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.

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.

Learning procedures that measure how random perturbations of unit activities correlatewith changes in reinforcement are inefficient but simple to implement in hardware. Procedures like back-propagation (Rumelhart, Hinton and Williams, 1986) which compute how changes in activities affect theoutput error are much more efficient, but require more complex hardware. GEMINI is a hybrid procedure for multilayer networks, which shares many of the implementation advantages of correlational reinforcement proceduresbut is more efficient. GEMINI injects noise only at the first hidden layer and measures the resultant effect on the output error. A linear network associated with each hidden layer iteratively inverts the matrix which relates the noise to the error change, thereby obtaining the error-derivatives. No back-propagation is involved, thus allowing unknown non-linearitiesin the system. Two simulations demonstrate the effectiveness of GEMINI.

Learning procedures that measure how random perturbations of unit activities correlate with changes in reinforcement are inefficient but simple to implement in hardware. Procedures like back-propagation (Rumelhart, Hinton and Williams, 1986) which compute how changes in activities affect the output error are much more efficient, but require more complex hardware. GEMINI is a hybrid procedure for multilayer networks, which shares many of the implementation advantages of correlational reinforcement procedures but is more efficient. GEMINI injects noise only at the first hidden layer and measures the resultant effect on the output error. A linear network associated with each hidden layer iteratively inverts the matrix which relates the noise to the error change, thereby obtaining the error-derivatives. No back-propagation is involved, thus allowing unknown non-linearities in the system. Two simulations demonstrate the effectiveness of GEMINI.