We present a new connectionist planning method [TML90]. By interaction with an unknown environment, a world model is progressively constructed usinggradient descent. For deriving optimal actions with respect to future reinforcement, planning is applied in two steps: an experience network proposesa plan which is subsequently optimized by gradient descent with a chain of world models, so that an optimal reinforcement may be obtained when it is actually run. The appropriateness of this method is demonstrated by a robotics application and a pole balancing task.

We propose a new parallel-hierarchical neural network model to enable motor learning for simultaneous control of both trajectory and force.

Waltham, MA 02254 Abstract We have produced a VLSI circuit capable of learning to approximate arbitrary smoothof a single variable using a technique closely related to splines. The circuit effectively has 512 knots space on a uniform grid and has full support for learning. The circuit also can be used to approximate multi-variable functions as sum of splines. An interesting, and as of yet, nearly untapped set of applications for VLSI implementation ofneural network learning systems can be found in adaptive control and nonlinear signal processing. In most such applications, the learning task consists of approximating a real function of a small number of continuous variables from discrete data points.

We present and compare learning rate schedules for stochastic gradient descent, a general algorithm which includes LMS, online backpropagation andk-means clustering as special cases. We introduce "search-thenconverge" typeschedules which outperform the classical constant and "running average" (1ft) schedules both in speed of convergence and quality of solution.

This work addresses three problems with reinforcement learning and adaptive neuro-control:1.

Bruno Caprile I.R.S.T. Povo, Italy, 38050 Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.

Bell-shaped response curves are commonly found in biological neurons whenever a natural metric exist on the corresponding relevant stimulus variable (orientation, position in space, frequency, time delay, ...). As a result, they are often used in neural models in different context ranging from resolution enhancement and interpolation tolearning (see, for instance, Baldi et al. (1988), Moody et al. (1989) *and Division of Biology, California Institute of Technology. The complete title of this paper should read: "Computing with arrays of bell-shaped and sigmoid functions.

Determination of nearly optimalt or at least adequatet regions is left as an additional task that would require that the system dynamics be analyzedt which is not always possible. To address this problemt we move region boundaries adaptively t progressively altering the initial partitioning to a more appropriate representation with no need for a priori knowledge. Unlike previous work (Michiet 1968)t (Bartot 1983)t (Andersont 1982) which used fixed this approach produces adaptivecoderSt coders that contract and expand regions/ranges. During adaptationt frequently active regions/ranges contractt reducing the number of situations in which they will be activated, and increasing the chances that neighboring regions will receive input instead. This class of self-organization is discussed in Kohonen (Kohonent 1984)t (Rittert 1986t 1988).

We consider different types of single-hidden-Iayer feedforward nets: with or without direct input to output connections, and using either threshold orsigmoidal activation functions. The main results show that direct connections in threshold nets double the recognition but not the interpolation power,while using sigmoids rather than thresholds allows (at least) doubling both. Various results are also given on VC dimension and other measures of recognition capabilities.

Spherical Units can be used to construct dynamic reconfigurable consequential regions, the geometric bases for Shepard's (1987) theory of stimulus generalization in animals and humans. We derive from Shepard's (1987) generalization theory a particular multi-layer network with dynamic (centers and radii) spherical regions which possesses a specific mass function (Cauchy). This learning model generalizes the configural-cue network model (Gluck & Bower 1988): (1) configural cues can be learned and do not require pre-wiring the power-set of cues, (2) Consequential regions are continuous rather than discrete and (3) Competition amoungst receptive fields is shown to be increased by the global extent of a particular mass function (Cauchy). We compare other common mass functions (Gaussian; used in models of Moody & Darken; 1989, Krushke, 1990) or just standard backpropogation networks with hyperplane/logistic hidden units showing that neither fare as well as models of human generalization and learning.