Analog VLSI implementation of resonate-and-fire neuron

We propose an analog integrated circuit that implements a resonate-and-fire neuron (RFN) model based on the Lotka-Volterra (LV) system. The RFN model is a spiking neuron model that has second-order membrane dynamics, and thus exhibits fast damped subthreshold oscillation, resulting in the coincidence detection, frequency preference, and post-inhibitory rebound. The RFN circuit has been derived from the LV system to mimic such dynamical behavior of the RFN model. Through circuit simulations, we demonstrate that the RFN circuit can act as a coincidence detector and a band-pass filter at circuit level even in the presence of additive white noise and background random activity. These results show that our circuit is expected to be useful for very large-scale integration (VLSI) implementation of functional spiking neural networks.     

A model cortical circuit for the storage of temporal sequences

Despite the fact that temporal information processing is of particular significance in biological memory systems, not much has yet been explored about how these systems manage to store temporal information involved in sequences of stimuli. A neural network model capable of learning and recalling temporal sequences is proposed, based on a neural mechanism in which the sequences are expanded into a series of periodic rectangular oscillations. Thus, the mathematical framework underlying the model, to some extent, is concerned with the Walsh function series. The oscillatory activities generated by the interplay between excitatory and inhibitory neuron pools are transmitted to another neuron pool whose role in learning and retrieval is to modify the rhythms and phases of the rectangular oscillations. Thus, a basic functional neural circuit involves three different neuron pools. The modifiability of rhythms and phases is incorporated into the model with the aim of improving the quality of the retrieval. Numerical simulations were conducted to show the characteristic features of the learning as well as the performance of the model in memory recall.     

Spiking neural network model for memorizing sequences with forward and backward recall

We present an oscillatory network of conductance based spiking neurons of Hodgkin–Huxley type as a model of memory storage and retrieval of sequences of events (or objects). The model is inspired by psychological and neurobiological evidence on sequential memories. The building block of the model is an oscillatory module which contains excitatory and inhibitory neurons with all-to-all connections. The connection architecture comprises two layers. A lower layer represents consecutive events during their storage and recall. This layer is composed of oscillatory modules. Plastic excitatory connections between the modules are implemented using an STDP type learning rule for sequential storage. Excitatory neurons in the upper layer project star-like modifiable connections toward the excitatory lower layer neurons. These neurons in the upper layer are used to tag sequences of events represented in the lower layer. Computer simulations demonstrate good performance of the model including difficult cases when different sequences contain overlapping events. We show that the model with STDP type or anti-STDP type learning rules can be applied for the simulation of forward and backward replay of neural spikes respectively.     

Dense Neuron Clustering Explains Connectivity Statistics in Cortical Microcircuits

Local cortical circuits appear highly non-random, but the underlying connectivity rule remains elusive. Here, we analyze experimental data observed in layer 5 of rat neocortex and suggest a model for connectivity from which emerge essential observed non-random features of both wiring and weighting. These features include lognormal distributions of synaptic connection strength, anatomical clustering, and strong correlations between clustering and connection strength. Our model predicts that cortical microcircuits contain large groups of densely connected neurons which we call clusters. We show that such a cluster contains about one fifth of all excitatory neurons of a circuit which are very densely connected with stronger than average synapses. We demonstrate that such clustering plays an important role in the network dynamics, namely, it creates bistable neural spiking in small cortical circuits. Furthermore, introducing local clustering in large-scale networks leads to the emergence of various patterns of persistent local activity in an ongoing network activity. Thus, our results may bridge a gap between anatomical structure and persistent activity observed during working memory and other cognitive processes.     

Memory for events and their spatial context: models and experiments

The computational role of the hippocampus in memory has been characterized as: (i) an index to disparate neocortical storage sites; (ii) a time-limited store supporting neocortical long-term memory; and (iii) a content-addressable associative memory. These ideas are reviewed and related to several general aspects of episodic memory, including the differences between episodic, recognition and semantic memory, and whether hippocampal lesions differentially affect recent or remote memories. Some outstanding questions remain, such as: what characterizes episodic retrieval as opposed to other forms of read-out from memory; what triggers the storage of an event memory; and what are the neural mechanisms involved? To address these questions a neural-level model of the medial temporal and parietal roles in retrieval of the spatial context of an event is presented. This model combines the idea that retrieval of the rich context of real-life events is a central characteristic of episodic memory, and the idea that medial temporal allocentric representations are used in long-term storage while parietal egocentric representations are used to imagine, manipulate and re-experience the products of retrieval. The model is consistent with the known neural representation of spatial information in the brain, and provides an explanation for the involvement of Papez''s circuit in both the representation of heading direction and in the recollection of episodic information. Two experiments relating to the model are briefly described. A functional neuroimaging study of memory for the spatial context of life-like events in virtual reality provides support for the model''s functional localization. A neuropsychological experiment suggests that the hippocampus does store an allocentric representation of spatial locations.     

Membrane Capacitive Memory Alters Spiking in Neurons Described by the Fractional-Order Hodgkin-Huxley Model

Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity.     

Fading memory and kernel properties of generic cortical microcircuit models

It is quite difficult to construct circuits of spiking neurons that can carry out complex computational tasks. On the other hand even randomly connected circuits of spiking neurons can in principle be used for complex computational tasks such as time-warp invariant speech recognition. This is possible because such circuits have an inherent tendency to integrate incoming information in such a way that simple linear readouts can be trained to transform the current circuit activity into the target output for a very large number of computational tasks. Consequently we propose to analyze circuits of spiking neurons in terms of their roles as analog fading memory and non-linear kernels, rather than as implementations of specific computational operations and algorithms. This article is a sequel to [W. Maass, T. Natschl?ger, H. Markram, Real-time computing without stable states: a new framework for neural computation based on perturbations, Neural Comput. 14 (11) (2002) 2531-2560, Online available as #130 from: ], and contains new results about the performance of generic neural microcircuit models for the recognition of speech that is subject to linear and non-linear time-warps, as well as for computations on time-varying firing rates. These computations rely, apart from general properties of generic neural microcircuit models, just on capabilities of simple linear readouts trained by linear regression. This article also provides detailed data on the fading memory property of generic neural microcircuit models, and a quick review of other new results on the computational power of such circuits of spiking neurons.     

Using an Insect Mushroom Body Circuit to Encode Route Memory in Complex Natural Environments

Ants, like many other animals, use visual memory to follow extended routes through complex environments, but it is unknown how their small brains implement this capability. The mushroom body neuropils have been identified as a crucial memory circuit in the insect brain, but their function has mostly been explored for simple olfactory association tasks. We show that a spiking neural model of this circuit originally developed to describe fruitfly (Drosophila melanogaster) olfactory association, can also account for the ability of desert ants (Cataglyphis velox) to rapidly learn visual routes through complex natural environments. We further demonstrate that abstracting the key computational principles of this circuit, which include one-shot learning of sparse codes, enables the theoretical storage capacity of the ant mushroom body to be estimated at hundreds of independent images.     

A Spiking Neural Network Model of Model-Free Reinforcement Learning with High-Dimensional Sensory Input and Perceptual Ambiguity

A theoretical framework of reinforcement learning plays an important role in understanding action selection in animals. Spiking neural networks provide a theoretically grounded means to test computational hypotheses on neurally plausible algorithms of reinforcement learning through numerical simulation. However, most of these models cannot handle observations which are noisy, or occurred in the past, even though these are inevitable and constraining features of learning in real environments. This class of problem is formally known as partially observable reinforcement learning (PORL) problems. It provides a generalization of reinforcement learning to partially observable domains. In addition, observations in the real world tend to be rich and high-dimensional. In this work, we use a spiking neural network model to approximate the free energy of a restricted Boltzmann machine and apply it to the solution of PORL problems with high-dimensional observations. Our spiking network model solves maze tasks with perceptually ambiguous high-dimensional observations without knowledge of the true environment. An extended model with working memory also solves history-dependent tasks. The way spiking neural networks handle PORL problems may provide a glimpse into the underlying laws of neural information processing which can only be discovered through such a top-down approach.     

Nonlinear electronic circuit with neuron like bursting and spiking dynamics

It is difficult to design electronic nonlinear devices capable of reproducing complex oscillations because of the lack of general constructive rules, and because of stability problems related to the dynamical robustness of the circuits. This is particularly true for current analog electronic circuits that implement mathematical models of bursting and spiking neurons. Here we describe a novel, four-dimensional and dynamically robust nonlinear analog electronic circuit that is intrinsic excitable, and that displays frequency adaptation bursting and spiking oscillations. Despite differences from the classical Hodgkin–Huxley (HH) neuron model, its bifurcation sequences and dynamical properties are preserved, validating the circuit as a neuron model. The circuit's performance is based on a nonlinear interaction of fast–slow circuit blocks that can be clearly dissected, elucidating burst's starting, sustaining and stopping mechanisms, which may also operate in real neurons. Our analog circuit unit is easily linked and may be useful in building networks that perform in real-time.     

Graded,Dynamically Routable Information Processing with Synfire-Gated Synfire Chains

Coherent neural spiking and local field potentials are believed to be signatures of the binding and transfer of information in the brain. Coherent activity has now been measured experimentally in many regions of mammalian cortex. Recently experimental evidence has been presented suggesting that neural information is encoded and transferred in packets, i.e., in stereotypical, correlated spiking patterns of neural activity. Due to their relevance to coherent spiking, synfire chains are one of the main theoretical constructs that have been appealed to in order to describe coherent spiking and information transfer phenomena. However, for some time, it has been known that synchronous activity in feedforward networks asymptotically either approaches an attractor with fixed waveform and amplitude, or fails to propagate. This has limited the classical synfire chain’s ability to explain graded neuronal responses. Recently, we have shown that pulse-gated synfire chains are capable of propagating graded information coded in mean population current or firing rate amplitudes. In particular, we showed that it is possible to use one synfire chain to provide gating pulses and a second, pulse-gated synfire chain to propagate graded information. We called these circuits synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded information can rapidly cascade through a neural circuit, and show a correspondence between this type of transfer and a mean-field model in which gating pulses overlap in time. We show that SGSCs are robust in the presence of variability in population size, pulse timing and synaptic strength. Finally, we demonstrate the computational capabilities of SGSC-based information coding by implementing a self-contained, spike-based, modular neural circuit that is triggered by streaming input, processes the input, then makes a decision based on the processed information and shuts itself down.     

A hybrid neural network of addressable and content-addressable memory

We investigate the memory structure and retrieval of the brain and propose a hybrid neural network of addressable and content-addressable memory which is a special database model and can memorize and retrieve any piece of information (a binary pattern) both addressably and content-addressably. The architecture of this hybrid neural network is hierarchical and takes the form of a tree of slabs which consist of binary neurons with the same array. Simplex memory neural networks are considered as the slabs of basic memory units, being distributed on the terminal vertexes of the tree. It is shown by theoretical analysis that the hybrid neural network is able to be constructed with Hebbian and competitive learning rules, and some other important characteristics of its learning and memory behavior are also consistent with those of the brain. Moreover, we demonstrate the hybrid neural network on a set of ten binary numeral patters     

Cell assembly dynamics in detailed and abstract attractor models of cortical associative memory

Summary During the last few decades we have seen a convergence among ideas and hypotheses regarding functional principles underlying human memory. Hebb’s now more than fifty years old conjecture concerning synaptic plasticity and cell assemblies, formalized mathematically as attractor neural networks, has remained among the most viable and productive theoretical frameworks. It suggests plausible explanations for Gestalt aspects of active memory like perceptual completion, reconstruction and rivalry. We review the biological plausibility of these theories and discuss some critical issues concerning their associative memory functionality in the light of simulation studies of models with palimpsest memory properties. The focus is on memory properties and dynamics of networks modularized in terms of cortical minicolumns and hypercolumns. Biophysical compartmental models demonstrate attractor dynamics that support cell assembly operations with fast convergence and low firing rates. Using a scaling model we obtain reasonable relative connection densities and amplitudes. An abstract attractor network model reproduces systems level psychological phenomena seen in human memory experiments as the Sternberg and von Restorff effects. We conclude that there is today considerable substance in Hebb’s theory of cell assemblies and its attractor network formulations, and that they have contributed to increasing our understanding of cortical associative memory function. The criticism raised with regard to biological and psychological plausibility as well as low storage capacity, slow retrieval etc has largely been disproved. Rather, this paradigm has gained further support from new experimental data as well as computational modeling.     

A neuromorphic architecture for object recognition and motion anticipation using burst-STDP

In this work we investigate the possibilities offered by a minimal framework of artificial spiking neurons to be deployed in silico. Here we introduce a hierarchical network architecture of spiking neurons which learns to recognize moving objects in a visual environment and determine the correct motor output for each object. These tasks are learned through both supervised and unsupervised spike timing dependent plasticity (STDP). STDP is responsible for the strengthening (or weakening) of synapses in relation to pre- and post-synaptic spike times and has been described as a Hebbian paradigm taking place both in vitro and in vivo. We utilize a variation of STDP learning, called burst-STDP, which is based on the notion that, since spikes are expensive in terms of energy consumption, then strong bursting activity carries more information than single (sparse) spikes. Furthermore, this learning algorithm takes advantage of homeostatic renormalization, which has been hypothesized to promote memory consolidation during NREM sleep. Using this learning rule, we design a spiking neural network architecture capable of object recognition, motion detection, attention towards important objects, and motor control outputs. We demonstrate the abilities of our design in a simple environment with distractor objects, multiple objects moving concurrently, and in the presence of noise. Most importantly, we show how this neural network is capable of performing these tasks using a simple leaky-integrate-and-fire (LIF) neuron model with binary synapses, making it fully compatible with state-of-the-art digital neuromorphic hardware designs. As such, the building blocks and learning rules presented in this paper appear promising for scalable fully neuromorphic systems to be implemented in hardware chips.     

Balanced input allows optimal encoding in a stochastic binary neural network model: an analytical study

Recent neurophysiological experiments have demonstrated a remarkable effect of attention on the underlying neural activity that suggests for the first time that information encoding is indeed actively influenced by attention. Single cell recordings show that attention reduces both the neural variability and correlations in the attended condition with respect to the non-attended one. This reduction of variability and redundancy enhances the information associated with the detection and further processing of the attended stimulus. Beyond the attentional paradigm, the local activity in a neural circuit can be modulated in a number of ways, leading to the general question of understanding how the activity of such circuits is sensitive to these relatively small modulations. Here, using an analytically tractable neural network model, we demonstrate how this enhancement of information emerges when excitatory and inhibitory synaptic currents are balanced. In particular, we show that the network encoding sensitivity--as measured by the Fisher information--is maximized at the exact balance. Furthermore, we find a similar result for a more realistic spiking neural network model. As the regime of balanced inputs has been experimentally observed, these results suggest that this regime is functionally important from an information encoding standpoint.     

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.     

Cortical Plasticity Induced by Spike-Triggered Microstimulation in Primate Somatosensory Cortex

Electrical stimulation of the nervous system for therapeutic purposes, such as deep brain stimulation in the treatment of Parkinson’s disease, has been used for decades. Recently, increased attention has focused on using microstimulation to restore functions as diverse as somatosensation and memory. However, how microstimulation changes the neural substrate is still not fully understood. Microstimulation may cause cortical changes that could either compete with or complement natural neural processes, and could result in neuroplastic changes rendering the region dysfunctional or even epileptic. As part of our efforts to produce neuroprosthetic devices and to further study the effects of microstimulation on the cortex, we stimulated and recorded from microelectrode arrays in the hand area of the primary somatosensory cortex (area 1) in two awake macaque monkeys. We applied a simple neuroprosthetic microstimulation protocol to a pair of electrodes in the area 1 array, using either random pulses or pulses time-locked to the recorded spiking activity of a reference neuron. This setup was replicated using a computer model of the thalamocortical system, which consisted of 1980 spiking neurons distributed among six cortical layers and two thalamic nuclei. Experimentally, we found that spike-triggered microstimulation induced cortical plasticity, as shown by increased unit-pair mutual information, while random microstimulation did not. In addition, there was an increased response to touch following spike-triggered microstimulation, along with decreased neural variability. The computer model successfully reproduced both qualitative and quantitative aspects of the experimental findings. The physiological findings of this study suggest that even simple microstimulation protocols can be used to increase somatosensory information flow.     

Computational Modeling of Seizure Dynamics Using Coupled Neuronal Networks: Factors Shaping Epileptiform Activity

Epileptic seizure dynamics span multiple scales in space and time. Understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. Mathematical models have been developed to reproduce seizure dynamics across scales ranging from the single neuron to the neural population. In this study, we develop a network model of spiking neurons and systematically investigate the conditions, under which the network displays the emergent dynamic behaviors known from the Epileptor, which is a well-investigated abstract model of epileptic neural activity. This approach allows us to study the biophysical parameters and variables leading to epileptiform discharges at cellular and network levels. Our network model is composed of two neuronal populations, characterized by fast excitatory bursting neurons and regular spiking inhibitory neurons, embedded in a common extracellular environment represented by a slow variable. By systematically analyzing the parameter landscape offered by the simulation framework, we reproduce typical sequences of neural activity observed during status epilepticus. We find that exogenous fluctuations from extracellular environment and electro-tonic couplings play a major role in the progression of the seizure, which supports previous studies and further validates our model. We also investigate the influence of chemical synaptic coupling in the generation of spontaneous seizure-like events. Our results argue towards a temporal shift of typical spike waves with fast discharges as synaptic strengths are varied. We demonstrate that spike waves, including interictal spikes, are generated primarily by inhibitory neurons, whereas fast discharges during the wave part are due to excitatory neurons. Simulated traces are compared with in vivo experimental data from rodents at different stages of the disorder. We draw the conclusion that slow variations of global excitability, due to exogenous fluctuations from extracellular environment, and gap junction communication push the system into paroxysmal regimes. We discuss potential mechanisms underlying such machinery and the relevance of our approach, supporting previous detailed modeling studies and reflecting on the limitations of our methodology.     

A neural circuit model of emotional learning using two pathways with different granularity and speed of information processing

We propose a neural circuit model of emotional learning using two pathways with different granularity and speed of information processing. In order to derive a precise time process, we utilized a spiking model neuron proposed by Izhikevich and spike-timing-dependent synaptic plasticity (STDP) of both excitatory and inhibitory synapses. We conducted computer simulations to evaluate the proposed model. We demonstrate some aspects of emotional learning from the perspective of the time process. The agreement of the results with the previous behavioral experiments suggests that the structure and learning process of the proposed model are appropriate.     

Reactivation in Working Memory: An Attractor Network Model of Free Recall

The dynamic nature of human working memory, the general-purpose system for processing continuous input, while keeping no longer externally available information active in the background, is well captured in immediate free recall of supraspan word-lists. Free recall tasks produce several benchmark memory phenomena, like the U-shaped serial position curve, reflecting enhanced memory for early and late list items. To account for empirical data, including primacy and recency as well as contiguity effects, we propose here a neurobiologically based neural network model that unifies short- and long-term forms of memory and challenges both the standard view of working memory as persistent activity and dual-store accounts of free recall. Rapidly expressed and volatile synaptic plasticity, modulated intrinsic excitability, and spike-frequency adaptation are suggested as key cellular mechanisms underlying working memory encoding, reactivation and recall. Recent findings on the synaptic and molecular mechanisms behind early LTP and on spiking activity during delayed-match-to-sample tasks support this view.