Neural coding: computational and biophysical perspectives

Supervised Learning Algorithm Based on Spike Train Inner Product for Deep Spiking Neural Networks

By mimicking the hierarchical structure of human brain, deep spiking neural networks (DSNNs) can extract features from a lower level to a higher level gradually, and improve the performance for the processing of spatio-temporal information. Due to the complex hierarchical structure and implicit nonlinear mechanism, the formulation of spike train level supervised learning methods for DSNNs remains an important problem in this research area. Based on the definition of kernel function and spike trains inner product (STIP) as well as the idea of error backpropagation (BP), this paper firstly proposes a deep supervised learning algorithm for DSNNs named BP-STIP. Furthermore, in order to alleviate the intrinsic weight transport problem of the BP mechanism, feedback alignment (FA) and broadcast alignment (BA) mechanisms are utilized to optimize the error feedback mode of BP-STIP, and two deep supervised learning algorithms named FA-STIP and BA-STIP are also proposed. In the experiments, the effectiveness of the proposed three DSNN algorithms is verified on the MNIST digital image benchmark dataset, and the influence of different kernel functions on the learning performance of DSNNs with different network scales is analyzed. Experimental results show that the FA-STIP and BP-STIP algorithms can achieve 94.73% and 95.65% classification accuracy, which apparently possess better learning performance and stability compared with the benchmark algorithm BP-STIP.

Supervised Learning Algorithm for Multilayer Spiking Neural Networks with Long-Term Memory Spike Response Model

As a new brain-inspired computational model of artificial neural networks, spiking neural networks transmit and process information via precisely timed spike trains. Constructing efficient learning methods is a significant research field in spiking neural networks. In this paper, we present a supervised learning algorithm for multilayer feedforward spiking neural networks; all neurons can fire multiple spikes in all layers. The feedforward network consists of spiking neurons governed by biologically plausible long-term memory spike response model, in which the effect of earlier spikes on the refractoriness is not neglected to incorporate adaptation effects. The gradient descent method is employed to derive synaptic weight updating rule for learning spike trains. The proposed algorithm is tested and verified on spatiotemporal pattern learning problems, including a set of spike train learning tasks and nonlinear pattern classification problems on four UCI datasets. Simulation results indicate that the proposed algorithm can improve learning accuracy in comparison with other supervised learning algorithms.

Biomimetic Chaotic Sensor for Moderate Static Magnetic Field

The effects of a static magnetic field on systems with chaotic dynamical behavior have attracted little attention so far. Here, Chua’s electronic circuit with an inductor placed in a static uniform magnetic field operating in a chaotic double-scroll regime is studied experimentally. The effect of the magnetic field on the duty cycle factor and the spike count rate, with spikes defined by crossings between the scrolls of the double-scroll attractor, is described. A slow monotonic variation in the duty cycle factor and constant spike count rate is observed for magnetic field intensities up to the threshold, where both these metrics change severely; the dynamic trajectory remains on one scroll and spikes disappear. The dependence of the static magnetic field intensity on Chua’s circuit resistivity at the threshold is given. Two biomimetic magnetic chaotic sensors are proposed: one based on one Chua’s circuit and another that can have various transfer functions and is composed of several independent Chua’s circuits.

Microelectrode recordings in human epilepsy: a case for clinical translation

With their 'all-or-none' action potential responses, single neurons (or units) are accepted as the basic computational unit of the brain. There is extensive animal literature to support the mechanistic importance of studying neuronal firing as a way to understand neuronal microcircuits and brain function. Although most studies have emphasized physiology, there is increasing recognition that studying single units provides novel insight into system-level mechanisms of disease. Microelectrode recordings are becoming more common in humans, paralleling the increasing use of intracranial electroencephalography recordings in the context of presurgical evaluation in focal epilepsy. In addition to single-unit data, microelectrode recordings also record local field potentials and high-frequency oscillations, some of which may be different to that recorded by clinical macroelectrodes. However, microelectrodes are being used almost exclusively in research contexts and there are currently no indications for incorporating microelectrode recordings into routine clinical care. In this review, we summarize the lessons learnt from 65 years of microelectrode recordings in human epilepsy patients. We cover the electrode constructs that can be utilized, principles of how to record and process microelectrode data and insights into ictal dynamics, interictal dynamics and cognition. We end with a critique on the possibilities of incorporating single-unit recordings into clinical care, with a focus on potential clinical indications, each with their specific evidence base and challenges.

Ensemble inhibition and excitation in the human cortex: An Ising-model analysis with uncertainties

The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance is unclear due to lack of reliable error estimates. We therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive Markov-chain Monte Carlo after the convergence of the main optimization algorithm. We apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake-sleep cycle. Our analysis shows that the Ising model captures neuronal collective behavior much better than the independent model during wakefulness, light sleep, and deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled; ignoring the inhibitory effects of I neurons dramatically overestimates synchrony among E neurons. Furthermore, information-theoretic measures reveal that the Ising model explains about 80-95% of the correlations, depending on sleep state and neuron type. Thermodynamic measures show signatures of criticality, although we take this with a grain of salt as it may be merely a reflection of long-range neural correlations.

Noise activated bistable sensor based on chaotic system with output defined by temporal coding and firing rate

Traditional bistable sensors use external bias signal to drive its response between states and their detection strategy is based on the output power spectral density or the residence time difference (RTD) in two sensor states. Recently, the noise activated nonlinear dynamic sensors driven only by noise based on RTD technique have been proposed. Here, we present experimental results of dc voltage measurements by noise-driven bistable sensor based on electronic Chua's circuit operating in a chaotic regime where two single scroll attractors coexist. The output of the sensor is quantified by the proportion of the time the sensor stays in one state to the total observation time and by the spike-count rate with spikes defined by crossings between attractors. The relationship between the stimuli and particular observable for different noise intensities is obtained, the usefulness of each coding scheme is discussed, and the optimal noise intensity for detection is indicated. It is shown that the obtained relationship is the same for any observation time when population coding is used. The optimal time window for both detection and the number of units in population coding is found. Our results may be useful for analyses and understanding of the neural activity and in designing bistable storage elements at length scales where thermal fluctuations drastically increase and the effect of noise must be taken into consideration.

A plausible neural circuit for decision making and its formation based on reinforcement learning

A human's, or lower insects', behavior is dominated by its nervous system. Each stable behavior has its own inner steps and control rules, and is regulated by a neural circuit. Understanding how the brain influences perception, thought, and behavior is a central mandate of neuroscience. The phototactic flight of insects is a widely observed deterministic behavior. Since its movement is not stochastic, the behavior should be dominated by a neural circuit. Based on the basic firing characteristics of biological neurons and the neural circuit's constitution, we designed a plausible neural circuit for this phototactic behavior from logic perspective. The circuit's output layer, which generates a stable spike firing rate to encode flight commands, controls the insect's angular velocity when flying. The firing pattern and connection type of excitatory and inhibitory neurons are considered in this computational model. We simulated the circuit's information processing using a distributed PC array, and used the real-time average firing rate of output neuron clusters to drive a flying behavior simulation. In this paper, we also explored how a correct neural decision circuit is generated from network flow view through a bee's behavior experiment based on the reward and punishment feedback mechanism. The significance of this study: firstly, we designed a neural circuit to achieve the behavioral logic rules by strictly following the electrophysiological characteristics of biological neurons and anatomical facts. Secondly, our circuit's generality permits the design and implementation of behavioral logic rules based on the most general information processing and activity mode of biological neurons. Thirdly, through computer simulation, we achieved new understanding about the cooperative condition upon which multi-neurons achieve some behavioral control. Fourthly, this study aims in understanding the information encoding mechanism and how neural circuits achieve behavior control. Finally, this study also helps establish a transitional bridge between the microscopic activity of the nervous system and macroscopic animal behavior.

Life and consciousness - The Vedāntic view

In the past, philosophers, scientists, and even the general opinion, had no problem in accepting the existence of consciousness in the same way as the existence of the physical world. After the advent of Newtonian mechanics, science embraced a complete materialistic conception about reality. Scientists started proposing hypotheses like abiogenesis (origin of first life from accumulation of atoms and molecules) and the Big Bang theory (the explosion theory for explaining the origin of universe). How the universe came to be what it is now is a key philosophical question. The hypothesis that it came from Nothing (as proposed by Stephen Hawking, among others), proves to be dissembling, since the quantum vacuum can hardly be considered a void. In modern science, it is generally assumed that matter existed before the universe came to be. Modern science hypothesizes that the manifestation of life on Earth is nothing but a mere increment in the complexity of matter — and hence is an outcome of evolution of matter (chemical evolution) following the Big Bang. After the manifestation of life, modern science believed that chemical evolution transformed itself into biological evolution, which then had caused the entire biodiversity on our planet. The ontological view of the organism as a complex machine presumes life as just a chance occurrence, without any inner purpose. This approach in science leaves no room for the subjective aspect of consciousness in its attempt to know the world as the relationships among forces, atoms, and molecules. On the other hand, the Vedāntic view states that the origin of everything material and nonmaterial is sentient and absolute (unconditioned). Thus, sentient life is primitive and reproductive of itself – omne vivum ex vivo – life comes from life. This is the scientifically verified law of experience. Life is essentially cognitive and conscious. And, consciousness, which is fundamental, manifests itself in the gradational forms of all sentient and insentient nature. In contrast to the idea of objective evolution of bodies, as envisioned by Darwin and followers, Vedānta advocates the idea of subjective evolution of consciousness as the developing principle of the world. In this paper, an attempt has been made to highlight a few relevant developments supporting a sentient view of life in scientific research, which has caused a paradigm shift in our understanding of life and its origin.

EEG phase patterns reflect the representation of semantic categories of objects

Oscillations of electroencephalographic signals represent the cognitive processes arose from the behavioral task and sensory representations across the mental state activity. Previous studies have shown the relation between event-related EEG and sensory-cognitive representation and revealed that categorization of presented object can be successfully recognized using recorded EEG signals when subjects view objects. Here, EEG signals in conjunction with a multivariate pattern recognition technique were used for investigating the possibility to identify conceptual representation based on the presentation of 12 semantic categories of objects (5 exemplars per category). Using multivariate stimulus decoding methods, surprisingly, we demonstrate that how objects are discriminated from phase pattern of EEG signals across the time in low-frequency band (1-4 Hz), but not from power of oscillatory brain signals in the same frequency band. In contrast, discrimination accuracy from the power of EEG signals has significantly higher than the performance from phase of EEG signal in the high-frequency band (20-30 Hz). Moreover, our results indicate that how the accuracy of prediction changes between various areas of brain continuously across the time. In particular, we find that, during the object categorization task, the inter-trial phase coherence in low-frequency band is significantly higher than other frequency in various regions of interests. This measure is associated with decoding pattern across the time. These results suggest that the mechanism underlying conceptual representation can be mediated by the phase of oscillatory neural activity.

Coding of information in the phase of local field potentials within human medial temporal lobe

There is increasing evidence that the phase of ongoing oscillations plays a role in neural coding, but its relative importance throughout the brain has yet to be understood. We assessed single-trial phase coding in four temporal lobe and four frontal lobe regions of the human brain using local field potentials (LFPs) recorded during a card-matching task. In the temporal lobe, classification of correct/incorrect matches based on LFP phase was significantly better than classification based on amplitude and comparable to the full LFP signal. Surprisingly, in these regions, the correct/incorrect mean phases became aligned to one another before they diverged and coded for trial outcome. Neural responses in the amygdala were consistent with a mechanism of phase resetting, while parahippocampal gyrus activity was indicative of evoked potentials. These findings highlight the importance of phase coding in human medial temporal lobe and suggest that different brain regions may represent information in diverse ways.

Neuroscience: what we cannot model, we do not understand

To understand computations in neuronal circuits, a model of a small patch of cortex has been developed that can describe the firing regime in the visual system remarkably well.

Ecological expected utility and the mythical neural code

Neural spikes are an evolutionarily ancient innovation that remains nature’s unique mechanism for rapid, long distance information transfer. It is now known that neural spikes sub serve a wide variety of functions and essentially all of the basic questions about the communication role of spikes have been answered. Current efforts focus on the neural communication of probabilities and utility values involved in decision making. Significant progress is being made, but many framing issues remain. One basic problem is that the metaphor of a neural code suggests a communication network rather than a recurrent computational system like the real brain. We propose studying the various manifestations of neural spike signaling as adaptations that optimize a utility function called ecological expected utility.

A canonical neural circuit for cortical nonlinear operations

A few distinct cortical operations have been postulated over the past few years, suggested by experimental data on nonlinear neural response across different areas in the cortex. Among these, the energy model proposes the summation of quadrature pairs following a squaring nonlinearity in order to explain phase invariance of complex V1 cells. The divisive normalization model assumes a gain-controlling, divisive inhibition to explain sigmoid-like response profiles within a pool of neurons. A gaussian-like operation hypothesizes a bell-shaped response tuned to a specific, optimal pattern of activation of the presynaptic inputs. A max-like operation assumes the selection and transmission of the most active response among a set of neural inputs. We propose that these distinct neural operations can be computed by the same canonical circuitry, involving divisive normalization and polynomial nonlinearities, for different parameter values within the circuit. Hence, this canonical circuit may provide a unifying framework for several circuit models, such as the divisive normalization and the energy models. As a case in point, we consider a feedforward hierarchical model of the ventral pathway of the primate visual cortex, which is built on a combination of the gaussian-like and max-like operations. We show that when the two operations are approximated by the circuit proposed here, the model is capable of generating selective and invariant neural responses and performing object recognition, in good agreement with neurophysiological data.

Object selectivity of local field potentials and spikes in the macaque inferior temporal cortex

Local field potentials (LFPs) arise largely from dendritic activity over large brain regions and thus provide a measure of the input to and local processing within an area. We characterized LFPs and their relationship to spikes (multi and single unit) in monkey inferior temporal cortex (IT). LFP responses in IT to complex objects showed strong selectivity at 44% of the sites and tolerance to retinal position and size. The LFP preferences were poorly predicted by the spike preferences at the same site but were better explained by averaging spikes within approximately 3 mm. A comparison of separate sites suggests that selectivity is similar on a scale of approximately 800 microm for spikes and approximately 5 mm for LFPs. These observations imply that inputs to IT neurons convey selectivity for complex shapes and that such input may have an underlying organization spanning several millimeters.

Response of electrically coupled spiking neurons: a cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate vs. stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by n-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is alpha=1, while for deterministic spike propagation we obtain alpha=1/2, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.