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

The Theory of Localist Representation and of a Purely Abstract Cognitive System: The Evidence from Cortical Columns, Category Cells, and Multisensory Neurons

abstract: The debate about representation in the brain and the nature of the cognitive system has been going on for decades now. This paper examines the neurophysiological evidence, primarily from single cell recordings, to get a better perspective on both the issues. After an initial review of some basic concepts, the paper reviews the data from single cell recordings – in cortical columns and of category-selective and multisensory neurons. In neuroscience, columns in the neocortex (cortical columns) are understood to be a basic functional/computational unit. The paper reviews the fundamental discoveries about the columnar organization and finds that it reveals a massively parallel search mechanism. This columnar organization could be the most extensive neurophysiological evidence for the widespread use of localist representation in the brain. The paper also reviews studies of category-selective cells. The evidence for category-selective cells reveals that localist representation is also used to encode complex abstract concepts at the highest levels of processing in the brain. A third major issue is the nature of the cognitive system in the brain and whether there is a form that is purely abstract and encoded by single cells. To provide evidence for a single-cell based purely abstract cognitive system, the paper reviews some of the findings related to multisensory cells. It appears that there is widespread usage of multisensory cells in the brain in the same areas where sensory processing takes place. Plus there is evidence for abstract modality invariant cells at higher levels of cortical processing. Overall, that reveals the existence of a purely abstract cognitive system in the brain. The paper also argues that since there is no evidence for dense distributed representation and since sparse representation is actually used to encode memories, there is actually no evidence for distributed representation in the brain. Overall, it appears that, at an abstract level, the brain is a massively parallel, distributed computing system that is symbolic. The paper also explains how grounded cognition and other theories of the brain are fully compatible with localist representation and a purely abstract cognitive system.View the article as published at http://journal.frontiersin.org/article/10.3389/fpsyg.2017.00186/ful

A roadmap to integrate astrocytes into Systems Neuroscience.

Systems neuroscience is still mainly a neuronal field, despite the plethora of evidence supporting the fact that astrocytes modulate local neural circuits, networks, and complex behaviors. In this article, we sought to identify which types of studies are necessary to establish whether astrocytes, beyond their well-documented homeostatic and metabolic functions, perform computations implementing mathematical algorithms that sub-serve coding and higher-brain functions. First, we reviewed Systems-like studies that include astrocytes in order to identify computational operations that these cells may perform, using Ca2+ transients as their encoding language. The analysis suggests that astrocytes may carry out canonical computations in a time scale of subseconds to seconds in sensory processing, neuromodulation, brain state, memory formation, fear, and complex homeostatic reflexes. Next, we propose a list of actions to gain insight into the outstanding question of which variables are encoded by such computations. The application of statistical analyses based on machine learning, such as dimensionality reduction and decoding in the context of complex behaviors, combined with connectomics of astrocyte-neuronal circuits, is, in our view, fundamental undertakings. We also discuss technical and analytical approaches to study neuronal and astrocytic populations simultaneously, and the inclusion of astrocytes in advanced modeling of neural circuits, as well as in theories currently under exploration such as predictive coding and energy-efficient coding. Clarifying the relationship between astrocytic Ca2+ and brain coding may represent a leap forward toward novel approaches in the study of astrocytes in health and disease

Memory and information processing in neuromorphic systems

A striking difference between brain-inspired neuromorphic processors and current von Neumann processors architectures is the way in which memory and processing is organized. As Information and Communication Technologies continue to address the need for increased computational power through the increase of cores within a digital processor, neuromorphic engineers and scientists can complement this need by building processor architectures where memory is distributed with the processing. In this paper we present a survey of brain-inspired processor architectures that support models of cortical networks and deep neural networks. These architectures range from serial clocked implementations of multi-neuron systems to massively parallel asynchronous ones and from purely digital systems to mixed analog/digital systems which implement more biological-like models of neurons and synapses together with a suite of adaptation and learning mechanisms analogous to the ones found in biological nervous systems. We describe the advantages of the different approaches being pursued and present the challenges that need to be addressed for building artificial neural processing systems that can display the richness of behaviors seen in biological systems.Comment: Submitted to Proceedings of IEEE, review of recently proposed neuromorphic computing platforms and system

Representational geometry: integrating cognition, computation, and the brain

The cognitive concept of representation plays a key role in theories of brain information processing. However, linking neuronal activity to representational content and cognitive theory remains challenging. Recent studies have characterized the representational geometry of neural population codes by means of representational distance matrices, enabling researchers to compare representations across stages of processing and to test cognitive and computational theories. Representational geometry provides a useful intermediate level of description, capturing both the information represented in a neuronal population code and the format in which it is represented. We review recent insights gained with this approach in perception, memory, cognition, and action. Analyses of representational geometry can compare representations between models and the brain, and promise to explain brain computation as transformation of representational similarity structure

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

Nonlinear decoding of a complex movie from the mammalian retina

Retina is a paradigmatic system for studying sensory encoding: the transformation of light into spiking activity of ganglion cells. The inverse problem, where stimulus is reconstructed from spikes, has received less attention, especially for complex stimuli that should be reconstructed “pixel-by-pixel”. We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small randomly-moving discs. We constructed nonlinear (kernelized and neural network) decoders that improved significantly over linear results. An important contribution to this was the ability of nonlinear decoders to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous-like activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. We propose a general principle by which downstream circuitry could discriminate between spontaneous and stimulus-driven activity based solely on higher-order statistical structure in the incoming spike trains