We have calculated, both analytically and in simulations, the rate of convergence at long times in the backpropagation learning algorithm for networks with and without hidden units. Our basic finding for units using the standard sigmoid transfer function is lit convergence of the error for large t, with at most logarithmic corrections for networks with hidden units. Other transfer functions may lead to a 8lower polynomial rate of convergence. Our analytic calculations were presented in (Tesauro, He & Ahamd, 1989). Here we focus in more detail on our empirical measurements of the convergence rate in numerical simulations, which confirm our analytic results.

This work introduces a new method called Self Organizing Neural Network (SONN) algorithm and compares its performance with Back Propagation in a signal separation application. The problem is to separate two signals; a modem data signal and a male speech signal, added and transmitted through a 4 khz channel. The signals are sampled at 8 khz, and using supervised learning, an attempt is made to reconstruct them. The SONN is an algorithm that constructs its own network topology during training, which is shown to be much smaller than the BP network, faster to trained, and free from the trial-anderror network design that characterize BP. 1. INTRODUCTION The research in Neural Networks has witnessed major changes in algorithm design focus, motivated by the limitations perceived in the algorithms available at the time.

Parallel Distributed Structures Laboratory School of Electrical Engineering Purdue University W. Lafayette, IN. 47907 ChristophSchaefers ABSTRACT This work introduces a new method called Self Organizing Neural Network (SONN) algorithm and compares its performance with Back Propagation in a signal separation application. The problem is to separate two signals; a modem data signal and a male speech signal, added and transmitted through a 4 khz channel. The signals are sampled at8 khz, and using supervised learning, an attempt is made to reconstruct them. The SONN is an algorithm that constructs its own network topology during training, which is shown to be much smaller than the BP network, faster to trained, and free from the trial-anderror networkdesign that characterize BP. 1. INTRODUCTION The research in Neural Networks has witnessed major changes in algorithm design focus, motivated by the limitations perceived in the algorithms available at the time. With the extensive work performed in that last few years using multilayered networks, it was soon discovered that these networks present limitations in tasks The Cocktail Party Problem: 543 that: (a) are difficult to determine problem complexity a priori, and thus design network of the correct size, (b) training not only takes prohibitively long times, but requires a large number of samples as well as fine parameter adjustment, without guarantee of convergence, (c) such networks do not handle the system identification task efficiently for systems whose time varying structure changes radically, and, (d) the trained network is little more than a black box of weights and connections, revealing little about the problem structure; being hard to find the justification for the algorithm weight choice, or an explanation for the output decisions based on an input vector.

In this paper we compare regression and classification systems. A regression system can generate an output f for an input X, where both X and f are continuous and, perhaps, multidimensional. A classification system can generate an output class, C, for an input X, where X is continuous and multidimensional and C is a member of a finite alphabet. The statistical technique of Classification And Regression Trees (CART) was developed during the years 1973 (Meisel and Michalpoulos) through 1984 (Breiman el al).

We have calculated, both analytically and in simulations, the rate of convergence at long times in the backpropagation learning algorithm fornetworks with and without hidden units. Our basic finding for units using the standard sigmoid transfer function is lit convergence of the error for large t, with at most logarithmic corrections fornetworks with hidden units. Other transfer functions may lead to a 8lower polynomial rate of convergence. Our analytic calculations were presented in (Tesauro, He & Ahamd, 1989). Here we focus in more detail on our empirical measurements of the convergence ratein numerical simulations, which confirm our analytic results.

K. Y. Goldberg and B. A. Pearlmutter School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 ABSTRACT Computing the inverse dynamics of a robot ann is an active area of research in the control literature. We hope to learn the inverse dynamics by training a neural network on the measured response of a physical ann. The input to the network is a temporal window of measured positions; output is a vector of torques. We train the network on data measured from the first two joints of the CMU Direct-Drive Arm II as it moves through a randomly-generated sample of "pick-and-place" trajectories. We then test generalization with a new trajectory and compare its output with the torque measured at the physical arm.

A pool of handwritten signatures is used to train a neural network for the task of deciding whether or not a given signature is a forgery. The network is a feedforward net, with a binary image as input. There is a hidden layer, with a single unit output layer. The weights are adjusted according to the backpropagation algorithm. The signatures are entered into a C software program through the use of a Datacopy Electronic Digitizing Camera. The binary signatures are normalized and centered. The performance is examined as a function of the training set and network structure. The best scores are on the order of 2% true signature rejection with 2-4% false signature acceptance.

A pool of handwritten signatures is used to train a neural network for the task of deciding whether or not a given signature is a forgery. The network is a feedforward net, with a binary image as input. There is a hidden layer, with a single unit output layer. The weights are adjusted according to the backpropagation algorithm. The signatures are entered into a C software program through the use of a Datacopy Electronic Digitizing Camera. The binary signatures are normalized and centered. The performance is examined as a function of the training set and network structure. The best scores are on the order of 2% true signature rejection with 2-4% false signature acceptance.

K. Y. Goldberg and B. A. Pearlmutter School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 ABSTRACT Computing the inverse dynamics of a robot ann is an active area of research in the control literature. We hope to learn the inverse dynamics by training a neural network on the measured response of a physical ann. The input to the network is a temporal window of measured positions; output is a vector of torques. We train the network on data measured from the first two joints of the CMU Direct-Drive Arm II as it moves through a randomly-generated sample of "pick-and-place" trajectories. We then test generalization with a new trajectory and compare its output with the torque measured at the physical arm.

K. Y. Goldberg and B. A. Pearlmutter School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 ABSTRACT Computing the inverse dynamics of a robot ann is an active area of research in the control literature. We hope to learn the inverse dynamics by training a neural network on the measured response of a physical ann. The input to the network is a temporal window of measured positions; output is a vector of torques. We train the network on data measured from the first two joints of the CMU Direct-Drive Arm II as it moves through a randomly-generated sample of "pick-and-place" trajectories. We then test generalization with a new trajectory and compare its output with the torque measured at the physical arm.