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An introduction to RBM
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2012-11-06
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a complement material to bengio's deep machine learning for AI, detailed in restricted botlzman machine.
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Foundations and Trends
R
in
Machine Learning
Vol. 2, No. 1 (2009) 1–127
c
2009 Y. Bengio
DOI: 10.1561/2200000006
Learning Deep Architectures for AI
By Yoshua Bengio
Contents
1 Introduction 2
1.1 How do We Train Deep Architectures? 5
1.2 Intermediate Representations: Sharing Features and
Abstractions Across Tasks 7
1.3 Desiderata for Learning AI 10
1.4 Outline of the Paper 11
2 Theoretical Advantages of Deep Architectures 13
2.1 Computational Complexity 16
2.2 Informal Arguments 18
3 Local vs Non-Local Generalization 21
3.1 The Limits of Matching Local Templates 21
3.2 Learning Distributed Representations 27
4 Neural Networks for Deep Architectures 30
4.1 Multi-Layer Neural Networks 30
4.2 The Challenge of Training Deep Neural Networks 31
4.3 Unsupervised Learning for Deep Architectures 39
4.4 Deep Generative Architectures 40
4.5 Convolutional Neural Networks 43
4.6 Auto-Encoders 45
5 Energy-Based Models and Boltzmann Machines 48
5.1 Energy-Based Models and Products of Experts 48
5.2 Boltzmann Machines 53
5.3 Restricted Boltzmann Machines 55
5.4 Contrastive Divergence 59
6 Greedy Layer-Wise Training of Deep
Architectures 68
6.1 Layer-Wise Training of Deep Belief Networks 68
6.2 Training Stacked Auto-Encoders 71
6.3 Semi-Supervised and Partially Supervised Training 72
7 Variants of RBMs and Auto-Encoders 74
7.1 Sparse Representations in Auto-Encoders
and RBMs 74
7.2 Denoising Auto-Encoders 80
7.3 Lateral Connections 82
7.4 Conditional RBMs and Temporal RBMs 83
7.5 Factored RBMs 85
7.6 Generalizing RBMs and Contrastive Divergence 86
8 Stochastic Variational Bounds for Joint
Optimization of DBN Layers 89
8.1 Unfolding RBMs into Infinite Directed
Belief Networks 90
8.2 Variational Justification of Greedy Layer-wise Training 92
8.3 Joint Unsupervised Training of All the Layers 95
9 Looking Forward 99
9.1 Global Optimization Strategies 99
9.2 Why Unsupervised Learning is Important 105
9.3 Open Questions 106
10 Conclusion 110
Acknowledgments 112
References 113
Foundations and Trends
R
in
Machine Learning
Vol. 2, No. 1 (2009) 1–127
c
2009 Y. Bengio
DOI: 10.1561/2200000006
Learning Deep Architectures for AI
Yoshua Bengio
Dept. IRO, Universit´e de Montr´eal, C.P. 6128, Montreal, Qc, H3C 3J7,
Canada, yoshua.bengio@umontreal.ca
Abstract
Theoretical results suggest that in order to learn the kind of com-
plicated functions that can represent high-level abstractions (e.g., in
vision, language, and other AI-level tasks), one may need deep architec-
tures. Deep architectures are composed of multiple levels of non-linear
operations, such as in neural nets with many hidden layers or in com-
plicated propositional formulae re-using many sub-formulae. Searching
the parameter space of deep architectures is a difficult task, but learning
algorithms such as those for Deep Belief Networks have recently been
proposed to tackle this problem with notable success, beating the state-
of-the-art in certain areas. This monograph discusses the motivations
and principles regarding learning algorithms for deep architectures, in
particular those exploiting as building blocks unsupervised learning of
single-layer models such as Restricted Boltzmann Machines, used to
construct deeper models such as Deep Belief Networks.
1
Introduction
Allowing computers to model our world well enough to exhibit what
we call intelligence has been the focus of more than half a century of
research. To achieve this, it is clear that a large quantity of informa-
tion about our world should somehow be stored, explicitly or implicitly,
in the computer. Because it seems daunting to formalize manually all
that information in a form that computers can use to answer ques-
tions and generalize to new contexts, many researchers have turned
to learning algorithms to capture a large fraction of that information.
Much progress has been made to understand and improve learning
algorithms, but the challenge of artificial intelligence (AI) remains. Do
we have algorithms that can understand scenes and describe them in
natural language? Not really, except in very limited settings. Do we
have algorithms that can infer enough semantic concepts to be able to
interact with most humans using these concepts? No. If we consider
image understanding, one of the best specified of the AI tasks, we real-
ize that we do not yet have learning algorithms that can discover the
many visual and semantic concepts that would seem to be necessary to
interpret most images on the web. The situation is similar for other AI
tasks.
2
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