Fast Characterization of Input-Output Behavior of Non-Charge-Based Logic Devices by Machine Learning
Abstract
:1. Introduction
2. Classification Methods
2.1. Neighborhood-Voronoi
2.2. Explicit Design Space Decomposition
2.3. Probability of Feasibility
2.4. Entropy
2.5. Classifier Description
3. Logic Device Description
- (a)
- Input field applied along the y-axis: corresponds to mode M1;
- (b)
- Input field applied along the z-axis: corresponds to mode M2 (BUF and INV).
4. Results
4.1. Input Field Along Y-Axis
4.2. Input Field Along Z-Axis
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Zhirnov, V.V.; Cavin, R.K.; Hutchby, J.A.; Bourianoff, G.I. Limits to binary logic switch scaling—A gedanken model. Proc. IEEE 2003, 91, 1934–1939. [Google Scholar] [CrossRef] [Green Version]
- Moore, G.E. Cramming More Components Onto Integrated Circuits. Proc. IEEE 1998, 86, 82–85. [Google Scholar] [CrossRef]
- Hutchby, J.A.; Bourianoff, G.I.; Zhirnov, V.V.; Brewer, J.E. Extending the road beyond CMOS. IEEE Circuits Devices Mag. 2002, 18, 28–41. [Google Scholar] [CrossRef]
- Theis, T.N.; Wong, H.S.P. The End of Moore’s Law: A New Beginning for Information Technology. Comput. Sci. Eng. 2017, 19, 41–50. [Google Scholar] [CrossRef]
- Wolf, S.A.; Lu, J.; Stan, M.R.; Chen, E.; Treger, D.M. The Promise of Nanomagnetics and Spintronics for Future Logic and Universal Memory. Proc. IEEE 2011, 98, 2155–2168. [Google Scholar] [CrossRef]
- Nikonov, D.E.; Young, I.A. Overview of Beyond-CMOS Devices and a Uniform Methodology for Their Benchmarking. Proc. IEEE 2013, 101, 2498–2533. [Google Scholar] [CrossRef] [Green Version]
- Bernstein, K.; Cavin, R.K.; Porod, W.; Seabaugh, A.; Welser, J. Device and Architecture Outlook for Beyond CMOS Switches. Proc. IEEE 2010, 98, 2169–2184. [Google Scholar] [CrossRef]
- Nikonov, D.; Bourianoff, G.I.; Ghani, T. Proposal of a Spin Torque Majority Gate Logic. IEEE ELectron Device Lett. 2011, 32, 1128–1130. [Google Scholar] [CrossRef] [Green Version]
- Manfrini, M.; Kim, J.-V.; Petit-Watelot, S.; Roy, W.V.; Lagae, L.; Chappert, C.; Devolder, T. Propagation of magnetic vortices using nanocontacts as tunable attractors. Nat. Nanotechnol. 2014, 9, 121–125. [Google Scholar] [CrossRef]
- Dutta, S.; Sou-Chi, C.; Nickvash, K.; Dmitri, N.; Manipatruni, S.; Young, I.A.; Naeemi, A. Non-volatile Clocked Spin Wave Interconnect for Beyond-CMOS Nanomagnet Pipelines. Sci. Rep. 2015, 5, 9861. [Google Scholar] [CrossRef]
- Pan, C.; Naeemi, A. An Expanded Benchmarking of Beyond-CMOS Devices Based on Boolean and Neuromorphic Representative Circuits. IEEE J. Explor. Solid State Comput. Devices Circuits 2017, 3, 101–110. [Google Scholar] [CrossRef]
- Cowburn, R.P.; Welland, M.E. Room Temperature Magnetic Quantum Cellular Automata. Science 2000, 287, 1466–1468. [Google Scholar] [CrossRef] [PubMed]
- Csaba, G.; Imre, A.; Bernstein, G.H.; Porod, W.; Metlushko, V. Nanocomputing by field-coupled nanomagnets. IEEE Trans. Nanotechnol. 2002, 1, 209–213. [Google Scholar] [CrossRef] [Green Version]
- Breitkreutz, S.; Kiermaier, J.; Eichwald, I.; Hildbrand, C.; Csaba, G.; Schmitt-Landsiedel, D.; Becherer, M. Experimental Demonstration of a 1-Bit Full Adder in Perpendicular Nanomagnetic Logic. IEEE Trans. Magn. 2013, 49, 4464–4467. [Google Scholar] [CrossRef]
- Zografos, O.; Manfrini, M.; Vaysset, A.; Sorée, B.; Ciubotaru, F.; Adelmann, C.; Lauwereins, R.; Raghavan, P.; Iuliana, P.R. Exchange-driven Magnetic Logic. Sci. Rep. 2017, 7, 12154. [Google Scholar] [CrossRef] [PubMed]
- Donahue, M.; Porter, D. OOMMF User’s Guide, Version 1.0. 1999. Available online: http://math.nist.gov/oommf (accessed on 15 January 2019).
- Vansteenkiste, A.; Leliaert, J.; Dvornik, M.; Helsen, M.; Garcia-Sanchez, F.; Waeyenberge, B.V. The design and verification of MuMax3. AIP Adv. 2014, 4, 107133. [Google Scholar] [CrossRef] [Green Version]
- Singh, P.; Herten, J.V.D.; Deschrijver, D.; Couckuyt, I.; Dhaene, T. A sequential sampling strategy for adaptive classification of computationally expensive data. Struct. Multidiscip. Optim. 2017, 55, 1425–1438. [Google Scholar] [CrossRef]
- Omar, Y.A.J.; Paul, D.Y.; Muhaidat, S.; Karagiannidis, G.K.; Taha, K. Efficient Machine Learning for Big Data: A Review. Big Data Res. 2015, 2, 87–93. [Google Scholar]
- Singh, P.; Deschrijver, D.; Pissoort, D.; Dhaene, T. Adaptive classification algorithm for EMC-compliance testing of electronic devices. Electron. Lett. 2013, 49, 1526–1528. [Google Scholar] [CrossRef] [Green Version]
- Basudhar, A.; Dribusch, C.; Lacaze, S.; Missoum, S. Constrained efficient global optimization with support vector machines. Struct. Multidiscip. Optim. 2012, 46, 201–221. [Google Scholar] [CrossRef]
- Basudhar, A.; Missoum, S. An improved adaptive sampling scheme for the construction of explicit boundaries. Struct. Multidiscip. Optim. 2010, 42, 517–529. [Google Scholar] [CrossRef]
- Alexander, I.J.F.; Andy, J.K. Recent advances in surrogate-based optimization. Prog. Aerosp. Sci. 2009, 45, 50–79. [Google Scholar]
- Shannon, C.E. A Mathematical Theory of Communication. Assoc. Comput. Mach. 2001, 5, 3–55. [Google Scholar] [CrossRef]
- Cortes, C.; Vapnik, V. Support-vector networks. Mach. Learn. 1995, 20, 273–297. [Google Scholar] [CrossRef]
- Rasmussen, C.E.; Williams, C.K.I. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning); The MIT Press: Cambridge, MA, USA, 2005. [Google Scholar]
- Lee, W.S.; Liu, B. Learning with Positive and Unlabeled Examples Using Weighted Logistic Regression. In Proceedings of the Twentieth International Conference on International Conference on Machine Learning, ICML’03,Washington, DC, USA, 21–24 August 2003; AAAI Press: Palo Alto, CA, USA, 2003; pp. 448–455. [Google Scholar]
- Kaintura, A.; Foss, K.; Couckuyt, I.; Dhaene, T.; Zografos, O.; Vaysset, A.; Sorée, B. Machine Learning for Fast Characterization of Magnetic Logic Devices. In Proceedings of the 2018 IEEE Electrical Design of Advanced Packaging and Systems Symposium (EDAPS), Chandigarh, India, 16–18 December 2018; pp. 1–3. [Google Scholar]
- Crombecq, K.; Gorissen, D.; Deschrijver, D.; Dhaene, T. A Novel Hybrid Sequential Design Strategy for Global Surrogate Modeling of Computer Experiments. SIAM J. Sci. Comput. 2011, 33, 1948–1974. [Google Scholar] [CrossRef]
- Romero, V.J.; Burkardt, J.V.; Gunzburger, M.D.; Peterson, J.S. Comparison of pure and Latinized centroidal Voronoi tessellation against various other statistical sampling methods. Reliab. Eng. Syst. Saf. 2006, 91, 1266–1280. [Google Scholar] [CrossRef]
- Herten, J.V.D.; Couckuyt, I.; Deschrijver, D.; Dhaene, T. Adaptive classification under computational budget constraints using sequential data gathering. Adv. Eng. Softw. 2016, 99, 137–146. [Google Scholar] [CrossRef] [Green Version]
- Houlsby, N.; Huszár, F.; Ghahramani, Z.; Lengyel, M. Bayesian Active Learning for Classification and Preference Learning. arXiv 2011, arXiv:1112.5745. [Google Scholar]
- Forman, G. An Extensive Empirical Study of Feature Selection Metrics for Text Classification. J. Mach. Learn. Res. 2003, 3, 1289–1305. [Google Scholar]
- Felipe, A.C.V.; Venter, G.; Balabanov, V. An algorithm for fast optimal Latin hypercube design of experiments. Int. J. Numer. Methods Eng. 2010, 82, 135–156. [Google Scholar]
- Knudde, N.; Herten, J.V.D.; Dhaene, T.; Couckuyt, I. GPflowOpt: A Bayesian Optimization Library using TensorFlow. arXiv 2017, arXiv:1711.03845. [Google Scholar]
- Gorissen, D.; Couckuyt, I.; Demeester, P.; Dhaene, T.; Crombecq, K. A Surrogate Modeling and Adaptive Sampling Toolbox for Computer Based Design. J. Mach. Learn. Res. 2010, 11, 2051–2055. [Google Scholar]
- Sylvain, L.; Missoum, S. CODES: A Toolbox For Computational Design Version 1.0. 2015. Available online: www.codes.arizona.edu/toolbox (accessed on 15 January 2019).
Mode | Logic Operation |
---|---|
M1: State initialization | XX→X0 or XX→X1 |
M2: State propagation (BUF) | 0X→X0 or 1X→X1 |
M2: State propagation (INV) | 0X→X1 or 1X→X0 |
Algorithm | Classifier | Model Dependent | Number of Samples | Test Set | ||||
---|---|---|---|---|---|---|---|---|
Precision | Recall | Accuracy (%) | Mis. Obs. | |||||
0 | 1 | |||||||
SVM | 0.97 | 0.97 | 97.00 | 27 | 11 | |||
LHD | GP | X | 30 | 0.97 | 0.97 | 97.40 | 20 | 13 |
LR | 0.95 | 0.95 | 95.10 | 21 | 14 | |||
SVM | 0.99 | 0.99 | 99.44 | 2 | 5 | |||
EDSD | GP | SVM | 5 + 25 | 1.0 | 1.0 | 99.76 | 1 | 2 |
LR | 0.96 | 0.96 | 95.59 | 22 | 24 | |||
SVM | 0.98 | 0.98 | 97.95 | 6 | 20 | |||
NV | GP | X | 5 + 25 | 0.98 | 0.98 | 97.63 | 4 | 26 |
LR | 0.95 | 0.95 | 95.27 | 14 | 46 | |||
SVM | 0.99 | 0.99 | 98.58 | 2 | 16 | |||
Entropy | GP | GP | 5 + 25 | 0.99 | 0.99 | 98.81 | 0 | 15 |
LR | 0.95 | 0.94 | 94.44 | 7 | 63 | |||
SVM | 1.0 | 1 | 99.84 | 0 | 2 | |||
PoF | GP | GP | 5 + 25 | 1.0 | 1.0 | 99.92 | 0 | 1 |
LR | 0.95 | 0.95 | 94.80 | 9 | 57 |
Algorithm | Classifier | Model Dependent | Number of Samples | Test Set | |||||
---|---|---|---|---|---|---|---|---|---|
Precision | Recall | Accuracy (%) | Mis. Obs. | ||||||
0 | 1 | 2 | |||||||
SVM | 0.94 | 0.93 | 93.15 | 53 | 11 | 23 | |||
LHD | GP | X | 100 | 0.94 | 0.94 | 93.86 | 28 | 22 | 28 |
LR | 0.88 | 0.90 | 89.53 | 29 | 64 | 40 | |||
SVM | 0.98 | 0.98 | 97.79 | 11 | 8 | 9 | |||
EDSD | GP | SVM | 20 + 80 | 0.98 | 0.98 | 97.95 | 4 | 11 | 11 |
LR | 0.82 | 0.88 | 87.64 | 15 | 72 | 70 | |||
SVM | 0.98 | 0.98 | 97.95 | 9 | 6 | 11 | |||
NV | GP | X | 20 + 80 | 0.98 | 0.98 | 98.34 | 3 | 8 | 11 |
LR | 0.83 | 0.88 | 88.43 | 19 | 72 | 56 | |||
SVM | 0.97 | 0.97 | 96.69 | 17 | 5 | 20 | |||
Entropy | GP | GP | 20 + 80 | 0.97 | 0.97 | 96.93 | 14 | 3 | 22 |
LR | 0.90 | 0.91 | 90.79 | 21 | 64 | 32 | |||
SVM | 0.98 | 0.98 | 98.19 | 16 | 4 | 3 | |||
PoF | GP | GP | 20 + 80 | 0.99 | 0.99 | 98.58 | 3 | 7 | 8 |
LR | 0.81 | 0.86 | 86.46 | 13 | 72 | 87 |
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Kaintura, A.; Foss, K.; Zografos, O.; Couckuyt, I.; Vaysset, A.; Dhaene, T.; Sorée, B. Fast Characterization of Input-Output Behavior of Non-Charge-Based Logic Devices by Machine Learning. Electronics 2020, 9, 1381. https://doi.org/10.3390/electronics9091381
Kaintura A, Foss K, Zografos O, Couckuyt I, Vaysset A, Dhaene T, Sorée B. Fast Characterization of Input-Output Behavior of Non-Charge-Based Logic Devices by Machine Learning. Electronics. 2020; 9(9):1381. https://doi.org/10.3390/electronics9091381
Chicago/Turabian StyleKaintura, Arun, Kyle Foss, Odysseas Zografos, Ivo Couckuyt, Adrien Vaysset, Tom Dhaene, and Bart Sorée. 2020. "Fast Characterization of Input-Output Behavior of Non-Charge-Based Logic Devices by Machine Learning" Electronics 9, no. 9: 1381. https://doi.org/10.3390/electronics9091381