp is obtained by comparing it to the surrogates' coincidence count distributions. To evaluate the true performance of the surrogates we study the false positive (FP) and false negative (FN) rates for different configurations of parameters implemented in simulated data (rate modulation, regularity, non-stationarity across trials, co-variation of rates). Figure 1 False positive (a.) and false negative (b.) percentages for all tested surrogate methods across five different data types. Colors code FP and FN percentages. White squares mark the position of bars of 100% FP. Based on the FN and FP performances, we find spike train dithering (tr-di) as the most robust detector of excess coincidences amongst the selected surrogates methods. Its detection accuracy is seemingly unaffected by the level of complexity of the data and its sensitivity remains at acceptable levels. Still, tr-di smooths the firing rate profile on the time scale of the dither width, and it is expected to produce false positives is the case of abrupt transients in firing rate. With the aim of dealing with this issue, further work is being done on the development of novel methods taking into account the observed firing rate profile. Doing so enables an approximate mapping of non-stationary processes to stationary ones, through which more accurate surrogates can be generated. This study illustrates the serious need to select appropriate surrogate methods when evaluating the significance of correlations observed in a given data set. Not doing so can lead to false conclusions and misinterpretation of the data. We therefore strongly recommend to test the chosen method on synthetic data which is as similar as possible to the experimental data at hand, but yet does not contain the feature being tested for, before proceeding with the analysis to control for false positive results [11].