Armando Manduca Dept. of Physiology and Biophysics Mayo Clinic Rochester, MN 55905 PaulChristy Dept. of Diagnostic Radiology Mayo Clinic Rochester, MN 55905 Richard Ehman Dept. of Diagnostic Radiology Mayo Clinic Rochester, MN 55905 Abstract Avascular necrosis (AVN) of the femoral head is a common yet potentially seriousdisorder which can be detected in its very early stages with magnetic resonance imaging. We have developed multi-layer perceptron networks, trained with conjugate gradient optimization, which diagnose AVN from single magnetic resonance images of the femoral head with 100% accuracy on training data and 97% accuracy on test data. 1 INTRODUCTION Diagnostic radiology may be a very natural field of application for neural networks, since a simple answer is desired from a complex image, and the learning process that human experts undergo is to a large extent a supervised learning experience based on looking at large numbers of images with known interpretations. Although many workers have applied neural nets to various types of I-dimensional medical data (e.g. ECG and EEG waveforms), little work has been done on applying neural nets to diagnosis directly from medical images. We chose the diagnosis of avascular necrosis from magnetic resonance images as an ideal initial problem, because: the area in question is small and well-defined, its size and shape do not vary greatly between individuals, the condition (if present) is usually visible even at low spatial and gray level resolution on a single image, and real data is readily available.

Connections between spline approximation, approximation with rational functions, and feedforward neural networks are studied. The potential improvement in the degree of approximation in going from single to two hidden layer networks is examined. Some results of Birman and Solomjak regarding the degree of approximation achievable when knot positions are chosen on the basis of the probability distribution of examples rather than the function values are extended.

A CCD-based processor that we call the NNC2 is presented. The NNC2 implements a fully connected 192-input, 32-output two-layer network and can be cascaded to form multilayer networks or used in parallel for additional inputor output nodes. The device computes 1.92 x 10

This paper applies the theory of Probably Approximately Correct (PAC) learning to multiple output feedforward threshold networks in which the weights conform to certain equivalences. It is shown that the sample size for reliable learning can be bounded above by a formula similar to that required for single output networks with no equivalences. The best previously obtainedbounds are improved for all cases.

Biological retinas extract spatial and temporal features in an attempt to reduce the complexity of performing visual tasks. We have built and tested a silicon retina which encodes several useful temporal features found in vertebrate retinas.The cells in our silicon retina are selective to direction, highly sensitive to positive contrast changes around an ambient light level, and tuned to a particular velocity. Inhibitory connections in the null direction performthe direction selectivity we desire. This silicon retina is on a 4.6 x 6.8mm die and consists of a 47 x 41 array of photoreceptors.

Networks for reconstructing a sparse or noisy function often use an edge field to segment the function into homogeneous regions, This approach assumes that these regions do not overlap or have disjoint parts, which is often false. For example, images which contain regions split by an occluding objectcan't be properly reconstructed using this type of network. We have developed a network that overcomes these limitations, using support maps to represent the segmentation of a signal. In our approach, the support ofeach region in the signal is explicitly represented. Results from an initial implementation demonstrate that this method can reconstruct images and motion sequences which contain complicated occlusion.

In this work, the problem of establishing routes through random MINs (RMINs) in a shared-memory, distributed computing system is addressed.

This paper considers the problem of expressing predicate calculus in connectionist networksthat are based on energy minimization. Given a firstorder-logic knowledgebase and a bound k, a symmetric network is constructed (like a Boltzman machine or a Hopfield network) that searches for a proof for a given query. If a resolution-based proof of length no longer than k exists, then the global minima of the energy function that is associated with the network represent such proofs. The network that is generated is of size cubic in the bound k and linear in the knowledge size. There are no restrictions on the type of logic formulas that can be represented.

Feedforward networks composed of units which compute a sigmoidal function ofa weighted sum of their inputs have been much investigated. We tested the approximation and estimation capabilities of networks using functions more complex than sigmoids. Three classes of functions were tested: polynomials, rational functions, and flexible Fourier series. Unlike sigmoids,these classes can fit nonmonotonic functions. They were compared on three problems: prediction of Boston housing prices, the sunspot count, and robot arm inverse dynamics. The complex units attained clearlysuperior performance on the robot arm problem, which is a highly nonmonotonic, pure approximation problem. On the noisy and only mildly nonlinear Boston housing and sunspot problems, differences among the complex units were revealed; polynomials did poorly, whereas rationals and flexible Fourier series were comparable to sigmoids. 1 Introduction

This is an extension of previous work on recognizing isolated digits.