Approximation of sigmoid function and the derivative for hardware implementation of artificial neurons

Basterretxea, Koldo; Tarela, J. M.; Campo, I. del

doi:10.1049/ip-cds:20030607

Cited by 86 publications

(45 citation statements)

References 6 publications

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“…Our approach gives a better maximum error than both the first and second order approximation of [11]. [8] [ -8,8) N/A 0.0490 0.0247 Alippi et al [9] [ -8,8) N/A 0.0189 0.0087 Amin et al [10] [ [12] [-5,5] 5 0.0050 n/a Basterretxea et al (q=3) [13] [ -8,8) N/A 0.0222 0.0077 Tommiska (337) [14] [ -8,8) N/A 0.0039 0.0017 Tommiska (336) [14] [ -8,8) N/A 0.0077 0.0033 Tommiska (236) [14] [-4,4) N/A 0.0077 0.0040 Tommiska (235) [14] [ …”

Section: Resultsmentioning

confidence: 99%

“…The data representation and precision used in related research is shown in Table 1. [12] Single precision floating point Basterretxea et al [13] not discussed Tommiska-337 [14] 6…”

Section: Data Representation and Precision Requirementsmentioning

confidence: 99%

“…Furthermore, there is considerable variance within each category. For example, an A-Law companding technique is used in [8], a sum of steps approximation is used in [9], a multiplier-less piecewise approximation is presented in [10] and a recursive piecewise multiplier-less approximation is presented in [13]. An elementary function generator capable of multiple activation functions using a first and second order polynomial approximation is detailed in [11].…”

Section: Related Researchmentioning

confidence: 99%

See 2 more Smart Citations

An Efficient Hardware Architecture for a Neural Network Activation Function Generator

Larkin

Kinane

Mureşan

et al. 2006

Advances in Neural Networks - ISNN 2006

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Abstract. This paper proposes an efficient hardware architecture for a function generator suitable for an artificial neural network (ANN). A spline-based approximation function is designed that provides a good trade-off between accuracy and silicon area, whilst also being inherently scalable and adaptable for numerous activation functions. This has been achieved by using a minimax polynomial and through optimal placement of the approximating polynomials based on the results of a genetic algorithm. The approximation error of the proposed method compares favourably to all related research in this field. Efficient hardware multiplication circuitry is used in the implementation, which reduces the area overhead and increases the throughput.

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Section: Resultsmentioning

confidence: 99%

“…The data representation and precision used in related research is shown in Table 1. [12] Single precision floating point Basterretxea et al [13] not discussed Tommiska-337 [14] 6…”

Section: Data Representation and Precision Requirementsmentioning

confidence: 99%

Section: Related Researchmentioning

confidence: 99%

See 1 more Smart Citation

An Efficient Hardware Architecture for a Neural Network Activation Function Generator

Larkin

Kinane

Mureşan

et al. 2006

Advances in Neural Networks - ISNN 2006

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“…The implementation of the neuron's nonlinear activation function and their derivatives used by the learning algorithm, is often solved by a piecewise linear approximation [4,5,7,[17][18][19][20] . However, no implementation method has emerged as a universal solution.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The learning algorithm implementation remains the main difficulty when an autonomous system is planned regarding the running frequency. The implementation of the nonlinear activation function of neurons and its derivative used by the learning algorithm, is often solved by a linear approximation [4][5][6] but no implementation method has emerged as a universal solution [7] .…”

Section: Introductionmentioning

confidence: 99%

Digital Hardware Implementation of a Neural System Used for Nonlinear Adaptive Prediction

Faiedh¹,

Souani²,

Torki³

et al. 2006

J. of Computer Science

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Neural networks have been widely used for many applications in digital communications. They are able to give solutions to complex problems due to their nonlinear processing and their learning and generalization. Neural networks are one of the key technologies for the communication domain and accordingly a special effort may be expected to be paid to real time hardware implementation issues. In this study, it is proposed a digital hardware implementation of a neural system based on a multilayer perceptron (MLP). The neural system is used for the nonlinear adaptive prediction of nonstationary signals such as speech signals. The implemented architecture of the MLP is generated using a generic elementary neuron (EN). The polynomial approximation method is used to implement the sigmoidal activation function. The back-propagation algorithm is used to implant the prediction task. The circuit implementation architecture is detailed, for achieving real-time prediction for speech signals. The designed ASIC circuit includes a neural network block, an on-chip learning block and a memory used for storing the synaptic weights for updating.

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FPGA Neurocomputers

Omondi¹,

Rajapakse²,

Bajger³

FPGA Implementations of Neural Networks

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Approximation of sigmoid function and the derivative for hardware implementation of artificial neurons

Cited by 86 publications

References 6 publications

An Efficient Hardware Architecture for a Neural Network Activation Function Generator

An Efficient Hardware Architecture for a Neural Network Activation Function Generator

Digital Hardware Implementation of a Neural System Used for Nonlinear Adaptive Prediction

FPGA Neurocomputers

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