Multiplierless Implementation of Noisy Izhikevich Neuron With Low-Cost Digital Design

Investigation on Vision System: Digital FPGA Implementation in Case of Retina Rod Cells

The development of prostheses and treatments for illnesses and recovery has recently been centered on hardware modeling for various delicate biological components, including the nervous system, brain, eyes, and heart. The retina, being the thinnest and deepest layer of the eye, is of particular interest. In this study, we employ the Nyquist-Based Approximation of Retina Rod Cell (NBAoRRC) approach, which has been adapted to utilize Look-Up Tables (LUTs) rather than original functions, to implement rod cells in the retina using cost-effective hardware. In modern mathematical models, numerous nonlinear functions are used to represent the activity of these cells. However, these nonlinear functions would require a substantial amount of hardware for direct implementation and may not meet the required speed constraints. The proposed method eliminates the need for multiplication functions and utilizes a fast, cost-effective rod cell device. Simulation results demonstrate the extent to which the proposed model aligns with the behavior of the primary rod cell model, particularly in terms of dynamic behavior. Based on the results of hardware implementation using the Field-Programmable Gate Arrays (FPGA) board Virtex-5, the proposed model is shown to be reliable, consume 30 percent less power than the primary model, and have reduced hardware resource requirements. Based on the results of hardware implementation using the reconfigurable FPGA board Virtex-5, the proposed model is reliable, uses 30% less power consumption than the primary model in the worth state of the set of approximation method, and has a reduced hardware resource requirement. In fact, using the proposed model, this reduction in the power consumption can be achieved. Finally, in this article, by using the LUT which is systematically sampled (Nyquist rate), we were able to remove all costly operators in terms of hardware (digital) realization and achieve very good results in the field of digital implementation in two scales of network and single neuron.

Spiking Neural Networks and Mathematical Models

Neural networks are applied in various scientific fields such as medicine, engineering, pharmacology, etc. Investigating operations of neural networks refers to estimating the relationship among single neurons and their contributions to the network as well. Hence, studying a single neuron is an essential process to solve complex brain problems. Mathematical models that simulate neurons and the way they transmit information are proven to be an indispensable tool for neuroscientists. Constructing appropriate mathematical models to simulate information transmission of a biological neural network is a challenge for researchers, as in the real world, identical neurons in terms of their electrophysiological characteristics in different brain regions do not contribute in the same way to information transmission within a neural network due to the intrinsic characteristics. This review highlights four mathematical, single-compartment models: Hodgkin-Huxley, Izhikevich, Leaky Integrate, and Fire and Morris-Lecar, and discusses comparison among them in terms of their biological plausibility, computational complexity, and applications, according to modern literature.

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.

A High-Accuracy and Energy-Efficient CORDIC Based Izhikevich Neuron With Error Suppression and Compensation

Bio-inspired neuron models are the key building blocks of brain-like neural networks for brain-science exploration and neuromorphic engineering applications. The efficient hardware design of bio-inspired neuron models is one of the challenges to implement brain-like neural networks, as the balancing of model accuracy, energy consumption and hardware cost is very challenging. This paper proposes a high-accuracy and energy-efficient Fast-Convergence COordinate Rotation DIgital Computer (FC-CORDIC) based Izhikevich neuron design. For ensuring the model accuracy, an error propagation model of the Izhikevich neuron is presented for systematic error analysis and effective error reduction. Parameter-Tuning Error Compensation (PTEC) method and Bitwidth-Extension Error Suppression (BEES) method are proposed to reduce the error of Izhikevich neuron design effectively. In addition, by utilizing the FC-CORDIC instead of conventional CORDIC for square calculation in the Izhikevich model, the redundant CORDIC iterations are removed and therefore, both the accumulated errors and required computation are effectively reduced, which significantly improve the accuracy and energy efficiency. An optimized fixed-point design of FC-CORDIC is also proposed to save hardware overhead while ensuring the accuracy. FPGA implementation results exhibit that the proposed Izhikevich neuron design can achieve high accuracy and energy efficiency with an acceptable hardware overhead, among the state-of-the-art designs.

Memristive Izhikevich Spiking Neuron Model and Its Application in Oscillatory Associative Memory

The Izhikevich (IZH) spiking neuron model can display spiking and bursting behaviors of neurons. Based on the switching property and bio-plausibility of the memristor, the memristive Izhikevich (MIZH) spiking neuron model is built. Firstly, the MIZH spiking model is introduced and used to generate 23 spiking patterns. We compare the 23 spiking patterns produced by the IZH and MIZH spiking models. Secondly, the MIZH spiking model actively reproduces various neuronal behaviors, including the excitatory cortical neurons, the inhibitory cortical neurons, and other cortical neurons. Finally, the collective dynamic activities of the MIZH neuronal network are performed, and the MIZH oscillatory network is constructed. Experimental results illustrate that the constructed MIZH spiking neuron model performs high firing frequency and good frequency adaptation. The model can easily simulate various spiking and bursting patterns of distinct neurons in the brain. The MIZH neuronal network realizes the synchronous and asynchronous collective behaviors. The MIZH oscillatory network can memorize and retrieve the information patterns correctly and efficiently with high retrieval accuracy.

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.

A Mathematical Model for the Signal of Death and Emergence of Mind Out of Brain in Izhikevich Neuron Model

AIM:

In this paper, using a mathematical model, we will show that for special exchanged photons, the Hamiltonian of a collection of neurons tends to a constant number and all activities is stopped. These photons could be called as the dead photons. To this aim, we use concepts of Bio-BIon in Izhikevich Neuron model.

METHODS:

In a neuron, there is a page of Dendrite, a page of axon’s terminals and a tube of Schwann cells, axon and Myelin Sheath that connects them. These two pages and tube form a Bio-Bion. In a Bio-Bion, exchanging photons and some charged particles between terminals of dendrite and terminals of axon leads to the oscillation of neurons and transferring information. This Bion produces the Hamiltonian, wave equation and action potential of Izhikevich Neuron model. Also, this Bion determines the type of dependency of parameters of Izhikevich model on temperature and frequency and obtains the exact shape of membrane capacitance, resting membrane potential and instantaneous threshold potential.

RESULTS:

Under some conditions, waves of neurons in this BIon join to each other and potential shrinks to a delta function. Consequently, total Hamiltonian of the system tends to a constant number and system of neuron act like a dead system. Finally, this model indicates that all neurons have the ability to produce similar waves and signals like waves of the mind.

CONCLUSION:

Generalizing this to biology, we can claim that neurons out of the brain can produce signals of minding and imaging and thus mind isn’t confined to the brain.

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.