An alternative to the typical technique of selecting training examples independently from a fixed distribution is fonnulated and analyzed, in which the current example is presented repeatedly until the error for that item is reduced to some criterion value,; then, another item is randomly selected. The convergence time can be dramatically increased or decreased by this heuristic, depending on the task, and is very sensitive to the value of .

A method for transforming performance evaluation signals distal both in space and time into proximal signals usable by supervised learning algorithms, presented in [Jordan & Jacobs 90], is examined. A simple observation concerning differentiation through models trained with redundant inputs (as one of their networks is) explains a weakness in the original architecture and suggests a modification: an internal world model that encodes action-space exploration and, crucially, cancels input redundancy to the forward model is added. Learning time on an example task, cartpole balancing, is thereby reduced about 50 to 100 times. 1 INTRODUCTION In many learning control problems, the evaluation used to modify (and thus improve) control may not be available in terms of the controller's output: instead, it may be in terms of a spatial transformation of the controller's output variables (in which case we shall term it as being "distal in space"), or it may be available only several time steps into the future (termed as being "distal in time"). For example, control of a robot arm may be exerted in terms of joint angles, while evaluation may be in terms of the endpoint cartesian coordinates; furthermore, we may only wish to evaluate the endpoint coordinates reached after a certain period of time: the co- ·Current address: Computation and Neural Systems Program, California Institute of Technology, Pasadena CA.

Three methods for improving the performance of (gaussian) radial basis function (RBF) networks were tested on the NETtaik task. In RBF, a new example is classified by computing its Euclidean distance to a set of centers chosen by unsupervised methods. The application of supervised learning to learn a non-Euclidean distance metric was found to reduce the error rate of RBF networks, while supervised learning of each center's variance resultedin inferior performance. The best improvement in accuracy was achieved by networks called generalized radial basis function (GRBF) networks. In GRBF, the center locations are determined by supervised learning. After training on 1000 words, RBF classifies 56.5% of letters correct, while GRBF scores 73.4% letters correct (on a separate test set). From these and other experiments, we conclude that supervised learning of center locations can be very important for radial basis function learning.

An alternative to the typical technique of selecting training examples independently from a fixed distribution is fonnulated and analyzed, in which the current example is presented repeatedly until the error for that item is reduced to some criterion value,; then, another item is randomly selected.The convergence time can be dramatically increased or decreased by this heuristic, depending on the task, and is very sensitive to the value of .

A method for transforming performance evaluation signals distal both in space and time into proximal signals usable by supervised learning algorithms, presentedin [Jordan & Jacobs 90], is examined. A simple observation concerning differentiation through models trained with redundant inputs (as one of their networks is) explains a weakness in the original architecture and suggests a modification: an internal world model that encodes action-space exploration and, crucially, cancels input redundancy to the forward model is added. Learning time on an example task, cartpole balancing,is thereby reduced about 50 to 100 times. 1 INTRODUCTION In many learning control problems, the evaluation used to modify (and thus improve) controlmay not be available in terms of the controller's output: instead, it may be in terms of a spatial transformation of the controller's output variables (in which case we shall term it as being "distal in space"), or it may be available only several time steps into the future (termed as being "distal in time"). For example, control of a robot arm may be exerted in terms of joint angles, while evaluation may be in terms of the endpoint cartesian coordinates; furthermore, we may only wish to evaluate the endpoint coordinates reached after a certain period of time: the co- ·Current address: Computation and Neural Systems Program, California Institute of Technology, Pasadena CA. 563 564 Brody ordinatesreached at the end of some motion, for instance. In such cases, supervised learning methods are not directly applicable, and other techniques must be used. Here we study one such technique (proposed for cases where the evaluation is distal in both space and time by [Jordan & Jacobs 90)), analyse a source of its problems, and propose a simple solution for them which leads to fast, efficient learning. We first describe two methods, and then combine them into the "predictive forward modeling" technique with which we are concerned.

A massively parallel, all-digital, stochastic architecture - TlnMAN N - is described which performs competitive and Kohonen types of learning. A VLSI design is shown for a TlnMANN neuron which fits within a small, inexpensive MOSIS TinyChip frame, yet which can be used to build larger networks of several hundred neurons. The neuron operates at a speed of 15 MHz which allows the network to process 290,000 training examples per second. Use of level sensitive scan logic provides the chip with 100% fault coverage, permitting very reliable neural systems to be built.

Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.

We describe the application of a hybrid symbolic/connectionist machine learning algorithm to the task of recognizing important genetic sequences.

Recurrent Cascade-Correlation CRCC) is a recurrent version of the Cascade Correlation learning architecture of Fah I man and Lebiere [Fahlman, 1990]. RCC can learn from examples to map a sequence of inputs into a desired sequence of outputs. New hidden units with recurrent connections are added to the network as needed during training. In effect, the network builds up a finite-state machine tailored specifically for the current problem. RCC retains the advantages of Cascade-Correlation: fast learning, good generalization, automatic construction of a near-minimal multi-layered network, and incremental training. Initially the network contains only inputs, output units, and the connections between them.

A massively parallel, all-digital, stochastic architecture - TlnMAN N - is described which performs competitive and Kohonen types of learning. A VLSI design is shown for a TlnMANN neuron which fits within a small, inexpensive MOSIS TinyChip frame, yet which can be used to build larger networks of several hundred neurons. The neuron operates at a speed of 15 MHz which allows the network to process 290,000 training examples per second. Use of level sensitive scan logic provides the chip with 100% fault coverage, permitting very reliable neural systems to be built.