An analogue VLSI neural network has been designed and tested to perform cardiac morphology classification tasks. Analogue techniques were chosen to meet the strict power and area requirements of an Implantable Cardioverter Defibrillator (ICD) system. The robustness of the neural network architecture reduces the impact of noise, drift and offsets inherent in analogue approaches. The network is a 10:6:3 multi-layer percept ron with on chip digital weight storage, a bucket brigade input to feed the Intracardiac Electrogram (ICEG) to the network and has a winner take all circuit at the output. The network was trained in loop and included a commercial ICD in the signal processing path. The system has successfully distinguished arrhythmia for different patients with better than 90% true positive and true negative detections for dangerous rhythms which cannot be detected by present ICDs. The chip was implemented in 1.2um CMOS and consumes less than 200n W maximum average power in an area of 2.2 x 2.2mm2.

An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebb-like learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994), this model has no parameters which change over time and is able to continue learning, adding units and connections, until a performance criterion has been met. Applications of the model include vector quantization, clustering, and interpolation.

The TNM staging system has been used since the early 1960's to predict breast cancer patient outcome. In an attempt to increase prognostic accuracy, many putative prognostic factors have been identified. Because the TNM stage model can not accommodate these new factors, the proliferation of factors in breast cancer has lead to clinical confusion. What is required is a new computerized prognostic system that can test putative prognostic factors and integrate the predictive factors with the TNM variables in order to increase prognostic accuracy. Using the area under the curve of the receiver operating characteristic, we compare the accuracy of the following predictive models in terms of five year breast cancer-specific survival: pTNM staging system, principal component analysis, classification and regression trees, logistic regression, cascade correlation neural network, conjugate gradient descent neural, probabilistic neural network, and backpropagation neural network. Several statistical models are significantly more ac- 1064 Harry B. Burke, David B. Rosen, Philip H. Goodman

We present a new algorithm for finding low complexity networks with high generalization capability. The algorithm searches for large connected regions of so-called ''fiat'' minima of the error function. In the weight-space environment of a "flat" minimum, the error remains approximately constant. Using an MDL-based argument, flat minima can be shown to correspond to low expected overfitting. Although our algorithm requires the computation of second order derivatives, it has backprop's order of complexity. Experiments with feedforward and recurrent nets are described. In an application to stock market prediction, the method outperforms conventional backprop, weight decay, and "optimal brain surgeon".

Although artificial neural networks have been applied in a variety of real-world scenarios with remarkable success, they have often been criticized for exhibiting a low degree of human comprehensibility. Techniques that compile compact sets of symbolic rules out of artificial neural networks offer a promising perspective to overcome this obvious deficiency of neural network representations. This paper presents an approach to the extraction of if-then rules from artificial neural networks. Its key mechanism is validity interval analysis, which is a generic tool for extracting symbolic knowledge by propagating rule-like knowledge through Backpropagation-style neural networks. Empirical studies in a robot arm domain illustrate the appropriateness of the proposed method for extracting rules from networks with real-valued and distributed representations.

In financial market applications, it is typical to have limited amount of relevant training data, with high noise levels in the data. The information content of such data is modest, and while the learning process can try to make the most of what it has, it cannot create new information on its own. This poses a fundamental limitation on the 412 Yaser S. Abu-Mostafa

An application of reinforcement learning to a linear-quadratic, differential game is presented. The reinforcement learning system uses a recently developed algorithm, the residual gradient form of advantage updating. The game is a Markov Decision Process (MDP) with continuous time, states, and actions, linear dynamics, and a quadratic cost function. The game consists of two players, a missile and a plane; the missile pursues the plane and the plane evades the missile. The reinforcement learning algorithm for optimal control is modified for differential games in order to find the minimax point, rather than the maximum. Simulation results are compared to the optimal solution, demonstrating that the simulated reinforcement learning system converges to the optimal answer. The performance of both the residual gradient and non-residual gradient forms of advantage updating and Q-learning are compared. The results show that advantage updating converges faster than Q-learning in all simulations.

The performance of online algorithms for learning dichotomies is studied. In online learning, the number of examples P is equivalent to the learning time, since each example is presented only once. The learning curve, or generalization error as a function of P, depends on the schedule at which the learning rate is lowered.

In the last decade the outlines of the neural structures subserving the sense of direction have begun to emerge. Several investigations have shed light on the effects of vestibular input and visual input on the head direction representation. In this paper, a model is formulated of the neural mechanisms underlying the head direction system. The model is built out of simple ingredients, depending on nothing more complicated than connectional specificity, attractor dynamics, Hebbian learning, and sigmoidal nonlinearities, but it behaves in a sophisticated way and is consistent with most of the observed properties ofreal head direction cells. In addition it makes a number of predictions that ought to be testable by reasonably straightforward experiments.

Previous investigators have suggested that these cells may represent self-motion. Spiral patterns can also be generated by the relative motion of the observer and a particular object. An MST cell may then account for some portion of the complex flow field, and the set of active cells could encode the entire flow; in this manner, MST effectively segments moving objects. Such a grouping operation is essential in interpreting scenes containing several independent moving objects and observer motion. We describe a model based on the hypothesis that the selective tuning of MST cells reflects the grouping of object components undergoing coherent motion. Inputs to the model were generated from sequences of ray-traced images that simulated realistic motion situations, combining observer motion, eye movements, and independent object motion. The input representation was modeled after response properties of neurons in area MT, which provides the primary input to area MST. After applying an unsupervised learning algorithm, the units became tuned to patterns signaling coherent motion. The results match many of the known properties of MST cells and are consistent with recent studies indicating that these cells process 3-D object motion information.