A method for storing analog vectors in Hopfield's continuous feedback model is proposed. By analog vectors we mean vectors whose components are real-valued. The vectors to be stored are set as equilibria of the network. The network model consists of one layer of visible neurons and one layer of hidden neurons. We propose a learning algorithm, which results in adjusting the positions of the equilibria, as well as guaranteeing their stability.

We present a novel, modular, recurrent connectionist network architecture which learns to robustly perform incremental parsing of complex sentences. From sequential input, one word at a time, our networks learn to do semantic role assignment, noun phrase attachment, and clause structure recognition for sentences with passive constructions and center embedded clauses. The networks make syntactic and semantic predictions at every point in time, and previous predictions are revised as expectations are affirmed or violated with the arrival of new information. Our networks induce their own "grammar rules" for dynamically transforming an input sequence of words into a syntactic/semantic interpretation. These networks generalize and display tolerance to input which has been corrupted in ways common in spoken language.

Minimization of energy or error functions has proved to be a useful principle in the design and analysis of neural networks and neural algorithms. A brief list of examples include: the back-propagation algorithm, the use of optimization methods in computational vision, the application of analog networks to the approximate solution of NP complete problems and the Hopfield model of associative memory.

Given a set of input-output training samples, we describe a procedure for determining the time sequence of weights for a dynamic neural network to model an arbitrary input-output process. We formulate the input-output mapping problem as an optimal control problem, defining a performance index to be minimized as a function of time-varying weights. We solve the resulting nonlinear two-point-boundary-value problem, and this yields the training rule. For the performance index chosen, this rule turns out to be a continuous time generalization of the outer product rule earlier suggested heuristically by Hopfield for designing associative memories. Learning curves for the new technique are presented.

In this paper we describe the VLSI design and testing of a high capacity associative memory which we call the exponential correlation associative memory (ECAM). The prototype 3J.'-CMOS programmable chip is capable of storing 32 memory patterns of 24 bits each. The high capacity of the ECAM is partly due to the use of special exponentiation neurons, which are implemented via sub-threshold MOS transistors in this design. The prototype chip is capable of performing one associative recall in 3 J.'S.

We introduce a cost function for learning in feed-forward neural networks which is an explicit function of the internal representation in addition to the weights. The learning problem can then be formulated as two simple perceptrons and a search for internal representations. Back-propagation is recovered as a limit. The frequency of successful solutions is better for this algorithm than for back-propagation when weights and hidden units are updated on the same timescale i.e. once every learning step. 1 INTRODUCTION In their review of back-propagation in layered networks, Rumelhart et al. (1986) describe the learning process in terms of finding good "internal representations" of the input patterns on the hidden units. However, the search for these representations is an indirect one, since the variables which are adjusted in its course are the connection weights, not the activations of the hidden units themselves when specific input patterns are fed into the input layer. Rather, the internal representations are represented implicitly in the connection weight values. More recently, Grossman et al. (1988 and 1989)1 suggested a way in which the search for internal representations could be made much more explicit.

Neu.·al Network Analysis of Distributed Representations of Dynamical Sensory-Motor rrransformations in the Leech Shawn R. LockerYt Van Fangt and Terrence J. Sejnowski Computational Neurobiology Laboratory Salk Institute for Biological Studies Box 85800, San Diego, CA 92138 ABSTRACT Interneurons in leech ganglia receive multiple sensory inputs and make synaptic contacts with many motor neurons. These "hidden" units coordinate several different behaviors. We used physiological and anatomical constraints to construct a model of the local bending reflex. Dynamical networks were trained on experimentally derived input-output patterns using recurrent back-propagation. Units in the model were modified to include electrical synapses and multiple synaptic time constants.

We describe a model that can recognize two-dimensional shapes in an unsegmented image, independent of their orientation, position, and scale. The model, called TRAFFIC, efficiently represents the structural relation between an object and each of its component features by encoding the fixed viewpoint-invariant transformation from the feature's reference frame to the object's in the weights of a connectionist network. Using a hierarchy of such transformations, with increasing complexity of features at each successive layer, the network can recognize multiple objects in parallel. An implementation of TRAFFIC is described, along with experimental results demonstrating the network's ability to recognize constellations of stars in a viewpoint-invariant manner. 1 INTRODUCTION A key goal of machine vision is to recognize familiar objects in an unsegmented image, independent of their orientation, position, and scale. Massively parallel models have long been used for lower-level vision tasks, such as primitive feature extraction and stereo depth. Models addressing "higher-level" vision have generally been restricted to pattern matching types of problems, in which much of the inherent complexity of the domain has been eliminated or ignored.

We present two connectionist architectures for chunking of symbolic rewrite rules. One uses backpropagation learning, the other competitive learning. Although they were developed for chunking the same sorts of rules, the two differ in their representational abilities and learning behaviors.

The forward modeling approach is a methodology for learning control when data is available in distal coordinate systems. We extend previous work by considering how this methodology can be applied to the optimization of quantities that are distal not only in space but also in time. In many learning control problems, the output variables of the controller are not the natural coordinates in which to specify tasks and evaluate performance. Tasks are generally more naturally specified in "distal" coordinate systems (e.g., endpoint coordinates for manipulator motion) than in the "proximal" coordinate system of the controller (e.g., joint angles or torques). Furthermore, the relationship between proximal coordinates and distal coordinates is often not known a priori and, if known, not easily inverted. The forward modeling approach is a methodology for learning control when training data is available in distal coordinate systems. A forward model is a network that learns the transformation from proximal to distal coordinates so that distal specifications can be used in training the controller (Jordan & Rumelhart, 1990). The forward model can often be learned separately from the controller because it depends only on the dynamics of the controlled system and not on the closed-loop dynamics. In previous work, we studied forward models of kinematic transformations (Jordan, 1988, 1990) and state transitions (Jordan & Rumelhart, 1990).