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 arbitrary-length 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 NP-Hard problem, the architecture does appear capable of generating non-regular languages by exploiting fractal and chaotic dynamics. I end the paper with a hypothesis relating linguistic generative capacity to the behavioral regimes of non-linear dynamical systems.

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 population-based 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 ...

This paper discusses how a behavior-based 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 self-organized 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

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. Discrete-time 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 finite-state automata (DFAs) by applying clustering algorithms in the output space of recurrent state neurons. Our algorithm can extract different finite-state 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.

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 higher-level 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...

This article describes an approach to combining symbolic and connectionist approaches to machine learning. A three-stage 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.

Financial forecasting is an example of a signal processing problem which is challenging due to small sample sizes, high noise, non-stationarity, and non-linearity. 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 non-stationarity, 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...

Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in particular when time is a relevant parameter. This paper provides lower and upper bounds for the VC dimension of such networks. Several types of activation functions are discussed, including threshold, polynomial, piecewisepolynomial and sigmoidal functions. The bounds depend on two independent parameters: the number w of weights in the network, and the length k of the input sequence. In contrast, for feedforward networks, VC dimension bounds can be expressed as a function of w only. An important difference between recurrent and feedforward nets is that a fixed recurrent net can receive inputs of arbitrary length. Therefore we are particularly interested in the case k AE w. Ignoring multiplicative constants, the main results say roughly the following: ffl For architectures with activation oe = a...

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, Vapnik-Chervonenkis 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 k-dimensional 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...

One of the issues in any learning model is how it scales with problem size. The problem of learning finite state machine (FSMs) from examples with recurrent neural networks has been extensively explored. However, these results are somewhat disappointing in the sense that the machines that can be learned are too small to be competitive with existing grammatical inference algorithms. We show that a type of recurrent neural network (Narendra & Parthasarathy, 1990, IEEE Trans. Neural Networks, 1, 4-27) which has feedback but no hidden state neurons can learn a special type of FSM called a finite memory machine (FMM) under certain constraints. These machines have a large number of states (simulations are for 256 and 512 state FMMs) but have minimal order, relatively small depth and little logic when the FMM is implemented as a sequential machine,