Dynamic Quantization using Spike Generation Mechanisms

This paper introduces a neuro-inspired co-ding/decoding mechanism of a constant real value by using a Spike Generation Mechanism (SGM) and a combination of two Spike Interpretation Mechanisms (SIM). One of the most efficient and widely used SGMs to encode a real value is the Leaky-Integrate and Fire (LIF) model which produces a spike train. The duration of the spike train is bounded by a given time constraint. Seeking for a simple solution of how to interpret the spike train and to reconstruct the input value, we combine two different kinds of SIMs, the time-SIM and the rate-SIM. The time-SIM allows a high quality interpretation of the neural code and the rate-SIM allows a simple decoding mechanism by couting the spikes. The resulting coding/decoding process, called the Dual-SIM Quantizer (Dual-SIMQ), is a non-uniform quantizer. It is shown that it coincides with a uniform scalar quantizer under certain assumptions. Finally, it is also shown that the time constraint can be used to control automatically the reconstruction accuracy of this time-dependent quantizer

Neuromorphic Sampling of Signals in Shift-Invariant Spaces

Neuromorphic sampling is a paradigm shift in analog-to-digital conversion where the acquisition strategy is opportunistic and measurements are recorded only when there is a significant change in the signal. Neuromorphic sampling has given rise to a new class of event-based sensors called dynamic vision sensors or neuromorphic cameras. The neuromorphic sampling mechanism utilizes low power and provides high-dynamic range sensing with low latency and high temporal resolution. The measurements are sparse and have low redundancy making it convenient for downstream tasks. In this paper, we present a sampling-theoretic perspective to neuromorphic sensing of continuous-time signals. We establish a close connection between neuromorphic sampling and time-based sampling - where signals are encoded temporally. We analyse neuromorphic sampling of signals in shift-invariant spaces, in particular, bandlimited signals and polynomial splines. We present an iterative technique for perfect reconstruction subject to the events satisfying a density criterion. We also provide necessary and sufficient conditions for perfect reconstruction. Owing to practical limitations in meeting the sufficient conditions for perfect reconstruction, we extend the analysis to approximate reconstruction from sparse events. In the latter setting, we pose signal reconstruction as a continuous-domain linear inverse problem whose solution can be obtained by solving an equivalent finite-dimensional convex optimization program using a variable-splitting approach. We demonstrate the performance of the proposed algorithm and validate our claims via experiments on synthetic signals

Identification of linear and nonlinear sensory processing circuits from spiking neuron data

Inferring mathematical models of sensory processing systems directly from input-output observations, while making the fewest assumptions about the model equations and the types of measurements available, is still a major issue in computational neuroscience. This letter introduces two new approaches for identifying sensory circuit models consisting of linear and nonlinear filters in series with spiking neuron models, based only on the sampled analog input to the filter and the recorded spike train output of the spiking neuron. For an ideal integrate-and-fire neuron model, the first algorithm can identify the spiking neuron parameters as well as the structure and parameters of an arbitrary nonlinear filter connected to it. The second algorithm can identify the parameters of the more general leaky integrate-and-fire spiking neuron model, as well as the parameters of an arbitrary linear filter connected to it. Numerical studies involving simulated and real experimental recordings are used to demonstrate the applicability and evaluate the performance of the proposed algorithms

Modeling the formation process of grouping stimuli sets through cortical columns and microcircuits to feature neurons

A computational model of a self-structuring neuronal net is presented in which repetitively applied pattern sets induce the formation of cortical columns and microcircuits which decode distinct patterns after a learning phase. In a case study, it is demonstrated how specific neurons in a feature classifier layer become orientation selective if they receive bar patterns of different slopes from an input layer. The input layer is mapped and intertwined by self-evolving neuronal microcircuits to the feature classifier layer. In this topical overview, several models are discussed which indicate that the net formation converges in its functionality to a mathematical transform which maps the input pattern space to a feature representing output space. The self-learning of the mathematical transform is discussed and its implications are interpreted. Model assumptions are deduced which serve as a guide to apply model derived repetitive stimuli pattern sets to in vitro cultures of neuron ensembles to condition them to learn and execute a mathematical transform

Massively Parallel Spiking Neural Circuits: Encoding, Decoding and Functional Identification

This thesis presents a class of massively parallel spiking neural circuit architectures in which neurons are modeled by dendritic stimulus processors cascaded with spike generators. We investigate how visual stimuli can be represented by the spike times generated by the massively parallel neural circuits, how the spike times can be used to reconstruct and process visual stimuli, and the conditions when visual stimuli can be faithfully represented/reconstructed. Functional identification of the massively parallel neural circuits from spike times and its evaluation are also investigated. Together, this thesis offers a comprehensive analytic framework of massively parallel spiking neural circuit architectures arising in the study of early visual systems. In encoding, modeling of visual stimuli in reproducing kernel Hilbert spaces is presented, recognizing the importance of studying visual encoding in a rigorous mathematical framework. For massively parallel neural circuits with biophysical spike generators, I/O characterization of the biophysical spike generators becomes possible by introducing phase response curve manifolds for the biophysical spike generators. I/O characterization of the entire neural circuit can then be interpreted as generalized sampling in the Hilbert space. Multi-component dendritic stimulus processors are introduced to model visual encoding in stereoscopic color vision. It is also shown that encoding of visual stimuli by an ensemble of complex cells has the complexity of Volterra dendritic stimulus processors. Based on the I/O characterization, reconstruction algorithms are derived to decode, from spike times, visual stimuli encoded by these massively parallel neural circuits. Decoding problems are first formulated as spline interpolation problems. Conditions on faithful reconstruction are presented, allowing the probe of information content carried by the spikes. Algorithms are developed to qualify the decoding in massively parallel settings. For stereoscopic color visual stimuli, demixing of individual channels from an unlabeled set of spike trains is demonstrated. For encoding with complex cells, decoding problems are formulated as rank minimization problems. It is shown that the decoding algorithm does not suffer from the curse of dimensionality and thereby allows for a visual representation using biologically realistic neural resources. The study of visual stimuli encoding and decoding enables the functional identification of massively parallel neural circuits. The duality between decoding and functional identification suggests that algorithms for functional identification of the projection of dendritic stimulus processors onto the space of input stimuli can be formulated similarly to the decoding algorithms. Functional identification of dendritic stimulus processors of neurons carrying stereoscopic color information as well as that of energy processing in complex cells is demonstrated. Furthermore, this duality also inspires a novel method to evaluate the quality of functional identification of massively parallel spiking neural circuits. By reconstructing novel stimuli using identified circuit parameters, the evaluation of the entire identified circuit is reduced to intuitive comparisons in stimulus space. The use of biophysical spike generators advances a methodology in the study of intrinsic noise sources in neurons and their effects on stimulus representation and on precision of functional identification. These effects are investigated using a class of nonlinear neural circuits consisting of both feedforward and feedback Volterra dendritic stimulus processors and biophysical spike generators. It is shown that encoding with neural circuits with intrinsic noise sources can be interpreted as generalized sampling with noisy measurements. Effects of noise on decoding and functional identification are derived theoretically and were systematically investigated by extensive simulations. Finally, the massively parallel neural circuit architectures are shown to enable the implementation of identity preserving transformations in the spike domain using a switching matrix regulating the connection between encoding and decoding. Two realizations of the architectures are developed, and extensive examples using continuous visual streams are provided. Implications of this result on the problem of invariant object recognition in the spike domain are discussed

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

Reconstruction, identification and implementation methods for spiking neural circuits

Integrate-and-fire (IF) neurons are time encoding machines (TEMs) that convert the amplitude of an analog signal into a non-uniform, strictly increasing sequence of spike times. This thesis addresses three major issues in the field of computational neuroscience as well as neuromorphic engineering. The first problem is concerned with the formulation of the encoding performed by an IF neuron. The encoding mechanism is described mathematically by the t-transform equation, whose standard formulation is given by the projection of the stimulus onto a set of input dependent frame functions. As a consequence, the standard methods reconstruct the input of an IF neuron in a space spanned by a set of functions that depend on the stimulus. The process becomes computationally demanding when performing reconstruction from long sequences of spike times. The issue is addressed in this work by developing a new framework in which the IF encoding process is formulated as a problem of uniform sampling on a set of input independent time points. Based on this formulation, new algorithms are introduced for reconstructing the input of an IF neuron belonging to bandlimited as well as shift-invariant spaces. The algorithms are significantly faster, whilst providing a similar level of accuracy, compared to the standard reconstruction methods. Another important issue calls for inferring mathematical models for sensory processing systems directly from input-output observations. This problem was addressed before by performing identification of sensory circuits consisting of linear filters in series with ideal IF neurons, by reformulating the identification problem as one of stimulus reconstruction. The result was extended to circuits in which the ideal IF neuron was replaced by more biophysically realistic models, under the additional assumptions that the spiking neuron parameters are known a priori, or that input-output measurements of the spiking neuron are available. This thesis develops two new identification methodologies for [Nonlinear Filter]-[Ideal IF] and [Linear Filter]-[Leaky IF] circuits consisting of two steps: the estimation of the spiking neuron parameters and the identification of the filter. The methodologies are based on the reformulation of the circuit as a scaled filter in series with a modified spiking neuron. The first methodology identifies an unknown [Nonlinear Filter]-[Ideal IF] circuit from input-output data. The scaled nonlinear filter is estimated using the NARMAX identification methodology for the reconstructed filter output. The [Linear Filter]-[Leaky IF] circuit is identified with the second proposed methodology by first estimating the leaky IF parameters with arbitrary precision using specific stimuli sequences. The filter is subsequently identified using the NARMAX identification methodology. The third problem addressed in this work is given by the need of developing neuromorphic engineering circuits that perform mathematical computations in the spike domain. In this respect, this thesis developed a new representation between the time encoded input and output of a linear filter, where the TEM is represented by an ideal IF neuron. A new practical algorithm is developed based on this representation. The proposed algorithm is significantly faster than the alternative approach, which involves reconstructing the input, simulating the linear filter, and subsequently encoding the resulting output into a spike train

Sequential Statistical Signal Processing with Applications to Distributed Systems

Detection and estimation, two classical statistical signal processing problems with wellestablished theories, are traditionally studied under the fixed-sample-size and centralized setups, e.g., Neyman-Pearson target detection, and Bayesian parameter estimation. Recently, they appear in more challenging setups with stringent constraints on critical resources, e.g., time, energy, and bandwidth, in emerging technologies, such as wireless sensor networks, cognitive radio, smart grid, cyber-physical systems (CPS), internet of things (IoT), and networked control systems. These emerging systems have applications in a wide range of areas, such as communications, energy, the military, transportation, health care, and infrastructure. Sequential (i.e., online) methods suit much better to the ever-increasing demand on time-efficiency, and latency constraints than the conventional fixed-sample-size (i.e., offline) methods. Furthermore, as a result of decreasing device sizes and tendency to connect more and more devices, there are stringent energy and bandwidth constraints on devices (i.e., nodes) in a distributed system (i.e., network), requiring decentralized operation with low transmission rates. Hence, for statistical inference (e.g., detection and/or estimation) problems in distributed systems, today's challenge is achieving high performance (e.g., time efficiency) while satisfying resource (e.g., energy and bandwidth) constraints. In this thesis, we address this challenge by (i) first finding optimum (centralized) sequential schemes for detection, estimation, and joint detection and estimation if not available in the literature, (ii) and then developing their asymptotically optimal decentralized versions through an adaptive non-uniform sampling technique called level-triggered sampling. We propose and rigorously analyze decentralized detection, estimation, and joint detection and estimation schemes based on level-triggered sampling, resulting in a systematic theory of event-based statistical signal processing. We also show both analytically and numerically that the proposed schemes significantly outperform their counterparts based on conventional uniform sampling in terms of time efficiency. Moreover, they are compatible with the existing hardware as they work with discrete-time observations produced by conventional A/D converters. We apply the developed schemes to several problems, namely spectrum sensing and dynamic spectrum access in cognitive radio, state estimation and outage detection in smart grid, and target detection in multi-input multi-output (MIMO) wireless sensor networks

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