Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer
Restricted Boltzmann Machine (RBM) is an energy-based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate the exact gradient of the log-...
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Frontiers Media S.A.
2021-06-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2021.589626/full |
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| author | Vivek Dixit Vivek Dixit Raja Selvarajan Raja Selvarajan Muhammad A. Alam Muhammad A. Alam Travis S. Humble Sabre Kais Sabre Kais Sabre Kais |
| author_facet | Vivek Dixit Vivek Dixit Raja Selvarajan Raja Selvarajan Muhammad A. Alam Muhammad A. Alam Travis S. Humble Sabre Kais Sabre Kais Sabre Kais |
| author_sort | Vivek Dixit |
| collection | DOAJ |
| description | Restricted Boltzmann Machine (RBM) is an energy-based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate the exact gradient of the log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), where obtaining samples is faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results of RBM trained using quantum annealing are compared with the CD-based method. The performance of the two approaches is compared with respect to the classification accuracies, image reconstruction, and log-likelihood results. The classification accuracy results indicate comparable performances of the two methods. Image reconstruction and log-likelihood results show improved performance of the CD-based method. It is shown that the samples obtained from quantum annealer can be used to train an RBM on a 64-bit “bars and stripes” dataset with classification performance similar to an RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer could be useful as it eliminates computationally expensive MCMC steps of CD. |
| first_indexed | 2024-12-19T23:45:33Z |
| format | Article |
| id | doaj.art-9e0431e72f7c4871ba30ad0a0297a67c |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-19T23:45:33Z |
| publishDate | 2021-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-9e0431e72f7c4871ba30ad0a0297a67c2022-12-21T20:01:19ZengFrontiers Media S.A.Frontiers in Physics2296-424X2021-06-01910.3389/fphy.2021.589626589626Training Restricted Boltzmann Machines With a D-Wave Quantum AnnealerVivek Dixit0Vivek Dixit1Raja Selvarajan2Raja Selvarajan3Muhammad A. Alam4Muhammad A. Alam5Travis S. Humble6Sabre Kais7Sabre Kais8Sabre Kais9Department of Chemistry, Purdue University, West Lafayette, IN, United StatesDepartment of Physics and Astronomy, Purdue University, West Lafayette, IN, United StatesDepartment of Chemistry, Purdue University, West Lafayette, IN, United StatesDepartment of Physics and Astronomy, Purdue University, West Lafayette, IN, United StatesDepartment of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, United StatesBirck Nanotechnology Center, Purdue University, West Lafayette, IN, United StatesQuantum Computing Institute, Oak Ridge National Laboratory, Oak Ridge, TN, United StatesDepartment of Chemistry, Purdue University, West Lafayette, IN, United StatesDepartment of Physics and Astronomy, Purdue University, West Lafayette, IN, United StatesBirck Nanotechnology Center, Purdue University, West Lafayette, IN, United StatesRestricted Boltzmann Machine (RBM) is an energy-based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate the exact gradient of the log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), where obtaining samples is faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results of RBM trained using quantum annealing are compared with the CD-based method. The performance of the two approaches is compared with respect to the classification accuracies, image reconstruction, and log-likelihood results. The classification accuracy results indicate comparable performances of the two methods. Image reconstruction and log-likelihood results show improved performance of the CD-based method. It is shown that the samples obtained from quantum annealer can be used to train an RBM on a 64-bit “bars and stripes” dataset with classification performance similar to an RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer could be useful as it eliminates computationally expensive MCMC steps of CD.https://www.frontiersin.org/articles/10.3389/fphy.2021.589626/fullbars and stripesquantum annealingclassificationimage reconstructionlog-likelihoodmachine learning |
| spellingShingle | Vivek Dixit Vivek Dixit Raja Selvarajan Raja Selvarajan Muhammad A. Alam Muhammad A. Alam Travis S. Humble Sabre Kais Sabre Kais Sabre Kais Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer Frontiers in Physics bars and stripes quantum annealing classification image reconstruction log-likelihood machine learning |
| title | Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer |
| title_full | Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer |
| title_fullStr | Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer |
| title_full_unstemmed | Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer |
| title_short | Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer |
| title_sort | training restricted boltzmann machines with a d wave quantum annealer |
| topic | bars and stripes quantum annealing classification image reconstruction log-likelihood machine learning |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2021.589626/full |
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