A Scalable FPGA Architecture for Randomly Connected Networks of Hodgkin-Huxley Neurons

A lightweight data-driven spiking neuronal network model of Drosophila olfactory nervous system with dedicated hardware support

Data-driven spiking neuronal network (SNN) models enable in-silico analysis of the nervous system at the cellular and synaptic level. Therefore, they are a key tool for elucidating the information processing principles of the brain. While extensive research has focused on developing data-driven SNN models for mammalian brains, their complexity poses challenges in achieving precision. Network topology often relies on statistical inference, and the functions of specific brain regions and supporting neuronal activities remain unclear. Additionally, these models demand huge computing facilities and their simulation speed is considerably slower than real-time. Here, we propose a lightweight data-driven SNN model that strikes a balance between simplicity and reproducibility. The model is built using a qualitative modeling approach that can reproduce key dynamics of neuronal activity. We target the Drosophila olfactory nervous system, extracting its network topology from connectome data. The model was successfully implemented on a small entry-level field-programmable gate array and simulated the activity of a network in real-time. In addition, the model reproduced olfactory associative learning, the primary function of the olfactory system, and characteristic spiking activities of different neuron types. In sum, this paper propose a method for building data-driven SNN models from biological data. Our approach reproduces the function and neuronal activities of the nervous system and is lightweight, acceleratable with dedicated hardware, making it scalable to large-scale networks. Therefore, our approach is expected to play an important role in elucidating the brain's information processing at the cellular and synaptic level through an analysis-by-construction approach. In addition, it may be applicable to edge artificial intelligence systems in the future.

High-Matching and Low-Cost Realization of the FHN Neuron Model on Reconfigurable FPGA Board

The main objectives of neuromorphic engineering are the research, modeling, and implementation of neural functioning in the human brain. We provide a hardware solution that can replicate such a nature-inspired system by merging multiple scientific domains and is based on neural cell processes. This work provides a modified version of the original Fitz-Hugh Nagumo (FHN) neuron using a simple 2V term called Hybrid Piece-Wised Base-2 Model (HPWBM), which accurately reproduces numerous patterns of the original neuron model. With reduced terms, we suggest modifying the original nonlinear term to achieve high matching accuracy and little computing error. Time domain and phase portraits are used to validate the proposed model, which shows that it can reproduce all of the FHN model's properties with high accuracy and little mistake. We provide an effective digital hardware approach for large-scale neuron implementations based on resource-sharing and pipelining strategies. The Hardware Description Language (HDL) is used to construct the hardware on an FPGA as a proof of concept. The recommended model hardly uses 0.48 percent of the resources on a Virtex 4 FPGA board, according to the results of the hardware implementation. The circuit can run at a maximum frequency of 448.236 MHz, according to the static timing study.

Models Developed for Spiking Neural Networks

Emergence of deep neural networks (DNNs) has raised enormous attention towards artificial neural networks (ANNs) once again. They have become the state-of-the-art models and have won different machine learning challenges. Although these networks are inspired by the brain, they lack biological plausibility, and they have structural differences compared to the brain. Spiking neural networks (SNNs) have been around for a long time, and they have been investigated to understand the dynamics of the brain. However, their application in real-world and complicated machine learning tasks were limited. Recently, they have shown great potential in solving such tasks. Due to their energy efficiency and temporal dynamics there are many promises in their future development. In this work, we reviewed the structures and performances of SNNs on image classification tasks. The comparisons illustrate that these networks show great capabilities for more complicated problems. Furthermore, the simple learning rules developed for SNNs, such as STDP and R-STDP, can be a potential alternative to replace the backpropagation algorithm used in DNNs.•Different building blocks of spiking neural networks are explained in this work.•Developed models for SNNs are introduced based on their characteristics and building blocks.

Investigation on the Wilson Neuronal Model: Optimized Approximation and Digital Multiplierless Implementation

Neuromorphic engineering is an essential science field which incorporates the basic aspects of issues together such as: physics, mathematics, electronics, etc. The primary block in the Central Nervous System (CNS) is neurons that have functional roles such as: receiving, processing, and transmitting data in the brain. This paper presents Wilson Multiplierless Neuron (WMN) model which is a modified version of the original model. This model uses power-2 based functions, Look-Up Table (LUT) approach and shifters to apply a multiplierless digital realization leads to overhead costs reduction and increases in the final system frequency. The proposed model specifically follows the original neuron model in case of spiking patterns and also dynamical pathways. To validate the proposed model in digital hardware implementation, the FPGA board (Xilinx Virtex II XC2VP30) can be used. Hardware results show the increasing in the system frequency compared with the original model and other similar papers. Numerical results demonstrate that the proposed system speed-up is 210 MHz that is higher than the original one, 85 MHz. Additionally, the overall saving in FPGA resources for the proposed model is 96.86 % that is more than the original model, 95.13 %. From case study viewpoint for CNS consideration, a network consisting of Wilson neurons, synapses, and astrocytes have been considered to test the controlling effects on LTP and LTD processes for investigating the neuronal diseases (medical approaches) such as Epilepsy.

Neuromorphic Context-Dependent Learning Framework With Fault-Tolerant Spike Routing

Neuromorphic computing is a promising technology that realizes computation based on event-based spiking neural networks (SNNs). However, fault-tolerant on-chip learning remains a challenge in neuromorphic systems. This study presents the first scalable neuromorphic fault-tolerant context-dependent learning (FCL) hardware framework. We show how this system can learn associations between stimulation and response in two context-dependent learning tasks from experimental neuroscience, despite possible faults in the hardware nodes. Furthermore, we demonstrate how our novel fault-tolerant neuromorphic spike routing scheme can avoid multiple fault nodes successfully and can enhance the maximum throughput of the neuromorphic network by 0.9%-16.1% in comparison with previous studies. By utilizing the real-time computational capabilities and multiple-fault-tolerant property of the proposed system, the neuronal mechanisms underlying the spiking activities of neuromorphic networks can be readily explored. In addition, the proposed system can be applied in real-time learning and decision-making applications, brain-machine integration, and the investigation of brain cognition during learning.

FPGA Realization of Hodgkin-Huxley Neuronal Model

One of the appealing cases of the neuromorphic research area is the implementation of biological neural networks. The current study offers Multiplierless Hodgkin-Huxley Model (MHHM). This modified model may reproduce various spiking behaviors, like the biological HH neurons, with high accuracy. The presented modified model, in comparison to the original HH model, due to its exact similarity to the original model, has more top performances in the case of FPGA saving and more achievable frequency (speed-up). In this approach, the proposed model has a 69 % saving in FPGA resources and also the maximum frequency of 85 MHz that is more than other similar works. In this modification, all spiking behaviors of the original model have been generated with low error calculations. To validate the MHHM neuron, this proposed model has been implemented on digital hardware FPGA. This approach demonstrates that the original HH model and the proposed model have high similarity in terms of higher performance and digital hardware cost reduction.

Optimized Real-Time Biomimetic Neural Network on FPGA for Bio-hybridization

Neurological diseases can be studied by performing bio-hybrid experiments using a real-time biomimetic Spiking Neural Network (SNN) platform. The Hodgkin-Huxley model offers a set of equations including biophysical parameters which can serve as a base to represent different classes of neurons and affected cells. Also, connecting the artificial neurons to the biological cells would allow us to understand the effect of the SNN stimulation using different parameters on nerve cells. Thus, designing a real-time SNN could useful for the study of simulations of some part of the brain. Here, we present a different approach to optimize the Hodgkin-Huxley equations adapted for Field Programmable Gate Array (FPGA) implementation. The equations of the conductance have been unified to allow the use of same functions with different parameters for all ionic channels. The low resources and high-speed implementation also include features, such as synaptic noise using the Ornstein-Uhlenbeck process and different synapse receptors including AMPA, GABAa, GABAb, and NMDA receptors. The platform allows real-time modification of the neuron parameters and can output different cortical neuron families like Fast Spiking (FS), Regular Spiking (RS), Intrinsically Bursting (IB), and Low Threshold Spiking (LTS) neurons using a Digital to Analog Converter (DAC). Gaussian distribution of the synaptic noise highlights similarities with the biological noise. Also, cross-correlation between the implementation and the model shows strong correlations, and bifurcation analysis reproduces similar behavior compared to the original Hodgkin-Huxley model. The implementation of one core of calculation uses 3% of resources of the FPGA and computes in real-time 500 neurons with 25,000 synapses and synaptic noise which can be scaled up to 15,000 using all resources. This is the first step toward neuromorphic system which can be used for the simulation of bio-hybridization and for the study of neurological disorders or the advanced research on neuroprosthesis to regain lost function.

A Novel Nonlinear Function Evaluation Approach for Efficient FPGA Mapping of Neuron and Synaptic Plasticity Models

Efficient hardware realization of spiking neural networks is of great significance in a wide variety of applications, such as high-speed modeling and simulation of large-scale neural systems. Exploiting the key features of FPGAs, this paper presents a novel nonlinear function evaluation approach, based on an effective uniform piecewise linear segmentation method, to efficiently approximate the nonlinear terms of neuron and synaptic plasticity models targeting low-cost digital implementation. The proposed approach takes advantage of a high-speed and extremely simple segment address encoder unit regardless of the number of segments, and therefore is capable of accurately approximating a given nonlinear function with a large number of straight lines. In addition, this approach can be efficiently mapped into FPGAs with minimal hardware cost. To investigate the application of the proposed nonlinear function evaluation approach in low-cost neuromorphic circuit design, it is applied to four case studies: the Izhikevich and FitzHugh-Nagumo neuron models as 2-dimensional case studies, the Hindmarsh-Rose neuron model as a relatively complex 3-dimensional model containing two nonlinear terms, and a calcium-based synaptic plasticity model capable of producing various STDP curves. Simulation and FPGA synthesis results demonstrate that the hardware proposed for each case study is capable of producing various responses remarkably similar to the original model and significantly outperforms the previously published counterparts in terms of resource utilization and maximum clock frequency.