A learning algorithm for boltzmann machines
TL;DR: A general parallel search method is described, based on statistical mechanics, and it is shown how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge about a task domain in an efficient way.
About: This article is published in Cognitive Science.The article was published on 1985-01-01 and is currently open access. It has received 3727 citations till now. The article focuses on the topics: Massively parallel & Boltzmann machine.
Citations
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01 Jan 1998
TL;DR: In this article, a graph transformer network (GTN) is proposed for handwritten character recognition, which can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters.
Abstract: Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient based learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of 2D shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation recognition, and language modeling. A new learning paradigm, called graph transformer networks (GTN), allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure. Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training, and the flexibility of graph transformer networks. A graph transformer network for reading a bank cheque is also described. It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal cheques. It is deployed commercially and reads several million cheques per day.
42,067 citations
Book•
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TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.
38,208 citations
01 Jan 1988
TL;DR: This chapter contains sections titled: The Problem, The Generalized Delta Rule, Simulation Results, Some Further Generalizations, Conclusion.
Abstract: This chapter contains sections titled: The Problem, The Generalized Delta Rule, Simulation Results, Some Further Generalizations, Conclusion
17,604 citations
TL;DR: The chapter discusses two important directions of research to improve learning algorithms: the dynamic node generation, which is used by the cascade correlation algorithm; and designing learning algorithms where the choice of parameters is not an issue.
Abstract: Publisher Summary This chapter provides an account of different neural network architectures for pattern recognition. A neural network consists of several simple processing elements called neurons. Each neuron is connected to some other neurons and possibly to the input nodes. Neural networks provide a simple computing paradigm to perform complex recognition tasks in real time. The chapter categorizes neural networks into three types: single-layer networks, multilayer feedforward networks, and feedback networks. It discusses the gradient descent and the relaxation method as the two underlying mathematical themes for deriving learning algorithms. A lot of research activity is centered on learning algorithms because of their fundamental importance in neural networks. The chapter discusses two important directions of research to improve learning algorithms: the dynamic node generation, which is used by the cascade correlation algorithm; and designing learning algorithms where the choice of parameters is not an issue. It closes with the discussion of performance and implementation issues.
13,033 citations
Book•
24 Aug 2012
TL;DR: This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach, and is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.
Abstract: Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.
8,059 citations
Cites methods from "A learning algorithm for boltzmann ..."
...This algorithm was first proposed in (Ackley et al. 1985)....
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...For example, the Boltzmann machine (Ackley et al. 1985) is a pairwise MRF with hidden nodes h and visible nodes v, as shown in Figure 27....
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References
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TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Abstract: There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
41,772 citations
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Abstract: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.
35,161 citations
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Abstract: We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.
18,761 citations
"A learning algorithm for boltzmann ..." refers background or methods in this paper
...CONCLUSION The application of statistical mechanics to constraint satisfaction searches in parallel networks is a promising new area that has been discovered independently by several other groups (Geman & Geman, 1983; Smolensky, 1983)....
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... Feldman and Ballard (1982) present sketches of two implementations for this task; using the example of the transmission of the concept “wormy apple” from where it is recognized in the perceptual system to where the phrase “wormy apple” can be generated by the speech system....
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...terns ( Feldman & Ballard, 1982; Hinton & Anderson, 1981) that store their...
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...Some of these issues are discussed in greater detail elsewhere: Hinton and Sejnowski (1983b) and Geman and Geman (1983) describe the relation to Bayesian inference and to more conventional relaxation techniques; Fahlman, Hinton, and Sejnowski (1983) compare Boltzmann machines with some alternative…...
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...The individual units stand for “hypotheses,” but what is the relationship between these hypotheses and the kinds of concepts for which we have words? Some workers suggest that a concept should be represented in an essentially “local” fashion: The activation of one or a few computing units is the representation for a concept ( Feldman & Ballard, 1982 ); while others view concepts as “distributed” entities: A particular pattern of activity ......
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TL;DR: A model of a system having a large number of simple equivalent components, based on aspects of neurobiology but readily adapted to integrated circuits, produces a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size.
Abstract: Computational properties of use of biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.
16,652 citations
"A learning algorithm for boltzmann ..." refers background in this paper
...If hardware units make their decisions asynchronously, and if transmission times are negligible, then the system always settles into a local energy minimum (Hopfield, 1982)....
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...If hardware units make their decisions asynchronously, and if transmission times are negligible, then the system always settles into a local energy minimum ( Hopfield, 1982 )....
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...The resulting structure is related to a system described by Hopfield (1982), and as in his system, each global state of the network can be assigned a single number called the “energy” of that state....
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Book•
01 Jun 1972TL;DR: The aim of the book is to advance the understanding of how humans think by putting forth a theory of human problem solving, along with a body of empirical evidence that permits assessment of the theory.
Abstract: : The aim of the book is to advance the understanding of how humans think. It seeks to do so by putting forth a theory of human problem solving, along with a body of empirical evidence that permits assessment of the theory. (Author)
10,770 citations