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

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

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

Sparse algorithms for decoding and identification of neural circuits

The brain, as an information processing machine, surpasses any man-made computational device, both in terms of its capabilities and its efficiency. Neuroscience research has made great strides since the foundational works of Cajal and Golgi. However, we still have very little understanding about the algorithmic underpinnings of the brain as an information processor. Identifying mechanistic models of the functional building blocks of the brain will have significant impact not just on neuroscience, but also on artificial computational systems. This provides the main motivation for the work presented in this thesis, summarily i) biologically-inspired algorithms that can be efficiently implemented in silico, ii) functional identification of the processing in certain types of neural circuits, and iii) a collaborative ecosystem for brain research in a model organism, towards the synergistic goal of understanding functional mechanisms employed by the brain. First, this thesis provides a highly parallelizable, biologically-inspired, motion detection algorithm that is based upon the temporal processing of the local (spatial) phase of a visual stimulus. The relation of the phase based motion detector to the widely studied Reichardt detector model, is discussed. Examples are provided comparing the performance of the proposed algorithm with the Reichardt detector as well as the optic flow algorithm, which is the workhorse for motion detection in computer vision. Further, it is shown through examples that the phase based motion detection model provides intuitive explanations for reverse-phi based illusory motion percepts. Then, tractable algorithms are presented for decoding with and identification of neural circuits, comprised of processing that can be described by a second-order Volterra kernel (quadratic filter). It is shown that the Reichardt detector, as well as models of cortical complex cells, can be described by this structure. Examples are provided for decoding of visual stimuli encoded by a population of Reichardt detector cells and complex cells, as well as their identification from observed spike times. Further, the phase based motion detection model is shown to be equivalent to a second-order Volterra kernel acting on two normalized inputs. Subsequently, a general model that computes the ratio of two non-linear functionals, each comprising linear (first order Volterra kernel) and quadratic (second-order Volterra kernel) filters, is proposed. It is shown that, even under these highly non-linear operations, a population of cells can encode stimuli faithfully using a number of measurements that are proportional to the bandwidth of the input stimulus. Tractable algorithms are devised to identify the divisive normalization model and examples of identification are provided for both simulated and biological data. Additionally, an extended framework, comprising parallel channels of divisively normalized cells each subjected to further divisive normalization from lateral feedback connections, is proposed. An algorithm is formulated for identifying all the components in this extended framework from controlled stimulus presentation and observed outputs samples. Finally, the thesis puts forward the Fruit Fly Brain Observatory (FFBO), an initiative to enable a collaborative ecosystem for fruit fly brain research. Key applications in FFBO, and the software and computational infrastructure enabling them, are described along with case studies

29th Annual Computational Neuroscience Meeting: CNS*2020

Meeting abstracts This publication was funded by OCNS. The Supplement Editors declare that they have no competing interests. Virtual | 18-22 July 202

25th Annual Computational Neuroscience Meeting: CNS-2016

Abstracts of the 25th Annual Computational Neuroscience Meeting: CNS-2016 Seogwipo City, Jeju-do, South Korea. 2–7 July 201

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong

Harnessing Neural Dynamics as a Computational Resource

Researchers study nervous systems at levels of scale spanning several orders of magnitude, both in terms of time and space. While some parts of the brain are well understood at specific levels of description, there are few overarching theories that systematically bridge low-level mechanism and high-level function. The Neural Engineering Framework (NEF) is an attempt at providing such a theory. The NEF enables researchers to systematically map dynamical systems—corresponding to some hypothesised brain function—onto biologically constrained spiking neural networks. In this thesis, we present several extensions to the NEF that broaden both the range of neural resources that can be harnessed for spatiotemporal computation and the range of available biological constraints. Specifically, we suggest a method for harnessing the dynamics inherent in passive dendritic trees for computation, allowing us to construct single-layer spiking neural networks that, for some functions, achieve substantially lower errors than larger multi-layer networks. Furthermore, we suggest “temporal tuning” as a unifying approach to harnessing temporal resources for computation through time. This allows modellers to directly constrain networks to temporal tuning observed in nature, in ways not previously well-supported by the NEF. We then explore specific examples of neurally plausible dynamics using these techniques. In particular, we propose a new “information erasure” technique for constructing LTI systems generating temporal bases. Such LTI systems can be used to establish an optimal basis for spatiotemporal computation. We demonstrate how this captures “time cells” that have been observed throughout the brain. As well, we demonstrate the viability of our extensions by constructing an adaptive filter model of the cerebellum that successfully reproduces key features of eyeblink conditioning observed in neurobiological experiments. Outside the cognitive sciences, our work can help exploit resources available on existing neuromorphic computers, and inform future neuromorphic hardware design. In machine learning, our spatiotemporal NEF populations map cleanly onto the Legendre Memory Unit (LMU), a promising artificial neural network architecture for stream-to-stream processing that outperforms competing approaches. We find that one of our LTI systems derived through “information erasure” may serve as a computationally less expensive alternative to the LTI system commonly used in the LMU

Extracting Spatiotemporal Word and Semantic Representations from Multiscale Neurophysiological Recordings in Humans

With the recent advent of neuroimaging techniques, the majority of the research studying the neural basis of language processing has focused on the localization of various lexical and semantic functions. Unfortunately, the limited time resolution of functional neuroimaging prevents a detailed analysis of the dynamics involved in word recognition, and the hemodynamic basis of these techniques prevents the study of the underlying neurophysiology. Compounding this problem, current techniques for the analysis of high-dimensional neural data are mainly sensitive to large effects in a small area, preventing a thorough study of the distributed processing involved for representing semantic knowledge. This thesis demonstrates the use of multivariate machine-learning techniques for the study of the neural representation of semantic and speech information in electro/magneto-physiological recordings with high temporal resolution. Support vector machines (SVMs) allow for the decoding of semantic category and word-specific information from non-invasive electroencephalography (EEG) and magnetoenecephalography (MEG) and demonstrate the consistent, but spatially and temporally distributed nature of such information. Moreover, the anteroventral temporal lobe (avTL) may be important for coordinating these distributed representations, as supported by the presence of supramodal category-specific information in intracranial recordings from the avTL as early as 150ms after auditory or visual word presentation. Finally, to study the inputs to this lexico-semantic system, recordings from a high density microelectrode array in anterior superior temporal gyrus (aSTG) are obtained, and the recorded spiking activity demonstrates the presence of single neurons that respond specifically to speech sounds. The successful decoding of word identity from this firing rate information suggests that the aSTG may be involved in the population coding of acousto-phonetic speech information that is likely on the pathway for mapping speech-sounds to meaning in the avTL. The feasibility of extracting semantic and phonological information from multichannel neural recordings using machine learning techniques provides a powerful method for studying language using large datasets and has potential implications for the development of fast and intuitive communication prostheses.Engineering and Applied Science

Efficient Learning Machines

Computer scienc