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108
The induction of dynamical recognizers
 Machine Learning
, 1991
"... A higher order recurrent neural network architecture learns to recognize and generate languages after being "trained " on categorized exemplars. Studying these networks from the perspective of dynamical systems yields two interesting discoveries: First, a longitudinal examination of the learning pro ..."
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Cited by 214 (16 self)
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A higher order recurrent neural network architecture learns to recognize and generate languages after being "trained " on categorized exemplars. Studying these networks from the perspective of dynamical systems yields two interesting discoveries: First, a longitudinal examination of the learning process illustrates a new form of mechanical inference: Induction by phase transition. A small weight adjustment causes a "bifurcation" in the limit behavior of the network. This phase transition corresponds to the onset of the network’s capacity for generalizing to arbitrarylength strings. Second, a study of the automata resulting from the acquisition of previously published training sets indicates that while the architecture is not guaranteed to find a minimal finite automaton consistent with the given exemplars, which is an NPHard problem, the architecture does appear capable of generating nonregular languages by exploiting fractal and chaotic dynamics. I end the paper with a hypothesis relating linguistic generative capacity to the behavioral regimes of nonlinear dynamical systems.
Learning Machines
, 1965
"... This book is about machines that learn to discover hidden relationships in data. A constant sfream of data bombards our senses and millions of sensory channels carry information into our brains. Brains are also learning machines that condition, ..."
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Cited by 150 (0 self)
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This book is about machines that learn to discover hidden relationships in data. A constant sfream of data bombards our senses and millions of sensory channels carry information into our brains. Brains are also learning machines that condition,
KnowledgeBased Artificial Neural Networks
, 1994
"... Hybrid learning methods use theoretical knowledge of a domain and a set of classified examples to develop a method for accurately classifying examples not seen during training. The challenge of hybrid learning systems is to use the information provided by one source of information to offset informat ..."
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Cited by 145 (13 self)
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Hybrid learning methods use theoretical knowledge of a domain and a set of classified examples to develop a method for accurately classifying examples not seen during training. The challenge of hybrid learning systems is to use the information provided by one source of information to offset information missing from the other source. By so doing, a hybrid learning system should learn more effectively than systems that use only one of the information sources. KBANN(KnowledgeBased Artificial Neural Networks) is a hybrid learning system built on top of connectionist learning techniques. It maps problemspecific "domain theories", represented in propositional logic, into neural networks and then refines this reformulated knowledge using backpropagation. KBANN is evaluated by extensive empirical tests on two problems from molecular biology. Among other results, these tests show that the networks created by KBANN generalize better than a wide variety of learning systems, as well as several t...
Gradient calculation for dynamic recurrent neural networks: a survey
 IEEE Transactions on Neural Networks
, 1995
"... Abstract  We survey learning algorithms for recurrent neural networks with hidden units, and put the various techniques into a common framework. We discuss xedpoint learning algorithms, namely recurrent backpropagation and deterministic Boltzmann Machines, and non xedpoint algorithms, namely backp ..."
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Cited by 135 (3 self)
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Abstract  We survey learning algorithms for recurrent neural networks with hidden units, and put the various techniques into a common framework. We discuss xedpoint learning algorithms, namely recurrent backpropagation and deterministic Boltzmann Machines, and non xedpoint algorithms, namely backpropagation through time, Elman's history cuto, and Jordan's output feedback architecture. Forward propagation, an online technique that uses adjoint equations, and variations thereof, are also discussed. In many cases, the uni ed presentation leads to generalizations of various sorts. We discuss advantages and disadvantages of temporally continuous neural networks in contrast to clocked ones, continue with some \tricks of the trade" for training, using, and simulating continuous time and recurrent neural networks. We present somesimulations, and at the end, address issues of computational complexity and learning speed.
GradientBased Learning Algorithms for Recurrent Networks and Their Computational Complexity
, 1995
"... Introduction 1.1 Learning in Recurrent Networks Connectionist networks having feedback connections are interesting for a number of reasons. Biological neural networks are highly recurrently connected, and many authors have studied recurrent network models of various types of perceptual and memory pr ..."
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Cited by 115 (4 self)
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Introduction 1.1 Learning in Recurrent Networks Connectionist networks having feedback connections are interesting for a number of reasons. Biological neural networks are highly recurrently connected, and many authors have studied recurrent network models of various types of perceptual and memory processes. The general property making such networks interesting and potentially useful is that they manifest highly nonlinear dynamical behavior. One such type of dynamical behavior that has received much attention is that of settling to a fixed stable state, but probably of greater importance both biologically and from an engineering viewpoint are timevarying behaviors. Here we consider algorithms for training recurrent networks to perform temporal supervised learning tasks, in which the specification of desired behavior is in the form of specific examples of input and desired output trajectories. One example of such a task is sequence classification, where
Biologically Plausible Errordriven Learning using Local Activation Differences: The Generalized Recirculation Algorithm
 NEURAL COMPUTATION
, 1996
"... The error backpropagation learning algorithm (BP) is generally considered biologically implausible because it does not use locally available, activationbased variables. A version of BP that can be computed locally using bidirectional activation recirculation (Hinton & McClelland, 1988) instead of ..."
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Cited by 94 (10 self)
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The error backpropagation learning algorithm (BP) is generally considered biologically implausible because it does not use locally available, activationbased variables. A version of BP that can be computed locally using bidirectional activation recirculation (Hinton & McClelland, 1988) instead of backpropagated error derivatives is more biologically plausible. This paper presents a generalized version of the recirculation algorithm (GeneRec), which overcomes several limitations of the earlier algorithm by using a generic recurrent network with sigmoidal units that can learn arbitrary input/output mappings. However, the contrastiveHebbian learning algorithm (CHL, a.k.a. DBM or mean field learning) also uses local variables to perform errordriven learning in a sigmoidal recurrent network. CHL was derived in a stochastic framework (the Boltzmann machine), but has been extended to the deterministic case in various ways, all of which rely on problematic approximationsand assumptions, le...
Modelbased Learning for Mobile Robot Navigation from the Dynamical Systems Perspective
 IEEE Transactions on Systems, Man, and Cybernetics
, 1996
"... This paper discusses how a behaviorbased robot can construct a “symbolic process” that accounts for its deliberative thinking processes using models of the environment. The paper focuses on two essential problems; one is the symbol grounding problem and the other is how the internal symbolic proces ..."
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Cited by 80 (20 self)
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This paper discusses how a behaviorbased robot can construct a “symbolic process” that accounts for its deliberative thinking processes using models of the environment. The paper focuses on two essential problems; one is the symbol grounding problem and the other is how the internal symbolic processes can be situated with respect to the behavioral contexts. We investigate these problems by applying a dynamical system’s approach to the robot navigation learning problem. Our formulation, based on a forward modeling scheme using recurrent neural learning, shows that the robot is capable of learning grammatical structure hidden in the geometry of the workspace from the local sensory inputs through its navigational experiences. Furthermore, the robot is capable of generating diverse action plans to reach an arbitrary goal using the acquired forward model which incorporates chaotic dynamics. The essential claim is that the internal symbolic process, being embedded in the attractor, is grounded since it is selforganized solely through interaction with the physical world. It is also shown that structural stability arises in the interaction between the neural dynamics and the environmental dynamics, which accounts for the situatedness of the internal symbolic process. The experimental results using a mobile robot, equipped with a local sensor consisting of a laser range finder, verify our claims. 1 1
On The Problem Of Local Minima In Backpropagation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1992
"... Supervised Learning in MultiLayered Neural Networks (MLNs) has been recently proposed through the wellknown Backpropagation algorithm. This is a gradient method which can get stuck in local minima, as simple examples can show. In this paper, some conditions on the network architecture and the lear ..."
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Cited by 72 (17 self)
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Supervised Learning in MultiLayered Neural Networks (MLNs) has been recently proposed through the wellknown Backpropagation algorithm. This is a gradient method which can get stuck in local minima, as simple examples can show. In this paper, some conditions on the network architecture and the learning environment are proposed which ensure the convergence of the Backpropagation algorithm. It is proven in particular that the convergence holds if the classes are linearlyseparable. In this case, the experience gained in several experiments shows that MLNs exceed perceptrons in generalization to new examples. Index Terms MultiLayered Networks, learning environment, Backpropagation, pattern recognition, linearlyseparable classes. I. Introduction Supervised learning in MultiLayered Networks can be accomplished thanks to Backpropagation (BP ) ([19, 25, 31]). Its application to several different subjects [25], and, particularly, to pattern recognition ([3, 6, 8, 20, 27, 29]), has bee...
Fast Exact Multiplication by the Hessian
 Neural Computation
, 1994
"... Just storing the Hessian H (the matrix of second derivatives d^2 E/dw_i dw_j of the error E with respect to each pair of weights) of a large neural network is difficult. Since a common use of a large matrix like H is to compute its product with various vectors, we derive a technique that directly ca ..."
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Cited by 70 (4 self)
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Just storing the Hessian H (the matrix of second derivatives d^2 E/dw_i dw_j of the error E with respect to each pair of weights) of a large neural network is difficult. Since a common use of a large matrix like H is to compute its product with various vectors, we derive a technique that directly calculates Hv, where v is an arbitrary vector. This allows H to be treated as a generalized sparse matrix. To calculate Hv, we first define a differential operator R{f(w)} = (d/dr)f(w + rv)_{r=0}, note that R{grad_w} = Hv and R{w} = v, and then apply R{} to the equations used to compute grad_w. The result is an exact and numerically stable procedure for computing Hv, which takes about as much computation, and is about as local, as a gradient evaluation. We then apply the technique to backpropagation networks, recurrent backpropagation, and stochastic Boltzmann Machines. Finally, we show that this technique can be used at the heart of many iterative techniques for computing various properties of H, obviating the need for direct methods.
Extracting Comprehensible Models from Trained Neural Networks
, 1996
"... To Mom, Dad, and Susan, for their support and encouragement. ..."
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Cited by 69 (4 self)
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To Mom, Dad, and Susan, for their support and encouragement.