A new solution to the hyperbolic tangent implementation in hardware: polynomial modeling of the fractional exponential part
The most difficult part of an artificial neural network to implement in hardware is the nonlinear activation function. For most implementations, the function used is the hyperbolic tangent. This function has received much attention in relation to hardware implementation. Nevertheless, there is no co...
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| Published in | Neural computing & applications Vol. 23; no. 2; pp. 363 - 369 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
London
Springer London
01.08.2013
Springer |
| Subjects | |
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| ISSN | 0941-0643 1433-3058 |
| DOI | 10.1007/s00521-012-0919-0 |
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| Abstract | The most difficult part of an artificial neural network to implement in hardware is the nonlinear activation function. For most implementations, the function used is the hyperbolic tangent. This function has received much attention in relation to hardware implementation. Nevertheless, there is no consensus regarding the best solution. In this paper, we propose a new approach by implementing the hyperbolic tangent in hardware with a polynomial modeling of the fractional exponential part. The results in the paper then demonstrate, through the use of an example, that this solution is faster than the CORDIC algorithm, but slower than the piecewise linear solution with the same error. The advantage over the piecewise linear approach is that it uses less memory. |
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| AbstractList | The most difficult part of an artificial neural network to implement in hardware is the nonlinear activation function. For most implementations, the function used is the hyperbolic tangent. This function has received much attention in relation to hardware implementation. Nevertheless, there is no consensus regarding the best solution. In this paper, we propose a new approach by implementing the hyperbolic tangent in hardware with a polynomial modeling of the fractional exponential part. The results in the paper then demonstrate, through the use of an example, that this solution is faster than the CORDIC algorithm, but slower than the piecewise linear solution with the same error. The advantage over the piecewise linear approach is that it uses less memory. |
| Author | Jardim, Ricardo Nascimento, Ivo Morgado-Dias, Fernando |
| Author_xml | – sequence: 1 givenname: Ivo surname: Nascimento fullname: Nascimento, Ivo organization: Competence Center of Exact Science and Engineering and Madeira Interactive Technologies Institute, University of Madeira – sequence: 2 givenname: Ricardo surname: Jardim fullname: Jardim, Ricardo organization: Competence Center of Exact Science and Engineering and Madeira Interactive Technologies Institute, University of Madeira – sequence: 3 givenname: Fernando surname: Morgado-Dias fullname: Morgado-Dias, Fernando email: morgado@uma.pt organization: Competence Center of Exact Science and Engineering and Madeira Interactive Technologies Institute, University of Madeira |
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| Keywords | Hardware description languages Gate arrays CORDIC Algorithms implemented in hardware Neural networks Polynomial Neural computation Description language Error estimation Memory Attention Non linear function Neural network Algorithm Modeling Implementation Array Activation function |
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| References_xml | – reference: MisraJSahaIArtificial neural networks in hardware: a survey of two decades of progressNeurocomputing20107423925510.1016/j.neucom.2010.03.021 – reference: Ayala JL, Lomena AG, López-Vallejo M, Fernández A (2002) Design of a pipelined hardware architecture for real-time neural network computations. IEEE midwest symposium on circuits and systems, USA – reference: Liao Y (2012) Neural networks in hardware: a survey. Available in the internet at http://wwwcsif.cs.ucdavis.edu/~liaoy/research/NNhardware.pdf. Accessed Feb 2012 – reference: Lindsey C, Lindblad T (1995) Survey of neural network hardware. In: Rogers SK, Ruck DW (eds) Applications and science of artificial neural networks, SPIE 2492, pp 1194–1205 – reference: Soria-OlivasEMartín-GuerreroJDCamps-VallsGSerrano-LópezAJCalpe-MaravillaJGómez-ChovaLA low-complexity fuzzy activation function for artificial neural networksIEEE Trans Neural Networks20031461576157910.1109/TNN.2003.820444 – reference: FerreiraPRibeiroPAntunesADiasFMA high bit resolution FPGA implementation of a FNN with a new algorithm for the activation functionNeurocomputing2007711–3717710.1016/j.neucom.2006.11.028 – reference: KwanHKSimple sigmoid-like activation function suitable for digital hardware implementationElectron Lett199228151379138010.1049/el:19920877 – reference: FrounchiJKarimianGKeshtkarAAn artificial neural network hardware for bladder cancerEur J Sci Res20092714655 – reference: Hassibi K (2000) Detecting payment card fraud with neural networks. In: Lisboa P, Edisbury B, Vellido A (eds) Business applications of neural networks, progress in neural processing 13. World Scientific, Singapore – reference: Ghariani M, Kharrat MW, Masmoudin N, Kamoun L (2004) Electronic implementation of a neural observer in FPGA technology: application to the control of electric vehicle. 16th international conference on microelectronics – reference: Leon M, Castro A, Ascenccio R (1999) An artificial neural network on a field programmable gate array as a virtual sensor. In: Proceedings of the third international workshop on design of mixed-mode integrated circuits and applications, Puerto Vallarta, Mexico, pp 114–117 – reference: Qian M (2006) Application of CORDIC algorithm to neural networks VLSI design. IMACS multiconference on computational engineering in systems applications – reference: Ferreira P, Ribeiro P, Antunes A, Dias FM (2004) Artificial neural networks processor—a hardware implementation using a FPGA. Field-programmable logic and its applications, Belgium, LNCS-3203 – reference: Andraka R (1998) A survey of CORDIC algorithms for FPGA based computers. In: Proceedings of the ACM/SIGDA 6th international symposium on FPGA, Monterey, CA, USA, pp 191–200 – reference: DurenRWMarksRJIIReynoldsPDTrumboMLReal-time neural network inversion on the SRC-6e reconfigurable computerIEEE Trans Neural Networks200718388990110.1109/TNN.2007.891679 – reference: Chen X, Wang G, Zhou W, Chang S, Sun S (2006) Efficient sigmoid function for neural networks based FPGA design. ICIC 2006, LNCS 4113. Springer, Berlin, Heidelberg, pp 672–677 – reference: Soares AM, Pinto JOP, Bose BK, Leite LC, da Silva LEB, Romero ME (2006) Field programmable gate array (FPGA) based neural network implementation of stator flux oriented vector control of induction motor drive. IEEE international conference on industrial technology – reference: Rosado-MuñozASoria-OlivasEGomez-ChovaLVila FrancésJAn IP core and GUI for implementing multilayer perceptron with a fuzzy activation function on configurable logic devicesJ Univers Comput Sci2008141016781694 – reference: DiasFMAntunesAMotaAMArtificial neural networks: a review of commercial hardwareEng Appl Artif Intell20041794595210.1016/j.engappai.2004.08.011 – reference: Stieglitz T, Meyer J (2006) Biomedical microdevices for neural implants, vol 16. 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| SubjectTerms | Applied sciences Artificial Intelligence Computational Biology/Bioinformatics Computational Science and Engineering Computer Science Computer science; control theory; systems Data Mining and Knowledge Discovery Exact sciences and technology Image Processing and Computer Vision Inference from stochastic processes; time series analysis Learning and adaptive systems Mathematics Original Article Probability and statistics Probability and Statistics in Computer Science Sciences and techniques of general use Statistics |
| Title | A new solution to the hyperbolic tangent implementation in hardware: polynomial modeling of the fractional exponential part |
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