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A Comparative Study Between E-Neurons Mathematical Model and Circuit Model Mojtaba Daliri, Pietro Maris Ferreira, Geoffroy Klisnick, A

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A Comparative Study Between E-Neurons Mathematical Model and Circuit Model Mojtaba Daliri, Pietro Maris Ferreira, Geoffroy Klisnick, A A Comparative Study Between E-Neurons Mathematical model and Circuit model Mojtaba Daliri, Pietro Maris Ferreira, Geoffroy Klisnick, A. Benlarbi-Delai To cite this version: Mojtaba Daliri, Pietro Maris Ferreira, Geoffroy Klisnick, A. Benlarbi-Delai. A Comparative Study Between E-Neurons Mathematical model and Circuit model. IET Circuits, Devices & Systems, Insti- tution of Engineering and Technology, 2021, 10.1049/cds2.12017. hal-02948300 HAL Id: hal-02948300 https://hal.archives-ouvertes.fr/hal-02948300 Submitted on 24 Feb 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Copyright Received: 6 July 2020 Revised: 28 August 2020 Accepted: 15 September 2020 IET Circuits, Devices & Systems DOI: 10.1049/cds2.12017 ORIGINAL RESEARCH- PAPER- - A comparative study between E‐neurons mathematical model and circuit model M. Daliri1 | Pietro M. Ferreira2,3 | G. Klisnick2,3 | A. Benlarbi‐Delai2,3 1Department of Electrical Engineering, Imam Reza Abstract International University, Mashhad, Islamic Republic of Iran The basic concepts and techniques involved in the development and analysis of math- ematical models for individual neurons are reviewed. A spiking neuron model uses dif- 2Université Paris‐Saclay, CentraleSupélec, CNRS, Lab. de Génie Electrique et Electronique de Paris, ferential equations to represent various neuronal activities that have more compatibility Gif‐sur‐Yvette, France with circuit criteria and are chosen for developing a comparative study with circuit 3Sorbonne Université, CNRS, Lab. de Génie models. For this comparison, a new fully differential neuron that uses the fully differential Electrique et Electronique de Paris, Paris, France aspects to reach more balanced differential equations to mathematical model is presented. This comparative study of the circuit model and a neuron mathematical model provides a Correspondence quantitative understanding of the challenges between mathematical models and micro- M. Daliri, Department of Electrical Engineering, electronic circuit design criteria. Imam Reza International University, Mashhad, Islamic Republic of Iran. Email: [email protected] 1 | INTRODUCTION Choosing a special spiking neuron model for implementing different types of neurons has a significant impact on Spiking neurons are the most plausible models of biological increasing the design speed like the works have been done in neurons because they accurately mimic the natural mechanisms references [8,10]. of information processing and learning. Recently, extensive This appropriate mathematical model that is capable of research towards novel realizations of neuronal models and creating different kinds of neurons should have the flexibility computing paradigms as a complementary architecture to Von to produce different waveforms by only some simple variation Neumann systems has been done using electronic techniques to be compatible with circuit design criteria. such as CMOS chips [1–4]. These publications have demon- A spiking neuron model uses differential equations to strated that this technology is capable of impressive levels of represent various neuronal activities. Some of these activities interconnectivity and spike communication in neural‐inspired can lead to the generation of an action potential, which is the circuits. charge in electrical potential (voltage) associated with a neuron. The key challenge in achieving a complete neuronal network When a neuron reaches a certain threshold, it spikes, and the similar to the human body is to implement a variety of neurons in potential of the neuron resets. A popular simple neuron model electronic circuits to explore new paradigms for neuromorphic is proposed by reference [5]; a hybrid spiking neuron model is sensors and cortex neurons that are involved in brain‐sensory introduced in reference [11], and a number of spiking neuron perception. Most biologists agree with the classification of cor- models are discussed in reference [12]. A spiking model based tex neurons in six most fundamental classes of firing patterns on logistic function using an analytical approach is presented in observed in the mammalian neocortex [5]. The immediate ap- reference [13]. All of these models are developed for software‐ plications of such neurons are an artificial vision [6] and audition based computation and hardly could be used as a guideline for [7] by mimicking the retina and the cochlea, respectively. Many circuit design. efforts have been made to design and implement different types The mathematical model of reference [5] is supposed to be of neurons. However, fast‐spiking (FS) [8,9], low threshold‐ the base of the current comparative study. This selection is spiking (LTS) [10] neurons have been made so far. related to the ability of this model to produce different types of This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2021 The Authors. IET Circuits, Devices & Systems published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology. IET Circuits Devices Syst. 2021;15:175–182. wileyonlinelibrary.com/journal/cds2 - 175 176 - DALIRI ET AL. neurons with only changing the values of some constants. This 2. Computational efficiency: this factor shows the complexity feature can provide the right conditions to be used as a of a neuron model and can be classified into five categories reference for circuit design. Axon‐Hillock (AH) neuron is Very Low, Low, Medium, High and Very High. This factor considered as the base of neuron circuit implementation is related to the number of floating‐point operations needed because of more similarity differential circuit equations with to accomplish one millisecond (ms) of model simulation the equations of reference [5]. This comparative study between and the number of variables used in order to represent the the circuit analytical model and the mathematical model of neuron model (activation function). reference [5] provides a quantitative understanding of the challenges between mathematical models and microelectronic Various mathematical models for biological neurons have circuit design criteria. been developed to represent their biological activities. As it is To have a more symmetrical circuit equation to ones generally believed that neurons communicate with each other mentioned in reference [5] a refined new fully differential AH via action potentials, these models basically represent neuronal electronic neuron (e‐neuron) is presented for the first time. behaviour in terms of membrane potential and action poten- Circuit equations are extracted to be used in a comparative tial. Some most popular models are Hodgkin‐Huxley (HH), study with a mathematical model. integrate‐and‐fire (I&F), FitzHugh‐Nagumo (FHN), Morris‐ This new implementation of AH e‐neuron could double Lecar (ML), Wilson, Izhikevich, Hindmarsh‐Rose (HR) [14]. the output spikes with the same power budget and increase These neuron models represent some or all of the char- energy efficiency too. Doubling the output swing and miti- acteristics of the responses of real neurons. The exact gating the effects of temperature changes enables the power description of all these models is beyond the scope of this supply to be minimized and more power reduction could be article, but in a simple comparison (Table 1), the Integrate‐and‐ achieved. Fire model is the lowest model in consumption of computa- This paper is organized as follows. In Section 2 the required tional power; which it could be used in a simple simulation that information of neurons models such as the developed mathe- accuracy is not an important manner. While the HH model matical model of reference [5] is explained. In Section 3 the exhibit all neural behaviours, which could be used in applica- novel AH neuron model, reasons for choosing AH structure, tions where every single detail is needed, but this model re- and fully differential structure are explained. The proposed fully quires very huge computational power. Izhikevich model differential AH neuron and its simulation results are shown in exhibits most of the neural behaviours and does not require this section. The last part of this section is focussed on the new huge computational power, which it is the best model that proposed mathematical model of the fully differential neuron could be used in any simulation or implementation of spiking model. An adaptive comparison between neuron mathematical neural networks, for example hippocampus simulation, classi- model of reference [5] and the proposed model is presented in fication or solving engineering problems [14]. Section 4. A comparative study between the mathematical According to the given explanations, choosing a simple model and circuit model and certain issues related to developing mathematical model that can use the simplicity of Integrate‐ a mathematical model compatible with circuit design are given and‐Fire model and the accuracy of
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