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Dynamic analysis of Hopfield neural network with sigmoid-type activation function

PHYSICA SCRIPTA 2025年第3期100卷 035223-035223页

作者： Zhang, Yunzhen Yin, Xiaowei Chen, Chengjie Zhao, Guangzhe You, Yunkai Tao, Shaohua Xiong, Weihua Xuchang Univ Sch Informat Engn Xuchang 461000 Peoples R China Jilin Inst Chem Technol Sch Informat & Control Engn Jilin 132022 Peoples R China Jiangsu Univ Technol Sch Elect & Informat Engn Changzhou 213001 Peoples R China

The sigmoid function is a continuous and smooth nonlinear function, often called a logic function that exhibits an 'S'-shaped characteristic similar to the Tanh function, yet possesses a distinct positive threshold property that differentiates it from the Tanh function. To elaborate on the special dynamic behaviors induced by such functions, this paper proposes a sigmoid-type Hopfield neural network (sigmoid-HNN) using a sigmoid function as the activation function. With the sigmoid-HNN model, the boundedness is proven using the Lyapunov method, and the stability of the equilibrium point is clarified exhaustively. The complex kinetic behaviors influenced by the synaptic weights and external current stimulation are analyzed using two-parameter bifurcation diagrams, phase diagrams, bifurcation diagrams, and Lyapunov exponential spectra. The results show that the bifurcation behaviors of the sigmoid-HNN model exhibit remarkable similarity when adjusting the weight parameters and external stimuli;chaos crises frequently occur, and backward period-doubling bifurcation phenomena occur in both cases. In addition, PSIM was used to simulate an analog circuit to verify the response characteristics of the model. The simulation results are consistent with the experimental data, strongly confirming the feasibility of the system model at the physical level.

关键词： hopfield neural network sigmoid activation function complex dynamics analog circuit

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Classification of data on stacked autoencoder using modified sigmoid activation function

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2023年第1期44卷 1-18页

作者： Kumar, Arvind Sodhi, Sartaj Singh Comp Sci & Engn USICT GGSIPU Delhi India

A Neural Network is one of the techniques by which we classify data. In this paper, we have proposed an effectively stacked autoencoder with the help of a modified sigmoid activation function. We have made a two-layer stacked autoencoder with a modified sigmoid activation function. We have compared our autoencoder to the existing autoencoder technique. In the existing autoencoder technique, we generally use the logsigmoid activation function. But in multiple cases using this technique, we cannot achieve better results. In that case, we may use our technique for achieving better results. Our proposed autoencoder may achieve better results compared to this existing autoencoder technique. The reason behind this is that our modified sigmoid activation function gives more variations for different input values. We have tested our proposed autoencoder on the iris, glass, wine, ovarian, and digit image datasets for comparison propose. The existing autoencoder technique has achieved 96% accuracy on the iris, 91% accuracy on wine, 95.4% accuracy on ovarian, 96.3% accuracy on glass, and 98.7% accuracy on digit (image) dataset. Our proposed autoencoder has achieved 100% accuracy on the iris, wine, ovarian, and glass, and 99.4% accuracy on digit (image) datasets. For more verification of the effeteness of our proposed autoencoder, we have taken three more datasets. They are abalone, thyroid, and chemical datasets. Our proposed autoencoder has achieved 100% accuracy on the abalone and chemical, and 96% accuracy on thyroid datasets.

关键词： Autoencoder sigmoid activation function logsigmoid neural network classification stacked autoencoder

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10 GHz Optoelectronic Circuit With Variable sigmoid Shaped activation function for Photonic Neural Networks

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JOURNAL OF LIGHTWAVE TECHNOLOGY 2024年第22期42卷 7977-7988页

作者： Chrysostomidis, Themistoklis Roumpos, Ioannis Moralis-Pegios, Miltiadis Lambrecht, Joris CailLaud, Christophe Yin, Xin Pleros, Nikos Vyrsokinos, Konstantinos Aristotle Univ Thessaloniki Dept Phys Thessaloniki 54124 Greece Aristotle Univ Thessaloniki Ctr Interdisciplinary Res & Innovat Thessaloniki 54124 Greece Aristotle Univ Thessaloniki Dept Informat Thessaloniki Greece Aristotle Univ Thessaloniki Ctr Interdisciplinary Res & Innovat Thessaloniki Greece Univ Ghent IMEC Dept Informat Technol IDLab B-9052 Ghent Belgium Thales Res & Technol Joint Lab Nokia BellLabs V Lab 3 F-91767 Palaiseau France CEA LETI F-91767 Palaiseau France

This paper introduces an opto-electronic and opto-electronic-opto circuit capable of generating a sigmoid shaped non-linear activation function (NLAF) for photonic neural networks. The main element of the circuit is a III-V photonic integrated circuit featuring an O-band semiconductor optical amplifier (SOA) co-integrated with a uni-travelling carrier photodiode, connected to a Bi-CMOS transimpedance amplifier (TIA). Experimental results from two 10 GHz 32-level mirrored step-wise pulse sequences, and three 30-level random peak power pulse sequences, validate the proposed concept, showcasing the variation of the achieved sigmoid NLAF from nearly stepwise to linear by appropriately varying the SOA current, injection of an external CW signal and proper configuration of the TIA settings.

关键词： Semiconductor optical amplifiers Optical amplifiers Photonics Optical attenuators Stimulated emission Integrated optics Optical fibers Non-linear activation function optical neural networks opto-electronic photonic neural networks sigmoid activation function

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Voltage-to-Voltage sigmoid Neuron activation function Design for Artificial Neural Networks 13

Voltage-to-Voltage Sigmoid Neuron Activation Function Design...

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13th Latin America Symposium on Circuits and System (LASCAS)

作者： Moposita, Tatiana Trojman, Lionel Crupi, Felice Lanuzza, Marco Vladimirescu, Andrei Sorbonne Univ ISEP Inst Super Elect Paris Paris France Univ Calabria DIMES Arcavacata Di Rende Italy

ISBN: (纸本)9781665420082

An Artificial Neural Network (ANN) involves a complex network of interconnected nodes called artificial neurons (AN);the AN sums N weighted inputs and send thought the result to a non-linear activation function (AF). In this work, a modified version of the sigmoid activation function is proposed. To obtain a voltage-to-voltage (V-V) transfer function required by an specific ANN. The proposed solution uses a pseudo-differential pair configuration at the input as voltage to current converter. The proposed circuit is designed using a commercial PDK in 180nm (TSMC) and is simulated in Virtuoso (Cadence). This specific design enable to obtain the desired steepness of the sigmoid function by means of the proper transistor sizing. Simulation results of our specific design show that we can reach an average relative error of only 1.09 % for steepness of 1 as compared to the exact mathematical function, and a power consumption of 6.77 mu W for steepness of 10.

关键词： Artificial Neural Network non-linear transfer function sigmoid activation function pseudo differential pair

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Artificial Neural Network Modeling of Ti-6Al-4V Alloys to Correlate Their Microstructure and Mechanical Properties

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MATERIALS 2025年第5期18卷 1099-1099页

作者： Maurya, Anoop Kumar Narayana, Pasupuleti Lakshmi Yeom, Jong-Taek Hong, Jae-Keun Reddy, Nagireddy Gari Subba Korea Inst Mat Sci Lightweight Mat Res Div Chang Won 51508 South Korea Gyeongsang Natl Univ Engn Res Inst Sch Mat Sci & Engn Virtual Mat Lab Jinju 52828 South Korea

The heat treatment process of Ti-6Al-4V alloy alters its microstructural features such as prior-beta grain size, Widmanstatten alpha lath thickness, Widmanstatten alpha volume fraction, grain boundary alpha lath thickness, total alpha volume fraction, alpha colony size, and alpha platelet length. These microstructural features affect the material's mechanical properties (UTS, YS, and %EL). The relationship between microstructural features and mechanical properties is very complex and non-linear. To understand these relationships, we developed an artificial neural network (ANN) model using experimental datasets. The microstructural features are used as input parameters to feed the model and the mechanical properties (UTS, YS, and %EL) are the output parameters. The influence of microstructural parameters was investigated by the index of relative importance (IRI). The mean edge length, colony scale factor, alpha lath thickness, and volume fraction affect UTS more. The model-predicted results show that the UTS of Ti-6Al-4V decreases with the increase in prior beta grain size, Widmanstatten alpha lath thickness, grain boundaries alpha thickness, colony scale factor, and UTS increases with mean edge length.

关键词： artificial neural network (ANN) mechanical properties of Ti-6Al-4V alloy index of relative importance weight distribution sigmoid activation function

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Universal Approximation Using Probabilistic Neural Networks with sigmoid activation functions

Universal Approximation Using Probabilistic Neural Networks ...

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International Conference on Advances in Engineering and Technology Research (ICAETR),

作者： Murugadoss, R. Ramakrishnan, M. Sathyabama Univ Dept Comp Sci & Engn Madras Tamil Nadu India Velammal Engn Coll Dept Informat Technol Madras Tamil Nadu India

ISBN: (纸本)9781479963935

In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functional can uniformly approximate any continuous function of n real variables with support in the unit hypercube;only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single bidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks. The daily registration has N cases that each of the well-known stimulus-answer couples represents. The objective of this work is to develop a function that allows finding the vector of entrance variables t to the vector of exit variables P. F is any function, in this case the electric power consumption. Their modeling with Artificial Neural Network (ANN) is Multi a Percept ron Layer (PMC). Another form of modeling it is using Interpolation Algorithms (AI).

关键词： FPGA Neural Networks sigmoid activation function Schematic Tools

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Modelling thermal characteristics of cocoa butter using a feed-forward artificial neural network based on multilayer perceptron

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INTERNATIONAL JOURNAL OF FOOD SCIENCE AND TECHNOLOGY 2024年第11期59卷 8520-8528页

作者： Rostami, Omid Saberi, Farzad Mohammadi, Amirreza Kamalirousta, Leila Rosell, Cristina M. Gasparre, Nicola Shahid Beheshti Univ Med Sci Fac Nutr Sci & Food Technol Dept Food Sci & Technol Tehran 0098021 Iran Islamic Azad Univ Dept Food Sci & Technol Sci & Res Branch Tehran 0098021 Iran Zarkam Co Dept Res & Dev Zar Ind & Res Grp Hashtgerd 0098026 Iran Shiraz Univ Sch Agr Dept Food Sci & Technol Shiraz 0098071 Iran Univ Manitoba Dept Food & Human Nutr Sci Winnipeg MB R3T 2N2 Canada CSIC Inst Agrochem & Food Technol Valencia 46980 Spain

Cocoa butter is the most important ingredient of chocolate, which determines its melting behaviour. Variations in the melting characteristics of cocoa butter can profoundly affect the performance and suitability for their industrial utilisation. Over time, researchers have been attempting to establish a logical relationship between cocoa butter's unique thermal properties and the amount of saturated to unsaturated fatty acids in mono, di and triglycerides, and fatty acids (as major components), and free fatty acids, soap, primary oxidation products, minerals, moisture, phospholipids, tocopherols, unsaponifiable matters and metals (as minor components) found in cocoa butter. In this research, the thermal behaviours of thirteen samples of cocoa butter with different origins were investigated using isothermal differential scanning calorimetry. The cocoa butters starting temperature of crystallisation, temperature of maximum heat release, temperature of completed crystallisation and the enthalpy of heat release during recrystallisation were evaluated. In addition, the chemical composition (moisture, acidity, peroxide, minerals and soap content), fatty acid and triacylglycerol composition were used to establish an MLP-ANN with fourteen input neurons connected by two flexible, sigmoid activation function layers. The back-propagation was used to train the artificial neural network (ANN) structure and optimise the error of prediction. The study showed that the MLP algorithm can predict the thermal behaviour of CB samples with trace error, regardless of plant growth and extract process condition. This research presents a pioneering use of multilayer perceptron feedforward artificial neural networks to predict cocoa butter's thermal characteristics, vital in chocolate production. By incorporating diverse compositional factors, it sheds light on enhancing cocoa butter crystallisation behaviour, advancing predictive modelling in the chocolate industry, and minimising formulatio

关键词： Cocoa butter DSC multilayer perceptron sigmoid activation function

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Fast generalization error bound of deep learning without scale invariance of activation functions

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NEURAL NETWORKS 2020年 129卷 344-358页

作者： Terada, Yoshikazu Hirose, Ryoma Osaka Univ Grad Sch Engn Sci 1-3 Machikaneyama Cho Toyonaka Osaka 5608531 Japan RIKEN Ctr Adv Intelligence Project AIP Chuo Ku 1-4-1 Nihonbashi Tokyo 1030027 Japan

In the theoretical analysis of deep learning, discovering which features of deep learning lead to good performance is an important task. Using the framework for analyzing the generalization error developed by Suzuki (2018), we derive a fast learning rate for deep neural networks with general activation functions. According to Suzuki (2018), scale invariance of the activation functions is essential to derive tight error bounds. While the rectified linear unit (ReLU;Nair and Hinton, 2010) satisfies scale invariance, the other famous activation functions, such as the sigmoid, the hyperbolic tangent functions, and the exponential linear unit (ELU;Clevert et al., 2016), do not satisfy this condition. The existing analysis indicates the possibility that deep learning with non scale invariant activations may have a slower convergence rate of O(1/root n) whereas with scale invariant activation functions it can reach a faster rate. In this paper, without scale invariance of activation functions, we derive the tight generalization error bound which is essentially the same as that of Suzuki (2018). From this result, at least in the framework of Suzuki (2018), we show that scale invariance of the activation functions is not essential to obtain a fast rate of convergence. We also conclude that the theoretical framework proposed by Suzuki (2018) can be widely applied to the analysis of deep learning with general activation functions. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Deep learning Fast learning rate Empirical risk minimizer sigmoid activation function Exponential linear unit

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Derivation of NARX models by expanding activation functions in neural networks

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IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING 2019年第8期14卷 1209-1218页

作者： Inaoka, Hidenori Kobayashi, Kozue Nebuya, Satoru Kumagai, Hiroshi Tsuruta, Harukazu Fukuoka, Yutaka Kitasato Univ Sch Allied Hlth Sci Dept Basic Med Sci & Clin Med Minami Ku 1-15-1 Kitasato Sagamihara Kanagawa Japan Kitasato Univ Sch Allied Hlth Sci Dept Med Engn & Technol Minami Ku 1-15-1 Kitasato Sagamihara Kanagawa Japan Kogakuin Univ Fac Engn Dept Elect Engn Shinjuku Ku Tokyo Japan

A method was developed to derive an NARX model from a neural network so that the usability of open-source libraries for network learning was combined with the NARX advantage of revealing the system structure. After the neural network model was trained on input and output data, the sigmoid activation functions were expanded into Taylor series. Candidate parameters in the NARX model were calculated from the connection weights in the neural network and coefficients in the series. The NARX model structure was determined by the extended least-squares (ELS) method and the Bayesian information criterion (BIC). Correct NARX models were successfully detected in computer simulations and an experiment. The developed method can be used for any activation functions, including the sigmoid function, if they are expanded into Taylor series. (c) 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

关键词： nonlinear system identification neural network sigmoid activation function Bayesian information criterion Taylor series expansion extended least square method

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Compact yet efficient hardware implementation of artificial neural networks with customized topology

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EXPERT SYSTEMS WITH APPLICATIONS 2012年第10期39卷 9191-9206页

作者： Nedjah, Nadia da Silva, Rodrigo Martins Mourelle, Luiza de Macedo Univ Estado Rio De Janeiro Dept Elect Engn & Telecommun Fac Engn Rio De Janeiro Brazil Univ Estado Rio De Janeiro Fac Engn Dept Syst Engn & Computat Rio De Janeiro Brazil

There are several neural network implementations using either software, hardware-based or a hardware/software co-design. This work proposes a hardware architecture to implement an artificial neural network (ANN), whose topology is the multilayer perceptron (MLP). In this paper, we explore the parallelism of neural networks and allow on-the-fly changes of the number of inputs, number of layers and number of neurons per layer of the net. This reconfigurability characteristic permits that any application of ANNs may be implemented using the proposed hardware. In order to reduce the processing time that is spent in arithmetic computation, a real number is represented using a fraction of integers. In this way, the arithmetic is limited to integer operations, performed by fast combinational circuits. A simple state machine is required to control sums and products of fractions. sigmoid is used as the activation function in the proposed implementation. It is approximated by polynomials, whose underlying computation requires only sums and products. A theorem is introduced and proven so as to cover the arithmetic strategy of the computation of the activation function. Thus, the arithmetic circuitry used to implement the neuron weighted sum is reused for computing the sigmoid. This resource sharing decreased drastically the total area of the system. After modeling and simulation for functionality validation, the proposed architecture synthesized using reconfigurable hardware. The results are promising. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Artificial neural networks Hardware for neural networks Topology sigmoid activation function Parallelism FPGA

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