A numerical model for Hodgkin-Huxley neural stimulus reconstruction

The information about a neural activity is encoded in a neural response and usually the underlying stimulus that triggers the activity is unknown. This paper presents a numerical solution to reconstruct stimuli from Hodgkin-Huxley neural responses while retrieving the neural dynamics. The stimulus is reconstructed by first retrieving the maximal conductances of the ion channels and then solving the Hodgkin-Huxley equations for the stimulus. The results show that the reconstructed stimulus is a good approximation of the original stimulus, while the retrieved the neural dynamics, which represent the voltage-dependent changes in the ion channels, help to understand the changes in neural biochemistry. As high non-linearity of neural dynamics renders analytical inversion of a neuron an arduous task, a numerical approach provides a local solution to the problem of stimulus reconstruction and neural dynamics retrieval

Reconstructing Stimuli from the Spike Times of Leaky Integrate and Fire Neurons

Reconstructing stimuli from the spike trains of neurons is an important approach for understanding the neural code. One of the difficulties associated with this task is that signals which are varying continuously in time are encoded into sequences of discrete events or spikes. An important problem is to determine how much information about the continuously varying stimulus can be extracted from the time-points at which spikes were observed, especially if these time-points are subject to some sort of randomness. For the special case of spike trains generated by leaky integrate and fire neurons, noise can be introduced by allowing variations in the threshold every time a spike is released. A simple decoding algorithm previously derived for the noiseless case can be extended to the stochastic case, but turns out to be biased. Here, we review a solution to this problem, by presenting a simple yet efficient algorithm which greatly reduces the bias, and therefore leads to better decoding performance in the stochastic case

Consistent Recovery of Sensory Stimuli Encoded with MIMO Neural Circuits

We consider the problem of reconstructing finite energy stimuli encoded with a population of spiking leaky integrate-and-fire neurons. The reconstructed signal satisfies a consistency condition: when passed through the same neuron, it triggers the same spike train as the original stimulus. The recovered stimulus has to also minimize a quadratic smoothness optimality criterion. We formulate the reconstruction as a spline interpolation problem for scalar as well as vector valued stimuli and show that the recovery has a unique solution. We provide explicit reconstruction algorithms for stimuli encoded with single as well as a population of integrate-and-fire neurons. We demonstrate how our reconstruction algorithms can be applied to stimuli encoded with ON-OFF neural circuits with feedback. Finally, we extend the formalism to multi-input multi-output neural circuits and demonstrate that vector-valued finite energy signals can be efficiently encoded by a neural population provided that its size is beyond a threshold value. Examples are given that demonstrate the potential applications of our methodology to systems neuroscience and neuromorphic engineering

Neural oscillations as a signature of efficient coding in the presence of synaptic delays

Cortical networks exhibit ‘global oscillations’, in which neural spike times are entrained to an underlying oscillatory rhythm, but where individual neurons fire irregularly, on only a fraction of cycles. While the network dynamics underlying global oscillations have been well characterised, their function is debated. Here, we show that such global oscillations are a direct consequence of optimal efficient coding in spiking networks with synaptic delays and noise. To avoid firing unnecessary spikes, neurons need to share information about the network state. Ideally, membrane potentials should be strongly correlated and reflect a ‘prediction error’ while the spikes themselves are uncorrelated and occur rarely. We show that the most efficient representation is when: (i) spike times are entrained to a global Gamma rhythm (implying a consistent representation of the error); but (ii) few neurons fire on each cycle (implying high efficiency), while (iii) excitation and inhibition are tightly balanced. This suggests that cortical networks exhibiting such dynamics are tuned to achieve a maximally efficient population code

Minimum-error, energy-constrained source coding by sensory neurons

Neural coding, the process by which neurons represent, transmit, and manipulate physical signals, is critical to the function of the nervous system. Despite years of study, neural coding is still not fully understood. Efforts to model neural coding could improve both the understanding of the nervous system and the design of artificial devices which interact with neurons. Sensory receptors and neurons transduce physical signals into a sequence of action potentials, called a spike train. The principles which underly the translation from signal to spike train are still under investigation. From the perspective of an organism, neural codes which maximize the fidelity of the encoded signal (minimize encoding error), provide a competitive advantage. Selective pressure over evolutionary timescales has likely encouraged neural codes which minimize encoding error. At the same time, neural coding is metabolically expensive, which suggests that selective pressure would also encourage neural codes which minimize energy. Based on these assumptions, this work proposes a principle of neural coding which captures the trade-off between error and energy as a constrained optimization problem of minimizing encoding error while satisfying a constraint on energy. A solution to the proposed optimization problem is derived in the limit of high spike-rates. The solution is to track the instantaneous reconstruction error, and to time spikes when the error crosses a threshold value. In the limit of large signals, the threshold level is a constant, but in general it is signal dependent. This coding model, called the neural source coder, implies neurons should be able to track reconstruction error internally, using the error signal to precisely time spikes. Mathematically, this model is similar to existing adaptive threshold models, but it provides a new way to understand coding by sensory neurons. Comparing the predictions of the neural source coder to experimental data recorded from a peripheral neuron, the coder is able to predict spike times with considerable accuracy. Intriguingly, this is also true for a cortical neuron which has a low spike-rate. Reconstructions using the neural source coder show lower error than other spiking neuron models. The neural source coder also predicts the asymmetric spike-rate adaptation seen in sensory neurons (the primary-like response). An alternative expression for the neural source coder is as an instantaneous-rate coder of a rate function which depends on the signal, signal derivative, and encoding parameters. The instantaneous rate closely predicts experimental peri-stimulus time histograms. The addition of a stochastic threshold to the neural source coder accounts for the spike-time jitter observed in experimental datasets. Jittered spike-trains from the neural source coder show long-term interval statistics which closely match experimental recordings from a peripheral neuron. Moreover, the spike trains have strongly anti-correlated intervals, a feature observed in experimental data. Interestingly, jittered spike-trains do not improve reconstruction error for an individual neuron, but reconstruction error is reduced in simulations of small populations of independent neurons. This suggests that jittered spike-trains provide a method for small populations of sensory neurons to improve encoding error. Finally, a sound coding method for applying the neural source coder to timing spikes for cochlear implants is proposed. For each channel of the cochlear implant, a neural source coder can be used to time pulses to follow the patterns expected by peripheral neurons. Simulations show reduced reconstruction error compared to standard approaches using the signal envelope. Initial experiments with normal-hearing subjects show that a vocoder simulating this cochlear implant sound coding approach results in better speech perception thresholds when compared to a standard noise vocoder. Although further experiments with cochlear implant users are critical, initial results encourage further study of the proposed sound-coding method. Overall, the proposed principle of minimum-error, energy-constrained encoding for sensory neural coding can be implemented by a spike-timing model with a feedback loop which computes reconstruction error. This model of neural source coding predicts a wide range of experimental observations from both peripheral and cortical neurons. The close agreement between experimental data and the predictions of the neural source coder suggests a fundamental principle underlying neural coding

Identification of Dendritic Processing in Spiking Neural Circuits

A large body of experimental evidence points to sophisticated signal processing taking place at the level of dendritic trees and dendritic branches of neurons. This evidence suggests that, in addition to inferring the connectivity between neurons, identifying analog dendritic processing in individual cells is fundamentally important to understanding the underlying principles of neural computation. In this thesis, we develop a novel theoretical framework for the identification of dendritic processing directly from spike times produced by spiking neurons. The problem setting of spiking neurons is necessary since such neurons make up the majority of electrically excitable cells in most nervous systems and it is often hard or even impossible to directly monitor the activity within dendrites. Thus, action potentials produced by neurons often constitute the only causal and observable correlate of dendritic processing. In order to remain true to the underlying biophysics of electrically excitable cells, we employ well-established mechanistic models of action potential generation to describe the nonlinear mapping of the aggregate current produced by the tree into an asynchronous sequence of spikes. Specific models of spike generation considered include conductance-based models such as Hodgkin-Huxley, Morris-Lecar, Fitzhugh-Nagumo, as well as simpler models of the integrate-and-fire and threshold-and-fire type. The aggregate time-varying current driving the spike generator is taken to be produced by a dendritic stimulus processor, which is a nonlinear dynamical system capable of describing arbitrary linear and nonlinear transformations performed on one or more input stimuli. In the case of multiple stimuli, it can also describe the cross-coupling, or interaction, between various stimulus features. The behavior of the dendritic stimulus processor is fully captured by one or more kernels, which provide a characterization of the signal processing that is consistent with the broader cable theory description of dendritic trees. We prove that the neural identification problem, stated in terms of identifying the kernels of the dendritic stimulus processor, is mathematically dual to the neural population encoding problem. Specifically, we show that the collection of spikes produced by a single neuron in multiple experimental trials can be treated as a single multidimensional spike train of a population of neurons encoding the parameters of the dendritic stimulus processor. Using the theory of sampling in reproducing kernel Hilbert spaces, we then derive precise results demonstrating that, during any experiment, the entire neural circuit is projected onto the space of input stimuli and parameters of this projection are faithfully encoded in the spike train. Spike times are shown to correspond to generalized samples, or measurements, of this projection in a system of coordinates that is not fixed but is both neuron- and stimulus-dependent. We examine the theoretical conditions under which it may be possible to reconstruct the dendritic stimulus processor from these samples and derive corresponding experimental conditions for the minimum number of spikes and stimuli that need to be used. We also provide explicit algorithms for reconstructing the kernel projection and demonstrate that, under natural conditions, this projection converges to the true kernel. The developed methodology is quite general and can be applied to a number of neural circuits. In particular, the methods discussed span all sensory modalities, including vision, audition and olfaction, in which external stimuli are typically continuous functions of time and space. The results can also be applied to circuits in higher brain centers that receive multi-dimensional spike trains as input stimuli instead of continuous signals. In addition, the modularity of the approach allows one to extend it to mixed-signal circuits processing both continuous and spiking stimuli, to circuits with extensive lateral connections and feedback, as well as to multisensory circuits concurrently processing multiple stimuli of different dimensions, such as audio and video. Another important extension of the approach can be used to estimate the phase response curves of a neuron. All of the theoretical results are accompanied by detailed examples demonstrating the performance of the proposed identification algorithms. We employ both synthetic and naturalistic stimuli such as natural video and audio to highlight the power of the approach. Finally, we consider the implication of our work on problems pertaining to neural encoding and decoding and discuss promising directions for future research

Neuromorphic Engineering Editors' Pick 2021

This collection showcases well-received spontaneous articles from the past couple of years, which have been specially handpicked by our Chief Editors, Profs. André van Schaik and Bernabé Linares-Barranco. The work presented here highlights the broad diversity of research performed across the section and aims to put a spotlight on the main areas of interest. All research presented here displays strong advances in theory, experiment, and methodology with applications to compelling problems. This collection aims to further support Frontiers’ strong community by recognizing highly deserving authors