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Machine learning is a field of artificial intelligence that seeks to identify patterns in empirical data. Applications range from biomedical imaging to financial forecasting, but scalability remains ...

Machine learning is a field of artificial intelligence that seeks to identify patterns in empirical data. Applications range from biomedical imaging to financial forecasting, but scalability remains an issue: sophisticated algorithms do not scale well and they are hard to parallelize in a cluster or using GPUs. Quantum mechanics, on the other hand, is a traditional area for high-performance computing, and the underlying mathematical framework has attracted attention outside the domain of physics. Quantum inspired learning methods are at the confluence of the two respective fields, promising highly scalable algorithms that are also able to capture patterns where traditional approaches were less successful.

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- 1. High Performance Quantum Inspired Models in Machine Learning High Performance Quantum Inspired Models in Machine Learning Peter Wittek Swedish School of Library and Information Science University of Boras˚ 11/05/12
- 2. High Performance Quantum Inspired Models in Machine LearningOutline 1 Introducing Machine Learning 2 Scalability in Machine Learning 3 The emergence of quantum inspired methods 4 Digression 5 Experimental Results 6 Conclusions
- 3. High Performance Quantum Inspired Models in Machine Learning Introducing Machine LearningProblem Statement Patterns in data Fundamentally data-driven, not model-driven Statistical and non-statistical methods Of particular interest: kernel density estimators 0.2 0.15 Density function 0.1 0.05 0 -4 -2 0 2 4 6 8 x
- 4. High Performance Quantum Inspired Models in Machine Learning Introducing Machine LearningMethods Countless: every data set has its own method Supervised versus unsupervised Clustering, neural networks, support vector machines, genetic algorithms, etc. a) b)
- 5. High Performance Quantum Inspired Models in Machine Learning Scalability in Machine LearningScaling out Data-intensive processing: MapReduce Simple operations on a large volume Typically not the most sophisticated algorithms More interesting algorithms do not scale well
- 6. High Performance Quantum Inspired Models in Machine Learning The emergence of quantum inspired methodsSome concepts Classical systems Quantum mechanics Hamiltonian Hamiltonian Poisson bracket Commutator Newton’s law of motion Ehrenfest’s theorem Probability distribution Density operator Random variable Self-adjoint matrices Formula of total probability FTP with interference
- 7. High Performance Quantum Inspired Models in Machine Learning The emergence of quantum inspired methodsA brief history 1920s: Quantum mechanics and quantum probability theory 1933: “Classical” probability theory 1957: QM is in fact a probability theory 1990s: Nature/physics inspired learning methods 2000s: Quantum inspired learning
- 8. High Performance Quantum Inspired Models in Machine Learning The emergence of quantum inspired methodsWhy quantum? Fundamentally non-commutative Contextuality is everything (compare it to Bayes’ rule) Entanglement Superposition
- 9. High Performance Quantum Inspired Models in Machine Learning The emergence of quantum inspired methodsApplication ﬁelds A growing range of machine learning methods: particle swarm optimization, evolutionary algorithms, neural networks, etc. Particularly popular: language technology The meaning of a term is in superposition: the context collapses it to one sense. Entanglement: pet-ﬁsh problem The measurement is speciﬁc to the individual, the context is non-classical.
- 10. High Performance Quantum Inspired Models in Machine Learning The emergence of quantum inspired methodsA bonus QM is quintessentially linear BLAS is available on every hardware Combine ML with QM to arrive at scalable models
- 11. High Performance Quantum Inspired Models in Machine Learning DigressionQuantum Computing and Computational Intelligence Quantum information theory Level of abstraction: qubits Exponential explosion in representative power Good match for computational intelligence
- 12. High Performance Quantum Inspired Models in Machine Learning DigressionCloud computing Cloud cluster instances Assembling a GPU cluster in a matter of minutes Freedom of choice in software Available to anyone
- 13. High Performance Quantum Inspired Models in Machine Learning Experimental ResultsHardware and software AWS Cluster Instances 2x4 CPU cores per instance 2x Tesla C2050 24Gbyte of RAM Linux environment OpenMPI, CUDA
- 14. High Performance Quantum Inspired Models in Machine Learning Experimental ResultsDynamic Quantum Clustering Assign wave function to data points −(xi −xj )2 Initialize Gram matrix Nij = ψi |ψj = e 4σ 2 Calculate Hamiltonian: Hij = ψi |H|ψj = ψi |(T + V (x))|ψj . Calculate position operator Xij = ψi |x|ψj Compute eigendecomposition of N Compute square root of N Basis transformation of Hamiltonian Basis transformation of position operator repeat Compute matrix exponential of transformed Hamiltonian at time tn Compute expectation of value of position operator at time tn until
- 15. High Performance Quantum Inspired Models in Machine Learning Experimental ResultsDynamic Quantum Clustering
- 16. High Performance Quantum Inspired Models in Machine Learning Experimental ResultsDynamic Quantum Clustering 6 250 CPU GPU w/o memory transfer GPU with memory transfer 5 200 4 150 Speedup Time (s) 3 100 2 50 1 Without Memory Transfer With Memory Transfer 0 0 64 128 256 512 1024 2048 4096 8192 64 128 256 512 1024 2048 4096 8192 Matrix size Matrix size (c) Execution time, sin- (d) Speedup, single gle precision precision 6 180 CPU GPU w/o memory transfer GPU with memory transfer 160 5 140 4 120 100 Speedup Time (s) 3 80 2 60 40 1 20 Without Memory Transfer With Memory Transfer 0 0 64 128 256 512 1024 2048 4096 8192 64 128 256 512 1024 2048 4096 8192 Matrix size Matrix size (e) Execution time, (f) Speedup, double double precision precision
- 17. High Performance Quantum Inspired Models in Machine Learning Experimental ResultsSelf-organizing maps 2D neural network: M = n1 , . . . , nk Associated weight vectors: W = w1 (t), ..., wk (t) at time t Seek best matching neurons Adjust weights: wj (t + 1) = wj (t) + αhbj (t)[x(t) − wj (t)]
- 18. High Performance Quantum Inspired Models in Machine Learning Experimental ResultsSelf-organizing maps
- 19. High Performance Quantum Inspired Models in Machine Learning Experimental ResultsSelf-organizing maps Method Execution Speedup time over CPU CPU (64 cores) 2042s - GPU (16 Tesla) 433s 4.71x CPU (64 cores) 1882s - (One epoch) GPU (16 Tesla) 194s 9.68x (One epoch) Table: Execution time of self-organizing maps
- 20. High Performance Quantum Inspired Models in Machine Learning ConclusionsOngoing work Extending the range of algorithms Large-scale experiments Attempts at uniﬁcation
- 21. High Performance Quantum Inspired Models in Machine Learning ConclusionsSummary http://squalar.org/bsc_talk.pdf Parallel code, GPU computing, HPC in general are fairly new in machine learning QL methods solve the problem in a spectacular way Additional advantages: contextuality, entanglement, superposition

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