Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory

Newton's standard theory of gravitation is reformulated as a {\it gauge} theory of the {\it extended} Galilei Group. The Action principle is obtained by matching the {\it gauge} technique and a suitable limiting procedure from the ADM-De Witt action of general relativity coupled to a relativistic mass-point.Comment: 51 pages , compress, uuencode LaTex fil

Gauging tensor networks with belief propagation

Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm.Comment: 47 Pages. 11 Figure

Active Learning based on Data Uncertainty and Model Sensitivity

Robots can rapidly acquire new skills from demonstrations. However, during generalisation of skills or transitioning across fundamentally different skills, it is unclear whether the robot has the necessary knowledge to perform the task. Failing to detect missing information often leads to abrupt movements or to collisions with the environment. Active learning can quantify the uncertainty of performing the task and, in general, locate regions of missing information. We introduce a novel algorithm for active learning and demonstrate its utility for generating smooth trajectories. Our approach is based on deep generative models and metric learning in latent spaces. It relies on the Jacobian of the likelihood to detect non-smooth transitions in the latent space, i.e., transitions that lead to abrupt changes in the movement of the robot. When non-smooth transitions are detected, our algorithm asks for an additional demonstration from that specific region. The newly acquired knowledge modifies the data manifold and allows for learning a latent representation for generating smooth movements. We demonstrate the efficacy of our approach on generalising elementary skills, transitioning across different skills, and implicitly avoiding collisions with the environment. For our experiments, we use a simulated pendulum where we observe its motion from images and a 7-DoF anthropomorphic arm.Comment: Published on 2018 IEEE/RSJ International Conference on Intelligent Robots and Syste

Pareto Smoothed Importance Sampling

Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be noisy when the importance ratios have a heavy right tail. This routinely occurs when there are aspects of the target distribution that are not well captured by the approximating distribution, in which case more stable estimates can be obtained by modifying extreme importance ratios. We present a new method for stabilizing importance weights using a generalized Pareto distribution fit to the upper tail of the distribution of the simulated importance ratios. The method, which empirically performs better than existing methods for stabilizing importance sampling estimates, includes stabilized effective sample size estimates, Monte Carlo error estimates and convergence diagnostics.Comment: Major revision: 1) proofs for consistency, finite variance, and asymptotic normality, 2) justification of k<0.7 with theoretical computational complexity analysis, 3) major rewrit