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34
An Evolutionary Algorithm that Constructs Recurrent Neural Networks
 IEEE Transactions on Neural Networks
, 1994
"... Standard methods for inducing both the structure and weight values of recurrent neural networks fit an assumed class of architectures to every task. This simplification is necessary because the interactions between network structure and function are not well understood. Evolutionary computation, whi ..."
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Cited by 218 (15 self)
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Standard methods for inducing both the structure and weight values of recurrent neural networks fit an assumed class of architectures to every task. This simplification is necessary because the interactions between network structure and function are not well understood. Evolutionary computation, which includes genetic algorithms and evolutionary programming, is a populationbased search method that has shown promise in such complex tasks. This paper argues that genetic algorithms are inappropriate for network acquisition and describes an evolutionary program, called GNARL, that simultaneously acquires both the structure and weights for recurrent networks. This algorithm's empirical acquisition method allows for the emergence of complex behaviors and topologies that are potentially excluded by the artificial architectural constraints imposed in standard network induction methods. To Appear in: IEEE Transactions on Neural Networks January The Ohio State University January 17, 1996 1 ...
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.
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
Distributed Representations and Nested Compositional Structure
, 1994
"... Distributed representations are attractive for a number of reasons. They offer the possibility of representing concepts in a continuous space, they degrade gracefully with noise, and they can be processed in a parallel network of simple processing elements. However, the problem of representing neste ..."
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Cited by 62 (11 self)
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Distributed representations are attractive for a number of reasons. They offer the possibility of representing concepts in a continuous space, they degrade gracefully with noise, and they can be processed in a parallel network of simple processing elements. However, the problem of representing nested structure in distributed representations has been for some time a prominent concern of both proponents and critics of connectionism [Fodor and Pylyshyn 1988; Smolensky 1990; Hinton 1990]. The lack of connectionist representations for complex structure has held back progress in tackling higherlevel cognitive tasks such as language understanding and reasoning. In this thesis I review connectionist representations and propose a method for the distributed representation of nested structure, which I call "Holographic Reduced Representations " (HRRs). HRRs provide an implementation of Hinton's [1990] "reduced descriptions". HRRs use circular convolution to associate atomic items, which are rep...
Extraction of Rules from Discretetime Recurrent Neural Networks
, 1996
"... The extraction of symbolic knowledge from trained neural networks and the direct encoding of (partial) knowledge into networks prior to training are important issues. They allow the exchange of information between symbolic and connectionist knowledge representations. The focas of this paper is on t ..."
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Cited by 61 (15 self)
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The extraction of symbolic knowledge from trained neural networks and the direct encoding of (partial) knowledge into networks prior to training are important issues. They allow the exchange of information between symbolic and connectionist knowledge representations. The focas of this paper is on the quality of the rules that are extracted from recurrent neural networks. Discretetime recurrent neural networks can be trained to correctly classify strings of a regular language. Rules defining the learned grammar can be extracted from networks in the form of deterministic finitestate automata (DFAs) by applying clustering algorithms in the output space of recurrent state neurons. Our algorithm can extract different finitestate automata that are consistent with a training set from the same network. We compare the generalization performances of these different models and the trained network and we introduce a heuristic that permits us to choose among the consistent DFAs the model which best approximates the learned regular grammar.
A framework for combining symbolic and neural learning
, 1992
"... This article describes an approach to combining symbolic and connectionist approaches to machine learning. A threestage framework is presented and the research of several groups is reviewed with respect to this framework. The first stage involves the insertion of symbolic knowledge into neural netw ..."
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Cited by 56 (1 self)
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This article describes an approach to combining symbolic and connectionist approaches to machine learning. A threestage framework is presented and the research of several groups is reviewed with respect to this framework. The first stage involves the insertion of symbolic knowledge into neural networks, the second addresses the refinement of this prior knowledge in its neural representation, while the third concerns the extraction of the refined symbolic knowledge. Experimental results and open research issues are discussed.
Noisy Time Series Prediction using a Recurrent Neural Network and Grammatical Inference
 Machine Learning
, 2001
"... Financial forecasting is an example of a signal processing problem which is challenging due to small sample sizes, high noise, nonstationarity, and nonlinearity. Neural networks have been very successful in a number of signal processing applications. We discuss fundamental limitations and inherent ..."
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Cited by 47 (0 self)
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Financial forecasting is an example of a signal processing problem which is challenging due to small sample sizes, high noise, nonstationarity, and nonlinearity. Neural networks have been very successful in a number of signal processing applications. We discuss fundamental limitations and inherent difficulties when using neural networks for the processing of high noise, small sample size signals. We introduce a new intelligent signal processing method which addresses the difficulties. The method proposed uses conversion into a symbolic representation with a selforganizing map, and grammatical inference with recurrent neural networks. We apply the method to the prediction of daily foreign exchange rates, addressing difficulties with nonstationarity, overfitting, and unequal a priori class probabilities, and we find significant predictability in comprehensive experiments covering 5 different foreign exchange rates. The method correctly predicts the direction of change for th...
A Formal Definition of Intelligence Based on an Intensional Variant of Algorithmic Complexity
 In Proceedings of the International Symposium of Engineering of Intelligent Systems (EIS'98
, 1998
"... Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like lcalculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] ..."
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Cited by 30 (17 self)
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Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like lcalculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] with two remarkable features inherited from its objectoriented coding in C++: it is easily tunable for our needs, and it is efficient. We have made it even more reduced, removing any operand in the instruction set, even for the loop operations. We have only three registers which are AX (the accumulator), BX and CX. The operations Q b we have used for our experiment are in Table 1: LOOPTOP Decrements CX. If it is not equal to the first element jump to the program top.
On the Complexity of Computing and Learning with Multiplicative Neural Networks
 NEURAL COMPUTATION
"... In a great variety of neuron models neural inputs are combined using the summing operation. We introduce the concept of multiplicative neural networks that contain units which multiply their inputs instead of summing them and, thus, allow inputs to interact nonlinearly. The class of multiplicative n ..."
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Cited by 24 (3 self)
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In a great variety of neuron models neural inputs are combined using the summing operation. We introduce the concept of multiplicative neural networks that contain units which multiply their inputs instead of summing them and, thus, allow inputs to interact nonlinearly. The class of multiplicative neural networks comprises such widely known and well studied network types as higherorder networks and product unit networks. We investigate the complexity of computing and learning for multiplicative neural networks. In particular, we derive upper and lower bounds on the VapnikChervonenkis (VC) dimension and the pseudo dimension for various types of networks with multiplicative units. As the most general case, we consider feedforward networks consisting of product and sigmoidal units, showing that their pseudo dimension is bounded from above by a polynomial with the same order of magnitude as the currently best known bound for purely sigmoidal networks. Moreover, we show that this bound holds even in the case when the unit type, product or sigmoidal, may be learned. Crucial for these results are calculations of solution set components bounds for new network classes. As to lower bounds we construct product unit networks of fixed depth with superlinear VC dimension. For sigmoidal networks of higher order we establish polynomial bounds that, in contrast to previous results, do not involve any restriction of the network order. We further consider various classes of higherorder units, also known as sigmapi units, that are characterized by connectivity constraints. In terms of these we derive some asymptotically tight bounds.
Sample Complexity for Learning Recurrent Perceptron Mappings
 IEEE Trans. Inform. Theory
, 1996
"... Recurrent perceptron classifiers generalize the classical perceptron model. They take into account those correlations and dependences among input coordinates which arise from linear digital filtering. This paper provides tight bounds on sample complexity associated to the fitting of such models to e ..."
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Cited by 23 (10 self)
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Recurrent perceptron classifiers generalize the classical perceptron model. They take into account those correlations and dependences among input coordinates which arise from linear digital filtering. This paper provides tight bounds on sample complexity associated to the fitting of such models to experimental data. Keywords: perceptrons, recurrent models, neural networks, learning, VapnikChervonenkis dimension 1 Introduction One of the most popular approaches to binary pattern classification, underlying many statistical techniques, is based on perceptrons or linear discriminants ; see for instance the classical reference [9]. In this context, one is interested in classifying kdimensional input patterns v = (v 1 ; : : : ; v k ) into two disjoint classes A + and A \Gamma . A perceptron P which classifies vectors into A + and A \Gamma is characterized by a vector (of "weights") ~c 2 R k , and operates as follows. One forms the inner product ~c:v = c 1 v 1 + : : : c k v k . I...