A neurophysiologically-based model is presented that controls a simulated kinematic arm during goal-directed reaches. The network generates a quasi-feedforward motor command that is learned using training signals generated by corrective movements. For each target, the network selects and sets the output of a subset of pattern generators. During the movement, feedback from proprioceptors turns off the pattern generators. The task facing individual pattern generators is to recognize when the arm reaches the target and to turn off. A distributed representation of the motor command that resembles population vectors seen in vivo was produced naturally by these simulations.

Recently synchronization phenomena in neural networks have attracted considerable attention. Gray et al. (1989, 1990) as well as Eckhorn et al. (1988) provided electrophysiological evidence that neurons in the visual cortex of cats discharge in a semi-synchronous, oscillatory manner in the 40 Hz range and that the firing activity of neurons up to 10 mm away is phase-locked with a mean phase-shift of less than 3 msec. It has been proposed that this phase synchronization can solve the binding problem for figure-ground segregation (von der Malsburg and Schneider, 1986) and underly visual attention and awareness (Crick and Koch, 1990). A number of theoretical explanations based on coupled (relaxation) oscillator mod-117 118 Schuster and Koch els have been proposed for burst synchronization (Sompolinsky et al., 1990). The crucial issue of phase synchronization has also recently been addressed by Bush and Douglas (1991), who simulated the dynamics of a network consisting of bursty, layer V pyramidal cells coupled to a common pool of basket cells inhibiting all pyramidal cells.

Because of the complexity of the application and the large amount of data, the problem cannot be solved by using a single method. The solution we propose is to build multimodules NN architectures where several NN cooperate together. Such system suffer from generic problem for whom we propose solutions. They allow to reach accurate performances for multi-valued function approximations and probability estimations. The results are compared with six other methods which have been used for this problem. We show that the methodology we have developed is general and can be used for a large variety of applications.

We have created new networks to unmix signals which have been mixed either with time delays or via filtering. We first show that a subset of the Herault-Jutten learning rules fulfills a principle of minimum output power. We then apply this principle to extensions of the Herault-Jutten network which have delays in the feedback path. Our networks perform well on real speech and music signals that have been mixed using time delays or filtering.

We present the "Multi-State Time Delay Neural Network" (MS-TDNN) as an extension of the TDNN to robust word recognition.

Learning structure in temporally-extended sequences is a difficult computational problem because only a fraction of the relevant information is available at any instant. Although variants of back propagation can in principle be used to find structure in sequences, in practice they are not sufficiently powerful to discover arbitrary contingencies, especially those spanning long temporal intervals or involving high order statistics. For example, in designing a connectionist network for music composition, we have encountered the problem that the net is able to learn musical structure that occurs locally in time-e.g., relations among notes within a musical phrase-but not structure that occurs over longer time periods--e.g., relations among phrases. To address this problem, we require a means of constructing a reduced deacription of the sequence that makes global aspects more explicit or more readily detectable. I propose to achieve this using hidden units that operate with different time constants.

We present here an interesting experiment in'quick modeling' by humans, performed independently on small samples, in several languages and two continents, over the last three years. Comparisons to decision tree procedures and neural net processing are given. From these, we conjecture that human reasoning is better represented by the latter, but substantially different from both. Implications for the'strong convergence hypothesis' between neural networks and machine learning are discussed, now expanded to include human reasoning comparisons. 1 INTRODUCTION Until recently the fields of symbolic and connectionist learning evolved separately. Suddenly in the last two years a significant number of papers comparing the two methodologies have appeared. A beginning synthesis of these two fields was forged at the NIPS '90 Workshop #5 last year (Pratt and Norton, 1990), where one may find a good bibliography of the recent work of Atlas, Dietterich, Omohundro, Sanger, Shavlik, Tsoi, Utgoff and others. It was at that NIPS '90 Workshop that we learned of these studies, most of which concentrate on performance comparisons of decision tree algorithms (such as ID3, CART) and neural net algorithms (such as Perceptrons, Backpropagation). Independently three years ago we had looked at Quinlan's ID3 scheme (Quinlan, 1984) and intuitively and rather instantly not agreeing with the generalization he obtains by ID3 from a sample of 8 items generalized to 12 items, we subjected this example to a variety of human experiments. We report our findings, as compared to the performance of ID3 and also to various neural net computations.

Self-organizing feature maps like the Kohonen map (Kohonen, 1989, Ritter et al., 1990) not only provide a plausible explanation for the formation of maps in brains, e.g. in the visual system (Obermayer et al., 1990), but have also been applied to problems like vector quantization, or robot arm control (Martinetz et al., 1990). The underlying organizing principle is the preservation of neighborhood relations. For this principle to lead to a most useful map, the topological structure of the output space must roughly fit the structure of the input data. However, in technical 1141 1142 Bauer, Pawelzik, and Geisel applications this structure is often not a priory known. For this reason several attempts have been made to modify the Kohonen-algorithm such, that not only the weights, but also the output space topology itself is adapted during learning (Kangas et al., 1990, Martinetz et al., 1991). Our contribution is also concerned with optimal output space topologies, but we follow a different approach, which avoids a possibly complicated structure of the output space. First we describe a quantitative measure for the preservation of neighborhood relations in maps, the topographic product P. The topographic product had been invented under the name of" wavering product" in nonlinear dynamics in order to optimize the embeddings of chaotic attractors (Liebert et al., 1991).

Automatic determination of proper neural network topology by trimming oversized networks is an important area of study, which has previously been addressed using a variety of techniques. In this paper, we present Information Measure Based Skeletonisation (IMBS), a new approach to this problem where superfluous hidden units are removed based on their information measure (1M). This measure, borrowed from decision tree induction techniques, reflects the degree to which the hyperplane formed by a hidden unit discriminates between training data classes. We show the results of applying IMBS to three classification tasks and demonstrate that it removes a substantial number of hidden units without significantly affecting network performance.

A constructive algorithm is proposed for feed-forward neural networks, which uses node-splitting in the hidden layers to build large networks from smaller ones. The small network forms an approximate model of a set of training data, and the split creates a larger more powerful network which is initialised with the approximate solution already found. The insufficiency of the smaller network in modelling the system which generated the data leads to oscillation in those hidden nodes whose weight vectors cover regions in the input space where more detail is required in the model. These nodes are identified and split in two using principal component analysis, allowing the new nodes t.o cover the two main modes of each oscillating vector. Nodes are selected for splitting using principal component analysis on the oscillating weight vectors, or by examining the Hessian matrix of second derivatives of the network error with respect to the weight.s.