We present two neural network controller learning schemes based on feedbackerror-learning and modular architecture for recognition and control of multiple manipulated objects. In the first scheme, a Gating Network is trained to acquire object-specific representations for recognition of a number of objects (or sets of objects). In the second scheme, an Estimation Network is trained to acquire function-specific, rather than object-specific, representations which directly estimate physical parameters. Both recognition networks are trained to identify manipulated objects using somatic and/or visual information. After learning, appropriate motor commands for manipulation of each object are issued by the control networks.

Networks for reconstructing a sparse or noisy function often use an edge field to segment the function into homogeneous regions, This approach assumes that these regions do not overlap or have disjoint parts, which is often false. For example, images which contain regions split by an occluding object can't be properly reconstructed using this type of network. We have developed a network that overcomes these limitations, using support maps to represent the segmentation of a signal. In our approach, the support of each region in the signal is explicitly represented. Results from an initial implementation demonstrate that this method can reconstruct images and motion sequences which contain complicated occlusion.

Network vision systems must make inferences from evidential information across levels of representational abstraction, from low level invariants, through intermediate scene segments, to high level behaviorally relevant object descriptions. This paper shows that such networks can be realized as Markov Random Fields (MRFs). We show first how to construct an MRF functionally equivalent to a Hough transform parameter network, thus establishing a principled probabilistic basis for visual networks. Second, we show that these MRF parameter networks are more capable and flexible than traditional methods. In particular, they have a well-defined probabilistic interpretation, intrinsically incorporate feedback, and offer richer representations and decision capabilities.

Trajectory generation finds interesting applications in the field of robotics, automation, filtering, or time series prediction. Neural networks, with their ability to learn from examples, have been proposed very early on for solving nonlinear control problems adaptively. Several neural net architectures have been proposed for trajectory generation, most notably recurrent networks, either with discrete time and externalloops (Jordan, 1986), or with continuous time (Pearlmutter, 1988). Aside from being recurrent, these networks are not specifically tailored for trajectory generation. It has been shown that specific architectures, such as the Time Delay Neural Networks (Lang and Hinton, 1988), or convolutional networks in general, are better than fully connected networks at recognizing time sequences such as speech (Waibel et al., 1989), or pen trajectories (Guyon et al., 1991). We show that special architectures can also be devised for trajectory generation, with dramatic performance improvement.

This work discusses various optimization techniques which were proposed in models for controlling arm movements. In particular, the minimum-muscle-tension-change model is investigated. A dynamic simulator of the monkey's arm, including seventeen single and double joint muscles, is utilized to generate horizontal hand movements. The hand trajectories produced by this algorithm are discussed.

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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.

Trajectory generation finds interesting applications in the field of robotics, automation, filtering,or time series prediction. Neural networks, with their ability to learn from examples, have been proposed very early on for solving nonlinear control problems adaptively.Several neural net architectures have been proposed for trajectory generation, most notably recurrent networks, either with discrete time and externalloops (Jordan,1986), or with continuous time (Pearlmutter, 1988). Aside from being recurrent, these networks are not specifically tailored for trajectory generation. Ithas been shown that specific architectures, such as the Time Delay Neural Networks (Lang and Hinton, 1988), or convolutional networks in general, are better than fully connected networks at recognizing time sequences such as speech (Waibel et al., 1989), or pen trajectories (Guyon et al., 1991). We show that special architectures canalso be devised for trajectory generation, with dramatic performance improvement.

Networks for reconstructing a sparse or noisy function often use an edge field to segment the function into homogeneous regions, This approach assumes that these regions do not overlap or have disjoint parts, which is often false. For example, images which contain regions split by an occluding objectcan't be properly reconstructed using this type of network. We have developed a network that overcomes these limitations, using support maps to represent the segmentation of a signal. In our approach, the support ofeach region in the signal is explicitly represented. Results from an initial implementation demonstrate that this method can reconstruct images and motion sequences which contain complicated occlusion.

Using the double-step target displacement paradigm the mechanisms underlying armtrajectory modification were investigated. Using short (10-110 msec) inter-stimulus intervals the resulting hand motions were initially directed in between the first and second target locations. The kinematic features of the modified motions were accounted for by the superposition scheme, which involves the vectorial addition of two independent point-topoint motionunits: one for moving the hand toward an internally specified location and a second one for moving between that location and the final target location. The similarity between the inferred internally specified locations andpreviously reported measured endpoints of the first saccades in double-step eye-movement studies may suggest similarities between perceived targetlocations in eye and hand motor control.