Approximate Learning Algorithm in Boltzmann Machines

Boltzmann machines can be regarded as Markov random fields. For binary cases, they are equivalent to the Ising spin model in statistical mechanics. Learning systems in Boltzmann machines are one of the NP-hard problems. Thus, in general we have to use approximate methods to construct practical learning algorithms in this context. In this letter, we propose new and practical learning algorithms for Boltzmann machines by using the belief propagation algorithm and the linear response approximation, which are often referred as advanced mean field methods. Finally, we show the validity of our algorithm using numerical experiments.

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A quantum simulation approach for a three-dimensional Ising spin model—Comparison to mean field theory

AIP Advances ◽

10.1063/1.4983212 ◽

2017 ◽

Vol 7 (5) ◽

pp. 055103

Author(s):

Zhaosen Liu ◽

Orion Ciftja

Keyword(s):

Field Theory ◽

Model Comparison ◽

Mean Field Theory ◽

Mean Field ◽

Three Dimensional ◽

Quantum Simulation ◽

Spin Model ◽

Simulation Approach ◽

Ising Spin

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Learning in Boltzmann Trees

Neural Computation ◽

10.1162/neco.1994.6.6.1174 ◽

1994 ◽

Vol 6 (6) ◽

pp. 1174-1184 ◽

Cited By ~ 15

Author(s):

Lawrence Saul ◽

Michael I. Jordan

Keyword(s):

Supervised Learning ◽

Gradient Descent ◽

Learning Algorithm ◽

Mean Field ◽

Large Family ◽

Weight Space ◽

Hidden Symmetries ◽

Boltzmann Machines ◽

Field Annealing

We introduce a large family of Boltzmann machines that can be trained by standard gradient descent. The networks can have one or more layers of hidden units, with tree-like connectivity. We show how to implement the supervised learning algorithm for these Boltzmann machines exactly, without resort to simulated or mean-field annealing. The stochastic averages that yield the gradients in weight space are computed by the technique of decimation. We present results on the problems of N-bit parity and the detection of hidden symmetries.

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Reinforcement learning using quantum Boltzmann machines

Quantum Information and Computation ◽

10.26421/qic18.1-2-3 ◽

2018 ◽

Vol 18 (1&2) ◽

pp. 51-74 ◽

Cited By ~ 2

Author(s):

Daniel Crawford ◽

Anna Levit ◽

Navid Ghadermarzy ◽

Jaspreet S. Oberoi ◽

Pooya Ronagh

Keyword(s):

Reinforcement Learning ◽

Learning Algorithm ◽

Transverse Field ◽

Boltzmann Machine ◽

Quantum Annealing ◽

Restricted Boltzmann Machines ◽

Boltzmann Machines ◽

Ising Spin ◽

Learning Tasks ◽

Deep Boltzmann Machine

We investigate whether quantum annealers with select chip layouts can outperform classical computers in reinforcement learning tasks. We associate a transverse field Ising spin Hamiltonian with a layout of qubits similar to that of a deep Boltzmann machine (DBM) and use simulated quantum annealing (SQA) to numerically simulate quantum sampling from this system. We design a reinforcement learning algorithm in which the set of visible nodes representing the states and actions of an optimal policy are the first and last layers of the deep network. In absence of a transverse field, our simulations show that DBMs are trained more effectively than restricted Boltzmann machines (RBM) with the same number of nodes. We then develop a framework for training the network as a quantum Boltzmann machine (QBM) in the presence of a significant transverse field for reinforcement learning. This method also outperforms the reinforcement learning method that uses RBMs.

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Efficient Learning in Boltzmann Machines Using Linear Response Theory

Neural Computation ◽

10.1162/089976698300017386 ◽

1998 ◽

Vol 10 (5) ◽

pp. 1137-1156 ◽

Cited By ~ 112

Author(s):

H. J. Kappen ◽

F. B. Rodríguez

Keyword(s):

Computational Complexity ◽

Learning Process ◽

Linear Response ◽

Learning Algorithm ◽

Mean Field Theory ◽

Mean Field ◽

Exact Algorithm ◽

Linear Response Theory ◽

Boltzmann Machines ◽

Efficient Learning

The learning process in Boltzmann machines is computationally very expensive. The computational complexity of the exact algorithm is exponential in the number of neurons. We present a new approximate learning algorithm for Boltzmann machines, based on mean-field theory and the linear response theorem. The computational complexity of the algorithm is cubic in the number of neurons. In the absence of hidden units, we show how the weights can be directly computed from the fixed-point equation of the learning rules. Thus, in this case we do not need to use a gradient descent procedure for the learning process. We show that the solutions of this method are close to the optimal solutions and give a significant improvement when correlations play a significant role. Finally, we apply the method to a pattern completion task and show good performance for networks up to 100 neurons.

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Dynamic mean-field approximation for the random-bond Ising-spin model

Physical Review B ◽

10.1103/physrevb.43.13638 ◽

1991 ◽

Vol 43 (16) ◽

pp. 13638-13640 ◽

Cited By ~ 1

Author(s):

J. C. Lin

Keyword(s):

Mean Field ◽

Field Approximation ◽

Spin Model ◽

Mean Field Approximation ◽

Ising Spin

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A New Learning Algorithm for Mean Field Boltzmann Machines

Artificial Neural Networks — ICANN 2002 - Lecture Notes in Computer Science ◽

10.1007/3-540-46084-5_57 ◽

2002 ◽

pp. 351-357 ◽

Cited By ~ 22

Author(s):

Max Welling ◽

Geoffrey E. Hinton

Keyword(s):

Learning Algorithm ◽

Mean Field ◽

Boltzmann Machines ◽

New Learning

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Intelligent system of English composition scoring model based on improved machine learning algorithm

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-189235 ◽

2020 ◽

pp. 1-11

Author(s):

Jie Liu ◽

Lin Lin ◽

Xiufang Liang

Keyword(s):

Machine Learning ◽

Evaluation System ◽

Intelligent System ◽

Learning Algorithm ◽

Learning Algorithms ◽

Machine Learning Algorithms ◽

Assessment System ◽

English Composition ◽

Region Extraction ◽

Constraint Model

The online English teaching system has certain requirements for the intelligent scoring system, and the most difficult stage of intelligent scoring in the English test is to score the English composition through the intelligent model. In order to improve the intelligence of English composition scoring, based on machine learning algorithms, this study combines intelligent image recognition technology to improve machine learning algorithms, and proposes an improved MSER-based character candidate region extraction algorithm and a convolutional neural network-based pseudo-character region filtering algorithm. In addition, in order to verify whether the algorithm model proposed in this paper meets the requirements of the group text, that is, to verify the feasibility of the algorithm, the performance of the model proposed in this study is analyzed through design experiments. Moreover, the basic conditions for composition scoring are input into the model as a constraint model. The research results show that the algorithm proposed in this paper has a certain practical effect, and it can be applied to the English assessment system and the online assessment system of the homework evaluation system algorithm system.

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