Integrate-and-fire Research Articles

Retina-Inspired Lightweight Spiking Convolutional Neural Network for Single-Image Dehazing.

Suspended particles in hazy medium absorb and scatter light, severely degrading imaging quality. Numerous single-image dehazing methods have been proposed to reconstruct clear images from hazy ones. However, most of them focus on increasing depth and width to improve dehazing performance, which incurs high computation and energy costs. To address this issue, we propose a lightweight spiking convolutional neural network (CNN) referred to as retina-inspired spiking CNN (RI-SCNN) for the reconstruction of hazy images. Unlike conventional dehazing techniques, first, our proposed network simulates the hierarchical structure and cellular function of the retina and devises five network modules to efficiently encode and extract image features through ON and OFF roads. Furthermore, the linear reconstruction mechanism is introduced to integrate the outputs from different roads, adaptively preserving regions with optimal details and constructing a comprehensive visual representation. Finally, by the transformed atmospheric scattering formula, our network can generate the dehazy image. Incorporating the microscale spiking mechanism of the brain, the entire network leverages discrete binary spike trains for information encoding and transmission, directly trained by spiking surrogate gradient learning on integrate-and-fire (IF) neurons. Experimental results demonstrate the superiority of the proposed RI-SCNN in terms of quantitative dehazing performance, qualitative visual effect, energy efficiency, and run speed. Considering its lightweight architecture with ultralow computation and energy costs, the network is encouraged to be deployed in the visual sensor hardware to improve overall performance.

Investigation of recessed‐source/drain SOI feedback FET‐based integrate and fire neuron circuit with compact model of threshold switching devices

AbstractIn this article, the investigation of recessed‐source/drain (Re‐S/D) SOI feedback FET (FBFET)‐based integrate and fire (IF) neuron circuit parameters is presented using a threshold switching device compact model. FBFETs offer high ION and low SS with minimal power consumption, operating efficiently at lower voltages and currents than conventional MOSFETs. Utilizing ION/IOFF ratio and threshold voltage limits (Vt2/Vt1) of the device, a model is developed to mimic hysteresis characteristics, which is then used to implement an IF neuron circuit. Our findings show that altering the Re‐S/D thickness between 0 and 50 nm enhances the ION of the device under study while decreasing hysteresis width. We detected a significant increase in output spike frequency of 46.8% and 65.14% for input current pulse amplitudes of 5 and 20 nA, respectively. Furthermore, increasing the Re‐S/D thickness from 0 to 50 nm led to a significant 29.97% enhancement in spike amplitude. In addition, when using input current pulse amplitudes of 5 and 20 nA, we saw energy savings per spike of 3.36% and 12.7%, respectively. At the same time, there was an increase in power of 8.69% and 9.54%. These enhancements in performance metrics establish our proposed integrate and fire neuron circuit as a promising candidate for efficient neuromorphic system implementation.

Memristors-coupled neuron models with multiple firing patterns and homogeneous and heterogeneous multistability

Abstract Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons. In this paper, two distinct scenarios, i.e., an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse, are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh–Rose neuron model. Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns. The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors. Finally, the simulation circuit and DSP hardware implementation results validate the physical mechanism, as well as the reliability of the biological neuron model.

Nonlinearities and timescales in neural models of temporal interference stimulation.

In temporal interference (TI) stimulation, neuronal cells react to two interfering sinusoidal electric fields with a slightly different frequency ( , in the range of about 1-4 kHz, in the range of about 1-100 Hz). It has been previously observed that for the same input intensity, the neurons do not react to a purely sinusoidal signal at or . This study seeks a better understanding of the largely unknown mechanisms underlying TI neuromodulation. To this end, single-compartment models are used to simulate computationally the response of neurons to the sinusoidal and TI waveform. This study compares five different neuron models: Hodgkin-Huxley (HH), Frankenhaeuser-Huxley (FH), along with leaky, exponential, and adaptive-exponential integrate-and-fire (IF). It was found that IF models do not entirely reflect the experimental behavior while the HH and FH model did qualitatively replicate the observed neural responses. Changing the time constants and steady state values of the ion gates in the FH model alters the response to both the sinusoidal and TI signal, possibly reducing the firing threshold of the sinusoidal input below that of the TI input. The results show that in the modified (simplified) model, TI stimulation is not qualitatively impacted by nonlinearities in the current-voltage relation. In contrast, ion channels have a significant impact on the neuronal response. This paper offers insights into neuronal biophysics and computational models of TI stimulation.

Energy-efficient synthetic antiferromagnetic skyrmion-based artificial neuronal device

Magnetic skyrmions offer unique characteristics such as nanoscale size, particle-like behavior, topological stability, and low depinning current density. These properties make them promising candidates for next-generation spintronics-based memory and neuromorphic computing. However, one of their distinctive features is their tendency to deviate from the direction of the applied driving force that may lead to the skyrmion annihilation at the edge of nanotrack during skyrmion motion, known as the skyrmion Hall effect (SkHE). To overcome this problem, synthetic antiferromagnetic (SAF) skyrmions that having bilayer coupling effect allows them to follow a straight path by nullifying SkHE making them alternative for ferromagnetic (FM) counterpart. This study proposes an integrate-and-fire (IF) artificial neuron model based on SAF skyrmions with asymmetric wedge-shaped nanotrack having self-sustainability of skyrmion numbers at the device window. The model leverages inter-skyrmion repulsion to replicate the IF mechanism of biological neuron. The device threshold, determined by the maximum number of pinned skyrmions at the device window, can be adjusted by tuning the current density applied to the nanotrack. Neuronal spikes occur when initial skyrmion reaches the detection unit after surpassing the device window by the accumulation of repulsive force that result in reduction of the device’s contriving current results to design of high energy efficient for neuromorphic computing. Furthermore, work implements a binarized neuronal network accelerator using proposed IF neuron and SAF-SOT-MRAM based synaptic devices for national institute of standards and technology database image classification. The presented approach achieves significantly higher energy efficiency compared to existing technologies like SRAM and STT-MRAM, with improvements of 2.31x and 1.36x, respectively. The presented accelerator achieves 1.42x and 1.07x higher throughput efficiency per Watt as compared to conventional SRAM and STT-MRAM based designs.

Coupled Memristor Oscillators for Neuromorphic Locomotion Control: Modeling and Analysis.

The recent surge of interest in brain-inspired architectures along with the development of nonlinear dynamical electronic devices and circuits has enabled energy-efficient hardware realizations of several important neurobiological systems and features. Central pattern generator (CPG) is one such neural system underlying the control of various rhythmic motor behaviors in animals. A CPG can produce spontaneous coordinated rhythmic output signals without any feedback mechanism, ideally realizable by a system of coupled oscillators. Bio-inspired robotics aims to use this approach to control the limb movement for synchronized locomotion. Hence, devising a compact and energy-efficient hardware platform to implement neuromorphic CPGs would be of great benefit for bio-inspired robotics. In this work, we demonstrate that four capacitively coupled vanadium dioxide (VO2) memristor-based oscillators can produce spatiotemporal patterns corresponding to the primary quadruped gaits. The phase relationships underlying the gait patterns are governed by four tunable bias voltages (or four coupling strengths) making the network programmable, reducing the complex problem of gait selection and dynamic interleg coordination to the choice of four control parameters. To this end, we first introduce a dynamical model for the VO2 memristive nanodevice, then perform analytical and bifurcation analysis of a single oscillator, and finally demonstrate the dynamics of coupled oscillators through extensive numerical simulations. We also show that adopting the presented model for a VO2 memristor reveals a striking resemblance between VO2 memristor oscillators and conductance-based biological neuron models such as the Morris-Lecar (ML) model. This can inspire and guide further research on implementation of neuromorphic memristor circuits that emulate neurobiological phenomena.

Thermodynamic analog of integrate-and-fire neuronal networks by maximum entropy modelling

Recent results have evidenced that spontaneous brain activity signals are organized in bursts with scale free features and long-range spatio-temporal correlations. These observations have stimulated a theoretical interpretation of results inspired in critical phenomena. In particular, relying on maximum entropy arguments, certain aspects of time-averaged experimental neuronal data have been recently described using Ising-like models, allowing the study of neuronal networks under an analogous thermodynamical framework. This method has been so far applied to a variety of experimental datasets, but never to a biologically inspired neuronal network with short and long-term plasticity. Here, we apply for the first time the Maximum Entropy method to an Integrate-and-fire (IF) model that can be tuned at criticality, offering a controlled setting for a systematic study of criticality and finite-size effects in spontaneous neuronal activity, as opposed to experiments. We consider generalized Ising Hamiltonians whose local magnetic fields and interaction parameters are assigned according to the average activity of single neurons and correlation functions between neurons of the IF networks in the critical state. We show that these Hamiltonians exhibit a spin glass phase for low temperatures, having mostly negative intrinsic fields and a bimodal distribution of interaction constants that tends to become unimodal for larger networks. Results evidence that the magnetization and the response functions exhibit the expected singular behavior near the critical point. Furthermore, we also found that networks with higher percentage of inhibitory neurons lead to Ising-like systems with reduced thermal fluctuations. Finally, considering only neuronal pairs associated with the largest correlation functions allows the study of larger system sizes.

Fluctuation-response relations for integrate-and-fire models with an absolute refractory period.

We study the problem of relating the spontaneous fluctuations of a stochastic integrate-and-fire (IF) model to the response of the instantaneous firing rate to time-dependent stimulation if the IF model is endowed with a non-vanishing refractory period and a finite (stereotypical) spike shape. This seemingly harmless addition to the model is shown to complicate the analysis put forward by Lindner Phys. Rev. Lett. (2022), i.e., the incorporation of the reset into the model equation, the Rice-like averaging of the stochastic differential equation, and the application of the Furutsu-Novikov theorem. We derive a still exact (although more complicated) fluctuation-response relation (FRR) for an IF model with refractory state and a white Gaussian background noise. We also briefly discuss an approximation for the case of a colored Gaussian noise and conclude with a summary and outlook on open problems.

Integrate-and-fire-type models of the lateral superior olive.

Neurons of the lateral superior olive (LSO) in the auditory brainstem play a fundamental role in binaural sound localization. Previous theoretical studies developed various types of neuronal models to study the physiological functions of the LSO. These models were usually tuned to a small set of physiological data with specific aims in mind. Therefore, it is unclear whether and how they can be related to each other, how widely applicable they are, and which model is suitable for what purposes. In this study, we address these questions for six different single-compartment integrate-and-fire (IF) type LSO models. The models are divided into two groups depending on their subthreshold responses: passive (linear) models with only the leak conductance and active (nonlinear) models with an additional low-voltage-activated potassium conductance that is prevalent among the auditory system. Each of these two groups is further subdivided into three subtypes according to the spike generation mechanism: one with simple threshold-crossing detection and voltage reset, one with threshold-crossing detection plus a current to mimic spike shapes, and one with a depolarizing exponential current for spiking. In our simulations, all six models were driven by identical synaptic inputs and calibrated with common criteria for binaural tuning. The resulting spike rates of the passive models were higher for intensive inputs and lower for temporally structured inputs than those of the active models, confirming the active function of the potassium current. Within each passive or active group, the simulated responses resembled each other, regardless of the spike generation types. These results, in combination with the analysis of computational costs, indicate that an active IF model is more suitable than a passive model for accurately reproducing temporal coding of LSO. The simulation of realistic spike shapes with an extended spiking mechanism added relatively small computational costs.

Strain-mediated multistate skyrmion for neuron devices.

Magnetic skyrmions are potential candidates for neuromorphic computing because of their inherent topological stability, low drive current density and nanoscale size. However, an artificial neuron device based on current-driven skyrmion motion cannot satisfy the requirement of energy efficiency and integration density due to hundreds of millions of interconnected neurons and synapses present in the deep networks. Here, we present a compact and energy efficient skyrmion-based artificial neuron consisting of ferromagnetic/heavy metal/ferroelectric layers which uses strain-mediated voltage manipulation of skyrmion states to mimic the Integrate-and-Fire (IF) function of biological neurons. By implementation of a spiking neural network (SNN) based on the proposed skyrmionic neuronal devices, it can achieve a high accuracy of 95.08% on a modified National Institute of Standards and Technology (MNIST) handwritten digit dataset, as well as a low power consumption of ∼46.8 fJ per epoch per neuron. The present work suggests a novel way to realize energy-efficient and high-density neuromorphic computing.

Dendritic filtering determines the frequency-dependent spike train correlations

Temporal correlation between neural discharge sequences induced by correlated synaptic inputs distributes widely in large population of neurons. However, how synaptic input frequency affects the spike train correlation remains largely unclear. To address this question, we use a pair of unconnected ball-and-stick (BS) model neurons of integrate-and-fire (IF) type to simulate the correlated spike trains when receiving the shared synaptic inputs with specific frequency at the distal dendrite. We derive the relevant simplified point (SP) neuron model analytically to well reproduce the BS model dynamics with suprathreshold inputs. We show that the output correlation is negatively correlated to input frequency, and this frequency-dependent correlation is modulated by dendritic morphologies and synaptic positions. Our results highlight the dependence of spike train correlation on input frequency and suggest that the dendritic filtering is a primary factor in shaping this correlation-frequency relationship using SP models and morphologically realistic model neurons. These predictions should be considered when understanding the neural population correlations. Data availabilityNo data was used for the research described in the article.

PATHFINDER: Designing Stimulus for Neuromodulation Through Data-Driven Inverse Estimation of Non-Linear Functions.

Using data-driven methods to design stimuli (e.g., electrical currents) which evoke desired neural responses in different neuron-types for applications in treating neural disorders. The problem of stimulus design is formulated as estimating the inverse of a many-to-one non-linear "forward" mapping, which takes as input the parameters of waveform and outputs the corresponding neural response, directly from the data. A novel optimization framework "PATHFINDER" is proposed in order to estimate the previously mentioned inverse mapping. A comparison with existing data-driven methods, namely conditional density estimation methods and numerical inversion of an estimated forward mapping is performed with different dataset sizes in toy examples and in detailed computational models of biological neurons. Using data from toy examples, as well as computational models of biological neurons, we show that PATHFINDER can outperform existing methods when the number of samples is low (i.e., a few hundred). Traditionally, the design of such stimuli has been model-driven and/or uses simplistic intuition, often aided by trial-and-error. Due to the inherent challenges in accurately modeling neural responses, as well as the sophistication of stimuli's effect on neural membrane potentials, data-driven approaches offer an attractive alternative. Our results suggest that PATHFINDER can be applied for optimizing stimulation parameters in experiments and treatments of neural disorders due to it requiring low number of data points.

BIOELECTRONICS RETINA MATHEMATICAL OPTIMIZATION-SIMULATION FOR INTEGRATE MODEL WITH BRAIN EVOLUTIONARY PRE-HYPOTHESES

Constrained evolutionary optimization algorithms for Integrate and Fire (IAF) classical retina model are programmed. The techniques applied are Pareto-Multiobjective (PMO) methods. Genetic Algorithm (GA) software is developed based on literature neuro-bioelectronics experimental dataset. Results take in handle subroutines functions and matrix-algebra method for setting constraints. Results show PMO 2D imaging charts and numerical values for IAF model, with optimal values for IS Input Current (IC) parameter. Bioelectronics applications for human vision improvements and extrapolation to life-origin pre-hypotheses are briefed.

An Adaptive Generalized Leaky Integrate-and-Fire Model for Hippocampal CA1 Pyramidal Neurons and Interneurons

Full-scale morphologically and biophysically realistic model networks, aiming at modeling multiple brain areas, provide an invaluable tool to make significant scientific advances from in-silico experiments on cognitive functions to digital twin implementations. Due to the current technical limitations of supercomputer systems in terms of computational power and memory requirements, these networks must be implemented using (at least) simplified neurons. A class of models which achieve a reasonable compromise between accuracy and computational efficiency is given by generalized leaky integrate-and fire models complemented by suitable initial and update conditions. However, we found that these models cannot reproduce the complex and highly variable firing dynamics exhibited by neurons in several brain regions, such as the hippocampus. In this work, we propose an adaptive generalized leaky integrate-and-fire model for hippocampal CA1 neurons and interneurons, in which the nonlinear nature of the firing dynamics is successfully reproduced by linear ordinary differential equations equipped with nonlinear and more realistic initial and update conditions after each spike event, which strictly depends on the external stimulation current. A mathematical analysis of the equilibria stability as well as the monotonicity properties of the analytical solution for the membrane potential allowed (i) to determine general constraints on model parameters, reducing the computational cost of an optimization procedure based on spike times in response to a set of constant currents injections; (ii) to identify additional constraints to quantitatively reproduce and predict the experimental traces from 85 neurons and interneurons in response to any stimulation protocol using constant and piecewise constant current injections. Finally, this approach allows to easily implement a procedure to create infinite copies of neurons with mathematically controlled firing properties, statistically indistinguishable from experiments, to better reproduce the full range and variability of the firing scenarios observed in a real network.

SPIDEN: deep Spiking Neural Networks for efficient image denoising.

In recent years, Deep Convolutional Neural Networks (DCNNs) have outreached the performance of classical algorithms for image restoration tasks. However, most of these methods are not suited for computational efficiency. In this work, we investigate Spiking Neural Networks (SNNs) for the specific and uncovered case of image denoising, with the goal of reaching the performance of conventional DCNN while reducing the computational cost. This task is challenging for two reasons. First, as denoising is a regression task, the network has to predict a continuous value (i.e., the noise amplitude) for each pixel of the image, with high precision. Moreover, state of the art results have been obtained with deep networks that are notably difficult to train in the spiking domain. To overcome these issues, we propose a formal analysis of the information conversion processing carried out by the Integrate and Fire (IF) spiking neurons and we formalize the trade-off between conversion error and activation sparsity in SNNs. We then propose, for the first time, an image denoising solution based on SNNs. The SNN networks are trained directly in the spike domain using surrogate gradient learning and backpropagation through time. Experimental results show that the proposed SNN provides a level of performance close to the state of the art with CNN based solutions. Specifically, our SNN achieves 30.18 dB of signal-to-noise ratio on the Set12 dataset, which is only 0.25 dB below the performance of the equivalent DCNN. Moreover we show that this performance can be achieved with low latency, i.e., using few timesteps, and with a significant level of sparsity. Finally, we analyze the energy consumption for different network latencies and network sizes. We show that the energy consumption of SNNs increases with longer latencies, making them more energy efficient compared to CNNs only for very small inference latencies. However, we also show that by increasing the network size, SNNs can provide competitive denoising performance while reducing the energy consumption by 20%.

A multiplier-free Rulkov neuron under memristive electromagnetic induction: Dynamics analysis, energy calculation, and circuit implementation

Establishing a realistic and multiplier-free implemented biological neuron model is significant for recognizing and understanding natural firing behaviors, as well as advancing the integration of neuromorphic circuits. Importantly, memristors play a crucial role in constructing memristive neuron and network models by simulating synapses or electromagnetic induction. However, existing models lack the consideration of initial-boosted extreme multistability and its associated energy analysis. To this end, we propose a multiplier-free implementation of the Rulkov neuron model and utilize a periodic memristor to represent the electromagnetic induction effect, thereby achieving the biomimetic modeling of the non-autonomous memristive Rulkov (mRulkov) neuron. First, theoretical analysis demonstrates that the stability distribution of the time-varying line equilibrium point is determined by both the parameters and the memristor’s initial condition. Furthermore, numerical simulations show that the mRulkov neuron can exhibit parameter-dependent local spiking, local hidden spiking, and periodic bursting firing behaviors. In addition, based on the periodic characteristics of the memductance function, the topological invariance of the mRulkov neuron is comprehensively proved. Therefore, local basins of attraction, bifurcation diagrams, and attractors related to extreme multistability can be boosted by switching the memristor’s initial condition. Significantly, the novel boosted extreme multistability is discovered in the Rulkov neuron for the first time. More importantly, the energy transition associated with the boosting dynamics is revealed through computing the Hamilton energy distribution. Finally, we develop a simulation circuit for the non-autonomous mRulkov neuron and confirm the effectiveness of the multiplier-free implementation and the accuracy of the numerical results through PSpice simulations.

COVID-19 classification based on a convolutional spiking neural network: A modified exponential IF neuron approach

The many fatalities due to this worldwide epidemic, referred to as COVID-19. A lack of resources has necessitated using scientifically validated procedures like computed tomography scans (CT scans) and chest X-rays to diagnose the illness early on COVID-19 and stop it from spreading across the population. Deep learning models have shown that these processors outperform traditional CPUs and GPUs regarding power and efficiency. Thanks to these processors, Spiking Neural Networks (SNNs) can be implemented more easily in real-world settings. The potential-based features used in the classifier are extracted from a DCSNN, built with a specific structure, and the corresponding proposed ME-IF neuron model. SNN neuron models are based on mathematical representations of biological neurons. Accordingly, have attempted to model SNNs based on a Modified Exponential Integrate-and-Fire (IF) neuron using a variety of deep learning packages. These methods have been used to distinguish between chest CT scan pictures that are COVID and those that are not. The proposed model surpasses several leading approaches with precision and an F1 score of 0.84. The drawback of DCSNN academics from all around the globe is still interested in learning more about how brains operate to develop computer algorithms.

Symbiosis of an artificial neural network and models of biological neurons: Training and testing

In this paper, we show the possibility of creating and identifying the features of an artificial neural network (ANN), which consists of mathematical models of biological neurons. The FitzHugh–Nagumo (FHN) system is used as a paradigmatic model demonstrating basic neuron activities. First, in order to reveal how biological neurons can be embedded within an ANN, we train the ANN with nonlinear neurons to solve a basic image recognition problem with an MNIST database; next, we describe how FHN systems can be introduced into this trained ANN. After all, we show that an ANN with FHN systems inside can be successfully trained with improved accuracy comparing with first trained ANN and then with inserted FHN systems. This approach opens up great opportunities in terms of the direction of analog neural networks, in which artificial neurons can be replaced by more appropriate biological ones.

Modeling Long-term Spike Frequency Adaptation in SA-I Afferent Neurons Using an Izhikevich-based Biological Neuron Model.

To develop a biomimetic artificial tactile sensing system capable of detecting sustained mechanical touch, we propose a novel biological neuron model (BNM) for slowly adapting type I (SA-I) afferent neurons. The proposed BNM is designed by modifying the Izhikevich model to incorporate long-term spike frequency adaptation. Adjusting the parameters renders the Izhikevich model describing various neuronal firing patterns. We also search for optimal parameter values for the proposed BNM to describe firing patterns of biological SA-I afferent neurons in response to sustained pressure longer than 1-second. We obtain the firing data of SA-I afferent neurons for six different mechanical pressure ranging from 0.1 mN to 300 mN from the ex-vivo experiment on SA-I afferent neurons in rodents. Upon finding the optimal parameters, we generate spike trains using the proposed BNM and compare the resulting spike trains to those of biological SA-I afferent neurons using the spike distance metrics. We verify that the proposed BNM can generate spike trains showing long-term adaptation, which is not achievable by other conventional models. Our new model may offer an essential function to artificial tactile sensing technology to perceive sustained mechanical touch.

Are SNNs Really More Energy-Efficient Than ANNs? an In-Depth Hardware-Aware Study

Spiking Neural Networks (SNNs) hold the promise of lower energy consumption in embedded hardware due to their spike-based computations compared to traditional Artificial Neural Networks (ANNs). The relative energy efficiency of this emerging technology compared to traditional digital hardware has not been fully explored. Many studies do not consider memory accesses, which account for an important fraction of the energy consumption, use naive ANN hardware implementations, or lack generality. In this paper, we compare the relative energy efficiency of classical digital implementations of ANNs with novel event-based SNN implementations based on variants of the Integrate and Fire (IF) model. We provide a theoretical upper bound on the relative energy efficiency of ANNs, by computing the maximum possible benefit from ANN data reuse and sparsity. We also use the Eyeriss ANN accelerator as a case study. We show that the simpler IF model is more energy-efficient than the Leaky IF and temporal continuous synapse models. Moreover, SNNs with the IF model can compete with efficient ANN implementations when there is a very high spike sparsity, i.e. between 0.15 and 1.38 spikes per synapse per inference, depending on the ANN implementation. Our analysis shows that hybrid ANN-SNN architectures, leveraging a SNN event-based approach in layers with high sparsity and ANN parallel processing for the others, are a promising new path for further energy savings.