Many technologies of interest to the Department of Energy (DOE) require hazardous operations in which intelligent machines could be used to advantage. Closest to home is the handling of radioactive material around reactors and processing plants, but similar problems arise with explosives and other hazardous chemicals. Underground mining puts humans at risk on a large scale, and underwater operations from exploration to maintenance of equipment and, eventually, to seabed mining have a similar potential. In fact, underwater robots have already been put to use (for example, Jason Jr. for surveillance of the remains of the sunken Titunic). At a minimum, such a machine should be able to perform a useful task (lift something, cut something, observe something) and move between some staging point and the location of the task.

The development of learning algorithms is generally based upon the minimization of an energy function. It is a fundamental requirement to compute the gradient of this energy function with respect to the various parameters of the neural architecture, e.g., synaptic weights, neural gain,etc. In principle, this requires solving a system of nonlinear equations for each parameter of the model, which is computationally very expensive. A new methodology for neural learning of time-dependent nonlinear mappings is presented. It exploits the concept of adjoint operators to enable a fast global computation of the network's response to perturbations in all the systems parameters. The importance of the time boundary conditions of the adjoint functions is discussed. An algorithm is presented in which the adjoint sensitivity equations are solved simultaneously (Le., forward in time) along with the nonlinear dynamics of the neural networks. This methodology makes real-time applications and hardware implementation of temporal learning feasible.

The development of learning algorithms is generally based upon the minimization of an energy function. It is a fundamental requirement to compute the gradient of this energy function with respect to the various parameters of the neural architecture, e.g., synaptic weights, neural gain,etc. In principle, this requires solving a system of nonlinear equations for each parameter of the model, which is computationally very expensive. A new methodology for neural learning of time-dependent nonlinear mappings is presented. It exploits the concept of adjoint operators to enable a fast global computation of the network's response to perturbations in all the systems parameters. The importance of the time boundary conditions of the adjoint functions is discussed. An algorithm is presented in which the adjoint sensitivity equations are solved simultaneously (Le., forward in time) along with the nonlinear dynamics of the neural networks. This methodology makes real-time applications and hardware implementation of temporal learning feasible.

The development of learning algorithms is generally based upon the minimization ofan energy function. It is a fundamental requirement to compute the gradient of this energy function with respect to the various parameters ofthe neural architecture, e.g., synaptic weights, neural gain,etc. In principle, this requires solving a system of nonlinear equations for each parameter of the model, which is computationally very expensive. A new methodology for neural learning of time-dependent nonlinear mappings is presented. It exploits the concept of adjoint operators to enable a fast global computation of the network's response to perturbations in all the systems parameters. The importance of the time boundary conditions of the adjoint functions is discussed. An algorithm is presented in which the adjoint sensitivity equations are solved simultaneously (Le., forward in time) along with the nonlinear dynamics of the neural networks. This methodology makes real-time applications and hardware implementation of temporal learning feasible.

A methodology for faster supervised learning in dynamical nonlinear neural networks is presented. It exploits the concept of adjoint operntors to enable computation of changes in the network's response due to perturbations in all system parameters, using the solution of a single set of appropriately constructed linear equations. The lower bound on speedup per learning iteration over conventional methods for calculating the neuromorphic energy gradient is O(N2), where N is the number of neurons in the network. 1 INTRODUCTION The biggest promise of artifcial neural networks as computational tools lies in the hope that they will enable fast processing and synthesis of complex information patterns. In particular, considerable efforts have recently been devoted to the formulation of efficent methodologies for learning (e.g., Rumelhart et al., 1986; Pineda, 1988; Pearlmutter, 1989; Williams and Zipser, 1989; Barhen, Gulati and Zak, 1989). The development of learning algorithms is generally based upon the minimization of a neuromorphic energy function. The fundamental requirement of such an approach is the computation of the gradient of this objective function with respect to the various parameters of the neural architecture, e.g., synaptic weights, neural Adjoint Operator Algorithms 499

A methodology for faster supervised learning in dynamical nonlinear neural networks is presented. It exploits the concept of adjoint operntors to enable computation of changes in the network's response due to perturbations in all system parameters, using the solution of a single set of appropriately constructed linear equations. The lower bound on speedup per learning iteration over conventional methods for calculating the neuromorphic energy gradient is O(N2), where N is the number of neurons in the network. 1 INTRODUCTION The biggest promise of artifcial neural networks as computational tools lies in the hope that they will enable fast processing and synthesis of complex information patterns. In particular, considerable efforts have recently been devoted to the formulation of efficent methodologies for learning (e.g., Rumelhart et al., 1986; Pineda, 1988; Pearlmutter, 1989; Williams and Zipser, 1989; Barhen, Gulati and Zak, 1989). The development of learning algorithms is generally based upon the minimization of a neuromorphic energy function. The fundamental requirement of such an approach is the computation of the gradient of this objective function with respect to the various parameters of the neural architecture, e.g., synaptic weights, neural Adjoint Operator Algorithms 499

A methodology for faster supervised learning in dynamical nonlinear neuralnetworks is presented. It exploits the concept of adjoint operntors to enable computation of changes in the network's response dueto perturbations in all system parameters, using the solution of a single set of appropriately constructed linear equations. The lower bound on speedup per learning iteration over conventional methodsfor calculating the neuromorphic energy gradient is O(N2), where N is the number of neurons in the network. 1 INTRODUCTION The biggest promise of artifcial neural networks as computational tools lies in the hope that they will enable fast processing and synthesis of complex information patterns. In particular, considerable efforts have recently been devoted to the formulation ofefficent methodologies for learning (e.g., Rumelhart et al., 1986; Pineda, 1988; Pearlmutter, 1989; Williams and Zipser, 1989; Barhen, Gulati and Zak, 1989). The development of learning algorithms is generally based upon the minimization of a neuromorphic energy function.

The Oak Ridge National Laboratory (ORNL) Center for Engineering Systems Advanced Research (CESAR) is a national center for multidisciplinary long-range research and development (R&D) in machine intelligence and advanced control theory. Intelligent machines (including sensor-based robots) can be viewed as artificially created operational systems capable of autonomous decision making and action. One goal of the research is autonomous remote operations in hazardous environments. This review describes highlights of CESAR research through 1986 and alludes to future plans.