A Classical-Quantum Hybrid Approach for Unsupervised Probabilistic Machine Learning
Abstract
For training unsupervised probabilistic machine learning models, matrix computation and sample generation are the two key steps. While GPUs excel at matrix computation, they use pseudo-random numbers to generate samples. Contrarily, Adiabatic Quantum Processors (AQP) use quantum mechanical systems to generate samples accurately and quickly, but are not suited for matrix computation. We present a Classical-Quantum Hybrid Approach for training unsupervised probabilistic machine learning models, leveraging GPUs for matrix computations and the D-Wave quantum sampling library for sample generation. We compare this approach to classical and quantum approaches across four performance metrics. Our results indicate that while the hybrid approach–which uses one AQP and one GPU–outperforms quantum and one of the classical approaches, it performs comparably to the GPU approach, and is outperformed by the CPU approach, which uses 56 high-end CPUs. Lastly, we compare sampling on AQP versus sampling library and show that AQP performs better.
Keywords
Quantum computing Machine learning Restricted boltzmann machines Deep belief networks MNISTReferences
- 1.LeCun, Y., Bengio, Y., Hinton, G.: Deep learning. nature 521(7553), 436 (2015)Google Scholar
- 2.Iandola, F.N., Moskewicz, M.W., Ashraf, K., Keutzer, K.: Firecaffe: near-linear acceleration of deep neural network training on compute clusters. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2592–2600 (2016)Google Scholar
- 3.Young, S.R., Rose, D.C., Karnowski, T.P., Lim, S.-H., Patton, R.M.: Optimizing deep learning hyper-parameters through an evolutionary algorithm. In: Proceedings of the Workshop on Machine Learning in High-Performance Computing Environments, p. 4, ACM (2015)Google Scholar
- 4.Kish, L.B.: End of moore’s law: thermal (noise) death of integration in micro and nano electronics. Phys. Lett. A 305(3–4), 144–149 (2002)CrossRefGoogle Scholar
- 5.Potok, T.E., Schuman, C.D., Young, S.R., Patton, R.M., Spedalieri, F., Liu, J., Yao, K.-T., Rose, G., Chakma, G.: A study of complex deep learning networks on high performance, neuromorphic, and quantum computers. In: Machine Learning in HPC Environments (MLHPC), Workshop on, pp. 47–55, IEEE (2016)Google Scholar
- 6.Amin, M.H., Andriyash, E., Rolfe, J., Kulchytskyy, B., Melko, R.: Quantum boltzmann machine arXiv preprint arXiv:1601.02036 (2016)
- 7.Gruska, J.: Quantum computing, vol. 2005. McGraw-Hill London (1999)Google Scholar
- 8.Rabitz, H., de Vivie-Riedle, R., Motzkus, M., Kompa, K.: Whither the future of controlling quantum phenomena? Science 288(5467), 824–828 (2000)CrossRefGoogle Scholar
- 9.Salakhutdinov, R., Mnih, A., Hinton, G.: Restricted boltzmann machines for collaborative filtering. In: Proceedings of the 24th international conference on Machine learning, pp. 791–798 ACM (2007)Google Scholar
- 10.Sarikaya, R., Hinton, G.E., Deoras, A.: Application of deep belief networks for natural language understanding. IEEE/ACM Trans. Audio, Speech, and Lang. Process. 22(4), 778–784 (2014)CrossRefGoogle Scholar
- 11.Watrous, J.: Quantum computational complexity. In: Encyclopedia of Complexity and Systems Science, pp. 7174–7201. Springer (2009)Google Scholar
- 12.Frisch, A.: Ibm qintroduction into quantum computing with live demo. In: System-on-Chip Conference (SOCC), 2017 30th IEEE International, pp. 1–2, IEEE (2017)Google Scholar
- 13.2018 CES: Intel advances quantum and neuromorphic computing research’ 2018. https://newsroom.intel.com/news/intel-advances-quantum-neuromorphic-computing-research/
- 14.Terhal, B.M.: Quantum supremacy, here we come. Nat. Phys. p. 1 (2018)Google Scholar
- 15.Johnson, M.W., Amin, M.H., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A.J., Johansson, J., Bunyk, P., et al.: Quantum annealing with manufactured spins. Nature 473(7346), 194 (2011)CrossRefGoogle Scholar
- 16.Denchev, V.S., Boixo, S., Isakov, S.V., Ding, N., Babbush, R., Smelyanskiy, V., Martinis, J., Neven, H.: What is the computational value of finite-range tunneling? Phys. Rev. X 6(3), 031015 (2016)Google Scholar
- 17.Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549(7671), 195 (2017)CrossRefGoogle Scholar
- 18.DeBenedictis, E.P.: A future with quantum machine learning. Computer 51(2), 68–71 (2018)CrossRefGoogle Scholar
- 19.Smolensky, P.: Information processing in dynamical systems: foundations of harmony theory. COLORADO UNIV AT BOULDER DEPT OF COMPUTER SCIENCE, Tech. Rep. (1986)Google Scholar
- 20.Hinton, G.E.: Training products of experts by minimizing contrastive divergence. Neural Comput. 14(8), 1771–1800 (2002)CrossRefGoogle Scholar
- 21.Fiore, U., Palmieri, F., Castiglione, A., De Santis, A.: Network anomaly detection with the restricted boltzmann machine. Neuro Comput. 122, 13–23 (2013)Google Scholar
- 22.Jaitly, N., Hinton, G.: Learning a better representation of speech soundwaves using restricted boltzmann machines. In: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 5884–5887, IEEE (2011)Google Scholar
- 23.Le Roux, N., Bengio, Y.: Representational power of restricted boltzmann machines and deep belief networks. Neural Comput. 20(6), 1631–1649 (2008)MathSciNetCrossRefGoogle Scholar
- 24.Hinton, G.E., Osindero, S., Teh, Y.-W.: A fast learning algorithm for deep belief nets. Neural Comput. 18(7), 1527–1554 (2006)MathSciNetCrossRefGoogle Scholar
- 25.Lee, H., Grosse, R., Ranganath, R., Ng, A.Y.: Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations. In: Proceedings of the 26th annual international conference on machine learning, pp. 609–616, ACM, 2009Google Scholar
- 26.Mohamed, A.-R., Yu, D., Deng, L.: Investigation of full-sequence training of deep belief networks for speech recognition. In: Eleventh Annual Conference of the International Speech Communication Association (2010)Google Scholar
- 27.Zhou, S., Chen, Q., Wang, X.: Fuzzy deep belief networks for semi-supervised sentiment classification. Neuro Comput. 131, 312–322 (2014)Google Scholar
- 28.Masci, J., Meier, U., Cireşan, D., Schmidhuber, J.: Stacked convolutional auto-encoders for hierarchical feature extraction. In: International Conference on Artificial Neural Networks, pp. 52–59. Springer (2011)Google Scholar
- 29.Oliphant, T.E.: A guide to NumPy, vol. 1. Trelgol Publishing USA (2006)Google Scholar
- 30.Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., Isard, M., et al.: Tensorflow: a system for large-scale machine learning. OSDI 16, 265–283 (2016)Google Scholar
- 31.D-Wave Systems Inc.: Training probabilistic models using d-wave sampling libraries (2018)Google Scholar
- 32.D-Wave Systems Inc.: Developer guide for python (2018)Google Scholar
- 33.Bierhorst, P., Knill, E., Glancy, S., Zhang, Y., Mink, A., Jordan, S., Rommal, A., Liu, Y.-K., Christensen, B., Nam, S.W., et al.: Experimentally generated randomness certified by the impossibility of superluminal signals. Nature 556(7700), 223 (2018)CrossRefGoogle Scholar