The error-bounded descriptional complexity of approximation networks

It is well known that artificial neural nets can be used as approximators of any continuous functions to any desired degree and therefore be used e.g. in high - speed, real-time process control. Nevertheless, for a given application and a given network architecture the non-trivial task remains to determine the necessary number of neurons and the necessary accuracy (number of bits) per weight for a satisfactory operation which are critical issues in VLSI and computer implementations of nontrivial tasks. In this paper the accuracy of the weights and the number of neurons are seen as general system parameters which determine the maximal approximation error by the absolute amount and the relative distribution of information contained in the network. We define as the error-bounded network descriptional complexity the minimal number of bits for a class of approximation networks which show a certain approximation error and achieve the conditions for this goal by the new principle of optimal information distribution. For two examples, a simple linear approximation of a non-linear, quadratic function and a non-linear approximation of the inverse kinematic transformation used in robot manipulator control, the principle of optimal information distribution gives the the optimal number of neurons and the resolutions of the variables, i.e. the minimal amount of storage for the neural net. Keywords: Kolmogorov complexity, e-Entropy, rate-distortion theory, approximation networks, information distribution, weight resolutions, Kohonen mapping, robot control

SA-Net: Deep Neural Network for Robot Trajectory Recognition from RGB-D Streams

Learning from demonstration (LfD) and imitation learning offer new paradigms for transferring task behavior to robots. A class of methods that enable such online learning require the robot to observe the task being performed and decompose the sensed streaming data into sequences of state-action pairs, which are then input to the methods. Thus, recognizing the state-action pairs correctly and quickly in sensed data is a crucial prerequisite for these methods. We present SA-Net a deep neural network architecture that recognizes state-action pairs from RGB-D data streams. SA-Net performed well in two diverse robotic applications of LfD -- one involving mobile ground robots and another involving a robotic manipulator -- which demonstrates that the architecture generalizes well to differing contexts. Comprehensive evaluations including deployment on a physical robot show that \sanet{} significantly improves on the accuracy of the previous method that utilizes traditional image processing and segmentation.Comment: (in press