We propose a model of the development of geometric reasoning in children that explicitly involves learning. The model uses a neural network that is initialized with an understanding of geometry similar to that of second-grade children. Through the presentation of a series of examples, the model is shown to develop an understanding of geometry similar to that of fifth-grade children who were trained using similar materials.

Neural network models have been criticized for their inability to make use of compositional representations. In this paper, we describe a series of psychological phenomena that demonstrate the role of structured representations in cognition. These findings suggest that people compare relational representations via a process of structural alignment. This process will have to be captured by any model of cognition, symbolic or subsymbolic.

We describe two successfully working, analog VLSI vision circuits that move beyond pixel-based early vision algorithms. One circuit, implementing the dynamic wires model, provides for dedicated lines of communication among groups of pixels that share a common property. The chip uses the dynamic wires model to compute the arclength of visual contours. Another circuit labels all points inside a given contour with one voltage and all other with another voltage. Its behavior is very robust, since small breaks in contours are automatically sealed, providing for Figure-Ground segregation in a noisy environment. Both chips are implemented using networks of resistors and switches and represent a step towards object level processing since a single voltage value encodes the property of an ensemble of pixels.

Networks with local inhibition are shown to have enhanced computational performance with respect to the classical Hopfield-like networks. In particular the critical capacity of the network is increased as well as its capability to store correlated patterns. Chaotic dynamic behaviour (exponentially long transients) of the devices indicates the overloading of the associative memory. An implementation based on a programmable logic device is here presented. A 16 neurons circuit is implemented whit a XILINK 4020 device.

The implementation uses noise injection and multiplicative correlation to estimate derivatives, as in [Anderson, Kerns 92]. One intended application of this technique is setting circuit parameters on-chip automatically, rather than manually [Kirk 91]. Gradient descent optimization may be used to adjust synapse weights for a backpropagation or other on-chip learning implementation. The approach combines the features of continuous multidimensional gradient descent and the potential for an annealing style of optimization. We present data measured from our analog VLSI implementation. 1 Introduction This work is similar to [Anderson, Kerns 92], but represents two advances. First, we describe the extension of the technique to multiple dimensions. Second, we demonstrate an implementation of the multidimensional technique in analog VLSI, and provide results measured from the chip. Unlike previous work using noise sources in adaptive systems, we use the noise as a means of estimating the gradient of a function f(y), rather than performing an annealing process [Alspector 88]. We also estimate gr-;:dients continuously in position and time, in contrast to [Umminger 89] and [J abri 91], which utilize discrete position gradient estimates.

The real time computation of motion from real images using a single chip with integrated sensors is a hard problem. We present two analog VLSI schemes that use pulse domain neuromorphic circuits to compute motion. Pulses of variable width, rather than graded potentials, represent a natural medium for evaluating temporal relationships.

We have designed, fabricated, and tested an analog VLSI chip which computes radial basis functions in parallel. We have developed a synapse circuit that approximates a quadratic function. We aggregate these circuits to form radial basis functions. These radial basis functions are then averaged together using a follower aggregator.

The planar thallium-201 myocardial perfusion scintigram is a widely used diagnostic technique for detecting and estimating the risk of coronary artery disease. Neural networks learned to interpret 100 thallium scintigrams as determined by individual expert ratings. Standard error backpropagation was compared to standard LMS, and LMS combined with one layer of RBF units. Using the "leave-one-out" method, generalization was tested on all 100 cases. Training time was determined automatically from cross-validation perfonnance. Best perfonnance was attained by the RBF/LMS network with three hidden units per view and compares favorably with human experts.

Hidden Markov Models (HMMs) can be applied to several important problems in molecular biology. We introduce a new convergent learning algorithm for HMMs that, unlike the classical Baum-Welch algorithm is smooth and can be applied online or in batch mode, with or without the usual Viterbi most likely path approximation. Left-right HMMs with insertion and deletion states are then trained to represent several protein families including immunoglobulins and kinases. In all cases, the models derived capture all the important statistical properties of the families and can be used efficiently in a number of important tasks such as multiple alignment, motif detection, and classification.

Our efforts proceed in the context of a problem suggested by the operational needs of a particular electric utility to make daily forecasts of short-term load or demand. Forecasts are made at midday (1 p.m.) on a weekday t ( Monday - Thursday), for the next evening peak e(t) (occuring usually about 8 p.m. in the winter), the daily minimum d(t