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【讲座】现代数学报告:Deep Learning based Geophysical Data Denoising and Inversion

报告题目:现代数学报告:Deep Learning based Geophysical Data Denoising and Inversion

报告人:马坚伟

教授  哈尔滨工业大学地球物理中心主任,数学系副主任

报告时间:2018-04-27 15:30

报告地点:清华大学近春园西楼三层报告厅

主办单位:丘成桐数学科学中心

简介:

Firstly, I will mainly talk about our recent applications of deep learning for seismic data denoising and velocity inversion. Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse time migration and other high-resolution seismic imaging techniques. We have investigated a novel method based on the deep fully convolutional neural network (FCN) for velocity model building (VMB) directly from raw seismograms. One key characteristic of the data-driven method is that it can automatically extract multi-layer useful features from the seismic traces for VMB without human-curated activities.

Then, I will simply report our recent development on frequency domain pooling based DL method. Our spectrum pooling is constructed by the Hartley transform and performs dimensionality reduction by truncating the feature maps in the frequency domain. Compared with the spectral pooling implemented by Fourier transform, our spectrum pooling requires much less computation since we do not need extra operation to ensure the output of spectral pooling is real except for transforming, spectrum cropping and padding. On the MNIST dataset, we empirically show that embedding our spectrum pooling in some existing convolutional neural networks (CNNs), by replacing its original pooling layers, is able to improve classification accuracy.

Finally, I will mention our next work on using the Wasserstein distance as the loss function of deep learning for the geophysical inverse problem. The Wasserstein distance does not only compare objects point by point, as standard Lp metrics, but instead quantifies how the mass is moved. This makes optimal transport natural for quantifying uncertainty and modeling deformations.

DL+Numerical PDE

ICLR2017 workshop version:link

Hoping approximation by neural network can overcome the curse of dimensionality to solve PDE in high dimensional space.

longer version.

Designed a physic based RNN with residual connection to do model reduction.(Reduce the dimension for a dynamic.)

arXiv

arXiv

Ref: http://about.2prime.cn/pde.html (@陆一平-北京大学-数学 )

DL+Physics

The following are recent papers combining the fields of physics - especially quantum mechanics - and machine learning. 

 

APPLYING MACHINE LEARNING TO PHYSICS

"A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems", Mustafa A. Mohamad, Themistoklis P. Sapsis, arXiv: 1804.07240, 4/2018

"Method to solve quantum few-body problems with artificial neural networks", Hiroki Saito, arXiv: 1804.06521, 4/2018

"Classicalization Clearly: Quantum Transition into States of Maximal Memory Storage Capacity", Gia Dvali, arXiv: 1804.06154, 4/2018

"Machine learning of phase transitions in the percolation and XY models", Wanzhou Zhang, Jiayu Liu, Tzu-Chieh Wei, arXiv: 1804.02709, 4/2018

"Complex energy landscapes in spiked-tensor and simple glassy models: ruggedness, arrangements of local minima and phase transitions", Valentina Ros, Gerard Ben Arous, Giulio Biroli, Chiara Cammarota, arXiv: 1804.02686, 4/2018

"Smallest Neural Network to Learn the Ising Criticality", Dongkyu Kim, Dong-Hee Kim, arXiv: 1804.02171, 4/2018

"Learning quantum models from quantum or classical data", Hilbert J Kappen, arXiv: 1803.11278, 3/2018

"Deep Learning Phase Segregation", Amir Barati Farimani, Joseph Gomes, Rishi Sharma, Franklin L. Lee, Vijay S. Pande, arXiv: 1803.08993, 3/2018

"A high-bias, low-variance introduction to Machine Learning for physicists", Pankaj Mehta, Marin Bukov, Ching-Hao Wang, Alexandre G. R. Day, Clint Richardson, Charles K. Fisher, David J. Schwab, arXiv: 1803.08823, 3/2018

"Parameter diagnostics of phases and phase transition learning by neural networks", Philippe Suchsland, Stefan Wessel, arXiv: 1802.09876, 2/2018

"Advantages of versatile neural-network decoding for topological codes", Nishad Maskara, Aleksander Kubica, Tomas Jochym-O'Connor, arXiv: 1802.08680, 2/2018

"Reinforcement Learning with Neural Networks for Quantum Feedback", Thomas Fösel, Petru Tighineanu, Talitha Weiss, Florian Marquardt, arXiv: 1802.05267, 2/2018

"Online Learning of Quantum States", Scott Aaronson, Xinyi Chen, Elad Hazan, Ashwin Nayak, arXiv: 1802.09025, 2/2018

"Deep neural decoders for near term fault-tolerant experiments", Christopher Chamberland, Pooya Ronagh, arXiv: 1802.06441, 2/2018

"Neural Network Renormalization Group", Shuo-Hui Li, Lei Wang, arXiv: 1802.02840, 2/2018

"Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification", Rohit Tripathy, Ilias Bilionis, arXiv: 1802.00850, 2/2018

"Experimentally detecting a quantum change point via Bayesian inference", Shang Yu, Chang-Jiang Huang, Jian-Shun Tang, Zhih-Ahn Jia, Yi-Tao Wang, Zhi-Jin Ke, Wei Liu, Xiao Liu, Zong-Quan Zhou, Ze-Di Cheng, Jin-Shi Xu, Yu-Chun Wu, Yuan-Yuan Zhao, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo, Gael Sentís, Ramon Muñoz-Tapia, arXiv: 1801.07508, 1/2018

"Generative Models for Stochastic Processes Using Convolutional Neural Networks", Fernando Fernandes Neto, arXiv: 1801.03523, 1/2018

"Pattern recognition techniques for Boson Sampling validation", Iris Agresti, Niko Viggianiello, Fulvio Flamini, Nicolò Spagnolo, Andrea Crespi, Roberto Osellame, Nathan Wiebe, Fabio Sciarrino, arXiv: 1712.06863, 12/2017

"Towards reduction of autocorrelation in HMC by machine learning", Akinori Tanaka, Akio Tomiya, arXiv: 1712.03893, 12/2017

"Deep Neural Network Detects Quantum Phase Transition", Shunta Arai, Masayuki Ohzeki, Kazuyuki Tanaka, arXiv: 1712.00371, 12/2017

"Experimental learning of quantum states", Andrea Rocchetto, Scott Aaronson, Simone Severini, Gonzalo Carvacho, Davide Poderini, Iris Agresti, Marco Bentivegna, Fabio Sciarrino, arXiv: 1712.00127, 11/2017

"Machine learning vortices at the Kosterlitz-Thouless transition", Matthew J. S. Beach, Anna Golubeva, Roger G. Melko, arXiv: 1710.09842, 10/2017

"Machine learning out-of-equilibrium phases of matter", Jordan Venderley, Vedika Khemani, Eun-Ah Kim, arXiv: 1711.00020, 10/2017

"Learning hard quantum distributions with variational autoencoders", Andrea Rocchetto, Edward Grant, Sergii Strelchuk, Giuseppe Carleo, Simone Severini, arXiv: 1710.00725, 10/2017

"Combining Machine Learning and Physics to Understand Glassy Systems", Samuel S. Schoenholz, arXiv: 1709.08015, 9/2017

"By-passing the Kohn-Sham equations with machine learning", Felix Brockherde, Leslie Vogt, Li Li, Mark E. Tuckerman, Kieron Burke, Klaus-Robert Müller, arXiv: 1609.02815, 9/2016

"Learning Disordered Topological Phases by Statistical Recovery of Symmetry", Nobuyuki Yoshioka, Yutaka Akagi, Hosho Katsura, arXiv: 1709.05790, 9/2017

"Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems", Yusuke Nomura, Andrew S. Darmawan, Youhei Yamaji, Masatoshi Imada, arXiv: 1709.06475, 9/2017

"Identifying Product Order with Restricted Boltzmann Machines", Wen-Jia Rao, Zhenyu Li, Qiong Zhu, Mingxing Luo, Xin Wan, arXiv: 1709.02597, 9/2017

"Machine learning & artificial intelligence in the quantum domain", Vedran Dunjko, Hans J. Briegel, arXiv: 1709.02779, 9/2017

"Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network", Tomohiro Mano, Tomi Ohtsuki, arXiv: 1709.00812, 9/2017

"Machine Learning Spatial Geometry from Entanglement Features", Yi-Zhuang You, Zhao Yang, Xiao-Liang Qi, arXiv: 1709.01223, 9/2017

"Machine Learning Topological Invariants with Neural Networks", Pengfei Zhang, Huitao Shen, Hui Zhai, arXiv: 1708.09401, 8/2017

"Extensive deep neural networks", Iryna Luchak, Kyle Mills, Kevin Ryczko, Adam Domurad, Isaac Tamblyn, arXiv: 1708.06686, 8/2017

"Learning Fermionic Critical Points", Natanael C. Costa, Wenjian Hu, Z. J. Bai, Richard T. Scalettar, Rajiv R. P. Singh, arXiv: 1708.04762, 8/2017

"Deep Learning the Ising Model Near Criticality", Alan Morningstar, Roger G. Melko, arXiv: 1708.04622, 8/2017

"Spectral Dynamics of Learning Restricted Boltzmann Machines", Aurélien Decelle, Giancarlo Fissore, Cyril Furtlehner, arXiv: 1708.02917, 8/2017

"Solving the Bose-Hubbard model with machine learning", Hiroki Saito, arXiv: 1707.09723, 7/2017

"Quantum dynamics in transverse-field Ising models from classical networks", Markus Schmitt, Markus Heyl, arXiv: 1707.06656, 7/2017

"Learning the Einstein-Podolsky-Rosen correlations on a Restricted Boltzmann Machine", Steven Weinstein, arXiv: 1707.03114, 7/2017

"Quantum phase recognition via unsupervised machine learning", Peter Broecker, Fakher F. Assaad, Simon Trebst, arXiv: 1707.00663, 7/2017

"Deep neural networks for direct, featureless learning through observation: the case of 2d spin models", K. Mills, I. Tamblyn, arXiv: 1706.09779, 6/2017

"Inverse Ising inference by combining Ornstein-Zernike theory with deep learning", Alpha A. Lee, arXiv: 1706.08466, 6/2017

"Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis", Ce Wang, Hui Zhai, arXiv: 1706.07977, 6/2017

"Self-Learning Phase Boundaries by Active Contours", Ye-Hua Liu, Evert P. L. van Nieuwenburg, arXiv: 1706.08111, 6/2017

"Machine-learning-assisted correction of correlated qubit errors in a topological code", P. Baireuther, T. E. O'Brien, B. Tarasinski, C. W. J. Beenakker, arXiv: 1705.07855, 5/2017

"Self-Learning Monte Carlo Method: Continuous-Time Algorithm", Yuki Nagai, Huitao Shen, Yang Qi, Junwei Liu, Liang Fu, arXiv: 1705.06724, 5/2017

"Criticality & Deep Learning II: Momentum Renormalisation Group", Dan Oprisa, Peter Toth, arXiv: 1705.11023, 5/2017

"Construction of Hamiltonians by supervised learning of energy and entanglement spectra", Hiroyuki Fujita, Yuya O. Nakagawa, Sho Sugiura, Masaki Oshikawa, arXiv: 1705.05372, 5/2017

"Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory", Sebastian Johann Wetzel, Manuel Scherzer, arXiv: 1705.05582, 5/2017

"Machine Learning Z2Z2 Quantum Spin Liquids with Quasi-particle Statistics", Yi Zhang, Roger G. Melko, Eun-Ah Kim, arXiv: 1705.01947, 5/2017

"Decoding Small Surface Codes with Feedforward Neural Networks", Savvas Varsamopoulos, Ben Criger, Koen Bertels, arXiv: 1705.00857, 5/2017

"A Separability-Entanglement Classifier via Machine Learning", Sirui Lu, Shilin Huang, Keren Li, Jun Li, Jianxin Chen, Dawei Lu, Zhengfeng Ji, Yi Shen, Duanlu Zhou, Bei Zeng, arXiv: 1705.01523, 5/2017

"Reinforcement Learning in Different Phases of Quantum Control", Marin Bukov, Alexandre G. R. Day, Dries Sels, Phillip Weinberg, Anatoli Polkovnikov, Pankaj Mehta, arXiv: 1705.00565, 5/2017

"Deterministic Quantum Annealing Expectation-Maximization Algorithm", Hideyuki Miyahara, Koji Tsumura, Yuki Sughiyama, arXiv: 1704.05822, 4/2017

"Mutual Information, Neural Networks and the Renormalization Group", Maciej Koch-Janusz, Zohar Ringel, arXiv: 1704.06279, 4/2017

"Kernel methods for interpretable machine learning of order parameters", Pedro Ponte, Roger G. Melko, arXiv: 1704.05848, 4/2017

"Approximating quantum many-body wave-functions using artificial neural networks", Zi Cai, Jinguo Liu, arXiv: 1704.05148, 4/2017

"Probing many-body localization with neural networks", Frank Schindler, Nicolas Regnault, Titus Neupert, arXiv: 1704.01578, 4/2017

"Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination", Wenjian Hu, Rajiv R. P. Singh, Richard T. Scalettar, arXiv: 1704.00080, 3/2017

"Many-body quantum state tomography with neural networks", Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer, Roger Melko, Giuseppe Carleo, arXiv: 1703.05334, 3/2017

"Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders", Sebastian Johann Wetzel, arXiv: 1703.02435, 3/2017

"Neural network representation of tensor network and chiral states", Yichen Huang, Joel E. Moore, arXiv: 1701.06246, 1/2017

"Equivalence of restricted Boltzmann machines and tensor network states", Jing Chen, Song Cheng, Haidong Xie, Lei Wang, Tao Xiang, arXiv: 1701.04831, 1/2017

"Efficient Representation of Quantum Many-body States with Deep Neural Networks", Xun Gao, Lu-Ming Duan, arXiv: 1701.05039, 1/2017

"Quantum Entanglement in Neural Network States", Dong-Ling Deng, Xiaopeng Li, S. Das Sarma, arXiv: 1701.04844, 1/2017

"Restricted Boltzmann Machines for the Long Range Ising Models", Ken-Ichi Aoki, Tamao Kobayashi, arXiv: 1701.00246, 1/2017

"Reinforcement Learning Using Quantum Boltzmann Machines", Daniel Crawford, Anna Levit, Navid Ghadermarzy, Jaspreet S. Oberoi, Pooya Ronagh, arXiv: 1612.05695, 12/2016

"Self-Learning Monte Carlo Method in Fermion Systems", Junwei Liu, Huitao Shen, Yang Qi, Zi Yang Meng, Liang Fu, arXiv: 1611.09364, 11/2016

"Sampling algorithms for validation of supervised learning models for Ising-like systems", Nataliya Portman, Isaac Tamblyn, arXiv: 1611.05891, 11/2016

"Quantum Loop Topography for Machine Learning", Yi Zhang, Eun-Ah Kim, arXiv: 1611.01518, 11/2016

"Learning phase transitions by confusion", Evert P. L. van Nieuwenburg, Ye-Hua Liu, Sebastian D. Huber, arXiv: 1610.02048, 10/2016

"A Neural Decoder for Topological Codes", Giacomo Torlai, Roger G. Melko, arXiv: 1610.04238, 10/2016

"Self-Learning Monte Carlo Method", Junwei Liu, Yang Qi, Zi Yang Meng, Liang Fu, arXiv: 1610.03137, 10/2016

"Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines", Li Huang, Lei Wang, arXiv: 1610.02746, 10/2016

"Machine Learning Topological States", Dong-Ling Deng, Xiaopeng Li, S. Das Sarma, arXiv: 1609.09060, 9/2016

"Pure density functional for strong correlations and the thermodynamic limit from machine learning", Li Li, Thomas E. Baker, Steven R. White, Kieron Burke, arXiv: 1609.03705, 9/2016

"Machine Learning Phases of Strongly Correlated Fermions", Kelvin Ch'ng, Juan Carrasquilla, Roger G. Melko, Ehsan Khatami, arXiv: 1609.02552, 9/2016

"Machine learning quantum phases of matter beyond the fermion sign problem", Peter Broecker, Juan Carrasquilla, Roger G. Melko, Simon Trebst, arXiv: 1608.07848, 8/2016

"Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions", Leonardo Banchi, Nicola Pancotti, Sougato Bose, arXiv: 1509.04298, 9/2015

"Learning Thermodynamics with Boltzmann Machines", Giacomo Torlai, Roger G. Melko, arXiv: 1606.02718, 6/2016

"Solving the Quantum Many-Body Problem with Artificial Neural Networks", Giuseppe Carleo, Matthias Troyer, arXiv: 1606.02318, 6/2016

"Discovering Phase Transitions with Unsupervised Learning", Lei Wang, arXiv: 1606.00318, 6/2016

"Machine learning phases of matter", Juan Carrasquilla, Roger G. Melko, arXiv: 1605.01735, 5/2016

"Understanding Machine-learned Density Functionals", Li Li, John C. Snyder, Isabelle M. Pelaschier, Jessica Huang, Uma-Naresh Niranjan, Paul Duncan, Matthias Rupp, Klaus-Robert Müller, Kieron Burke, arXiv: 1404.1333, 4/2014

PHYSICS-INSPIRED IDEAS APPLIED TO MACHINE LEARNING

"Supervised machine learning algorithms based on generalized Gibbs ensembles", Tatjana Puskarov, Axel Cortes Cubero, arXiv: 1804.03546, 4/2018

"The Loss Surface of XOR Artificial Neural Networks", Dhagash Mehta, Xiaojun Zhao, Edgar A. Bernal, David J. Wales, arXiv: 1804.02411, 4/2018

"Matrix Product Operators for Sequence to Sequence Learning", Chu Guo, Zhanming Jie, Wei Lu, Dario Poletti, arXiv: 1803.10908, 3/2018

"Protection against Cloning for Deep Learning", Richard Kenway, arXiv: 1803.10995, 3/2018

"Bridging Many-Body Quantum Physics and Deep Learning via Tensor Networks", Yoav Levine, Or Sharir, Nadav Cohen, Amnon Shashua, arXiv: 1803.09780, 3/2018

"Learning architectures based on quantum entanglement: a simple matrix product state algorithm for image recognition", Yuhan Liu, Xiao Zhang, Maciej Lewenstein, Shi-Ju Ran, arXiv: 1803.09111, 3/2018

"Comparing Dynamics: Deep Neural Networks versus Glassy Systems", M. Baity-Jesi, L. Sagun, M. Geiger, S. Spigler, G. Ben Arous, C. Cammarota, Y. LeCun, M. Wyart, G. Biroli, arXiv: 1803.06969, 3/2018

"Vulnerability of Deep Learning", Richard Kenway, arXiv: 1803.06111, 3/2018

"Thermodynamics of Restricted Boltzmann Machines and related learning dynamics", Aurélien Decelle, Giancarlo Fissore, Cyril Furtlehner, arXiv: 1803.01960, 3/2018

"Energy-entropy competition and the effectiveness of stochastic gradient descent in machine learning", Yao Zhang, Andrew M. Saxe, Madhu S. Advani, Alpha A. Lee, arXiv: 1803.01927, 3/2018

"Energy-entropy competition and the effectiveness of stochastic gradient descent in machine learning", Yao Zhang, Andrew M. Saxe, Madhu S. Advani, Alpha A. Lee, arXiv: 1803.01927, 3/2018

"The Mean-Field Approximation: Information Inequalities, Algorithms, and Complexity", Vishesh Jain, Frederic Koehler, Elchanan Mossel, arXiv: 1802.06126, 2/2018

"Inferring relevant features: from QFT to PCA", Cédric Bény, arXiv: 1802.05756, 2/2018

"Critical Percolation as a Framework to Analyze the Training of Deep Networks", Zohar Ringel, Rodrigo de Bem, arXiv: 1802.02154, 2/2018

"Scale-invariant Feature Extraction of Neural Network and Renormalization Group Flow", Satoshi Iso, Shotaro Shiba, Sumito Yokoo, arXiv: 1801.07172, 1/2018

"A relativistic extension of Hopfield neural networks via the mechanical analogy", Adriano Barra, Matteo Beccaria, Alberto Fachechi, arXiv: 1801.01743, 1/2018

"Learning Relevant Features of Data with Multi-scale Tensor Networks", E. M. Stoudenmire, arXiv: 1801.00315, 12/2017

"Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines", Song Cheng, Jing Chen, Lei Wang, arXiv: 1712.04144, 12/2017

"Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks", Pratik Chaudhari, Stefano Soatto, arXiv: 1710.11029, 10/2017

"A Correspondence Between Random Neural Networks and Statistical Field Theory", Samuel S. Schoenholz, Jeffrey Pennington, Jascha Sohl-Dickstein, arXiv: 1710.06570, 10/2017

"Entanglement Entropy of Target Functions for Image Classification and Convolutional Neural Network", Ya-Hui Zhang, arXiv: 1710.05520, 10/2017

"Machine Learning by Two-Dimensional Hierarchical Tensor Networks: A Quantum Information Theoretic Perspective on Deep Architectures", Ding Liu, Shi-Ju Ran, Peter Wittek, Cheng Peng, Raul Blázquez García, Gang Su, Maciej Lewenstein, arXiv: 1710.04833, 10/2017

"Neural Networks Quantum States, String-Bond States and chiral topological states", Ivan Glasser, Nicola Pancotti, Moritz August, Ivan D. Rodriguez, J. Ignacio Cirac, arXiv: 1710.04045, 10/2017

"Mean-field theory of input dimensionality reduction in unsupervised deep neural networks", Haiping Huang, arXiv: 1710.01467, 10/2017

"Machine Learning by Two-Dimensional Hierarchical Tensor Networks: A Quantum Information Theoretic Perspective on Deep Architectures", Ding Liu, Shi-Ju Ran, Peter Wittek, Cheng Peng, Raul Blázquez García, Gang Su, Maciej Lewenstein, arXiv: 1710.04833, 10/2017

"Unsupervised Generative Modeling Using Matrix Product States", Zhao-Yu Han, Jun Wang, Heng Fan, Lei Wang, Pan Zhang, arXiv: 1709.01662, 9/2017

"Deep Learning and Quantum Entanglement: Fundamental Connections with Implications to Network Design", Yoav Levine, David Yakira, Nadav Cohen, Amnon Shashua, arXiv: 1704.01552, 4/2017

"Opening the Black Box of Deep Neural Networks via Information", Ravid Shwartz-Ziv, Naftali Tishby, arXiv: 1703.00810, 3/2017

"Reinforcement Learning Using Quantum Boltzmann Machines", Daniel Crawford, Anna Levit, Navid Ghadermarzy, Jaspreet S. Oberoi, Pooya Ronagh, arXiv: 1612.05695, 12/2016

"Low-Rank Tensor Networks for Dimensionality Reduction and Large-Scale Optimization Problems: Perspectives and Challenges PART 1", A. Cichocki, N. Lee, I. V. Oseledets, A. -H. Phan, Q. Zhao, D. Mandic, arXiv: 1609.00893, 9/2016

"Why does deep and cheap learning work so well?", Henry W. Lin, Max Tegmark, David Rolnick, arXiv: 1608.08225, 8/2016

"Supervised Learning with Quantum-Inspired Tensor Networks", E. Miles Stoudenmire, David J. Schwab, arXiv: 1605.05775, 5/2016

"Exponential Machines", Alexander Novikov, Mikhail Trofimov, Ivan Oseledets, arXiv: 1605.03795, 5/2016

"Quantum Boltzmann Machine", Mohammad H. Amin, Evgeny Andriyash, Jason Rolfe, Bohdan Kulchytskyy, Roger Melko, arXiv: 1601.02036, 1/2016

"An exact mapping between the Variational Renormalization Group and Deep Learning", Pankaj Mehta, David J. Schwab, arXiv: 1410.3831, 10/2014

"Tensor Networks for Big Data Analytics and Large-Scale Optimization Problems", Andrzej Cichocki, arXiv: 1407.3124, 7/2014

QUANTUM COMPUTATION AND QUANTUM ALGORITHMS FOR MACHINE LEARNING

"Optimizing a Polynomial Function on a Quantum Simulator", Keren Li, Shijie Wei, Feihao Zhang, Pan Gao, Zengrong Zhou, Tao Xin, Xiaoting Wang, Guilu Long, arXiv: 1804.05231, 4/2018

"Differentiable Learning of Quantum Circuit Born Machine", Jin-Guo Liu, Lei Wang, arXiv: 1804.04168, 4/2018

"Hierarchical quantum classifiers", Edward Grant, Marcello Benedetti, Shuxiang Cao, Andrew Hallam, Joshua Lockhart, Vid Stojevic, Andrew G. Green, Simone Severini, arXiv: 1804.03680, 4/2018

"Strawberry Fields: A Software Platform for Photonic Quantum Computing", Nathan Killoran, Josh Izaac, Nicolás Quesada, Ville Bergholm, Matthew Amy, Christian Weedbrook, arXiv: 1804.03159, 4/2018

"Variational quantum simulation of imaginary time evolution with applications in chemistry and beyond", Sam McArdle, Suguru Endo, Ying Li, Simon Benjamin, Xiao Yuan, arXiv: 1804.03023, 4/2018

"Neural network decoder for topological color codes with circuit level noise", P. Baireuther, M. D. Caio, B. Criger, C. W. J. Beenakker, T. E. O'Brien, arXiv: 1804.02926, 4/2018

"Quantum Machine Learning Matrix Product States", Jacob Biamonte, arXiv: 1804.02398, 4/2018

"Classical Verification of Quantum Computations", Urmila Mahadev, arXiv: 1804.01082, 4/2018

"Circuit-centric quantum classifiers", Maria Schuld, Alex Bocharov, Krysta Svore, Nathan Wiebe, arXiv: 1804.00633, 4/2018

"A note on state preparation for quantum machine learning", Zhikuan Zhao, Vedran Dunjko, Jack K. Fitzsimons, Patrick Rebentrost, Joseph F. Fitzsimons, arXiv: 1804.00281, 4/2018

"Towards Quantum Machine Learning with Tensor Networks", William Huggins, Piyush Patel, K. Birgitta Whaley, E. Miles Stoudenmire, arXiv: 1803.11537, 3/2018

"Barren plateaus in quantum neural network training landscapes", Jarrod R. McClean, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, Hartmut Neven, arXiv: 1803.11173, 3/2018

"Quantum algorithms for training Gaussian Processes", Zhikuan Zhao, Jack K. Fitzsimons, Michael A. Osborne, Stephen J. Roberts, Joseph F. Fitzsimons, arXiv: 1803.10520, 3/2018

"Measurement-based adaptation protocol with quantum reinforcement learning", F. Albarrán-Arriagada, J. C. Retamal, E. Solano, L. Lamata, arXiv: 1803.05340, 3/2018

"Quantum Variational Autoencoder", Amir Khoshaman, Walter Vinci, Brandon Denis, Evgeny Andriyash, Mohammad H. Amin, arXiv: 1802.05779, 2/2018

"Learning DNFs under product distributions via μ-biased quantum Fourier sampling", Varun Kanade, Andrea Rocchetto, Simone Severini, arXiv: 1802.05690, 2/2018

"Taking gradients through experiments: LSTMs and memory proximal policy optimization for black-box quantum control", Moritz August, José Miguel Hernández-Lobato, arXiv: 1802.04063, 2/2018

"Leveraging Adiabatic Quantum Computation for Election Forecasting", Maxwell Henderson, John Novak, Tristan Cook, arXiv: 1802.00069, 1/2018

"A Quantum Extension of Variational Bayes Inference", Hideyuki Miyahara, Yuki Sughiyama, arXiv: 1712.04709, 12/2017

"A quantum algorithm to train neural networks using low-depth circuits", Guillaume Verdon, Michael Broughton, Jacob Biamonte, arXiv: 1712.05304, 12/2017

"Hardening Quantum Machine Learning Against Adversaries", Nathan Wiebe, Ram Shankar Siva Kumar, arXiv: 1711.06652, 11/2017

"An efficient quantum algorithm for generative machine learning", Xun Gao, Zhengyu Zhang, Luming Duan, arXiv: 1711.02038, 11/2017

"Learning Hidden Quantum Markov Models", Siddarth Srinivasan, Geoff Gordon, Byron Boots, arXiv: 1710.09016, 10/2017

"Enhanced Quantum Synchronization via Quantum Machine Learning", F. A. Cárdenas-López, M. Sanz, J. C. Retamal, E. Solano, arXiv: 1709.08519, 9/2017

"Generalized Quantum Reinforcement Learning with Quantum Technologies", F. A. Cárdenas-López, L. Lamata, J. C. Retamal, E. Solano, arXiv: 1709.07848, 9/2017

"Quantum Autoencoders via Quantum Adders with Genetic Algorithms", L. Lamata, U. Alvarez-Rodriguez, J. D. Martín-Guerrero, M. Sanz, E. Solano, arXiv: 1709.07409, 9/2017

"Quantum machine learning: a classical perspective", Carlo Ciliberto, Mark Herbster, Alessandro Davide Ialongo, Massimiliano Pontil, Andrea Rocchetto, Simone Severini, Leonard Wossnig, arXiv: 1707.08561, 7/2017

"Experimental Quantum Hamiltonian Learning", Jianwei Wang, Stefano Paesani, Raffaele Santagati, Sebastian Knauer, Antonio A. Gentile, Nathan Wiebe, Maurangelo Petruzzella, Jeremy L. O'Brien, John G. Rarity, Anthony Laing, Mark G. Thompson, arXiv: 1703.05402, 3/2017

"Tomography and Generative Data Modeling via Quantum Boltzmann Training", Maria Kieferova, Nathan Wiebe, arXiv: 1612.05204, 12/2016

"Quantum Machine Learning", Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, Seth Lloyd, arXiv: 1611.09347, 11/2016

"Quantum algorithms for supervised and unsupervised machine learning", Seth Lloyd, Masoud Mohseni, Patrick Rebentrost, arXiv: 1307.0411, 7/2013

"Improved Bounds on Quantum Learning Algorithms", Alp Atici, Rocco A. Servedio, arXiv: quant-ph/0411140, 11/2004

"The geometry of quantum learning", Markus Hunziker, David A. Meyer, Jihun Park, James Pommersheim, Mitch Rothstein, arXiv: quant-ph/0309059, 9/2003

 

Ref: https://physicsml.github.io/pages/papers.html

Dynamic Perspective Of DL

The first one uses the forward dynamic to describe the residual network.

Using Hamilton ODE to approach linearize stable. Approach better result when the number of label data is small.

The ODE which is the continuum limit of the residual net is the characteristics of a transport equation.

 

Ref: http://about.2prime.cn/pde.html (微信群中陆一平-北京大学-数学)

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