In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

[EX Q]: Recently, neural-network based forward dynamics models have been proposed that attempt to learn the dynamics of physical systems in a deterministic way. While near-term motion can be predicted accurately, long-term predictions suffer from accumulating input and prediction errors which can lead to plausible but different trajectories that diverge from the ground truth. A system that predicts distributions of the future physical states for long time horizons based on its uncertainty is thus a promising solution. In this work, we introduce a novel robust Monte Carlo sampling based graph-convolutional dropout method that allows us to sample multiple plausible trajectories for an initial state given a neural-network based forward dynamics predictor. By introducing a new shape preservation loss and training our dynamics model recurrently, we stabilize long-term predictions. We show that our model's long-term forward dynamics prediction errors on complicated physical interactions of rigid and deformable objects of various shapes are significantly lower than existing strong baselines. Lastly, we demonstrate how generating multiple trajectories with our Monte Carlo dropout method can be used to train model-free reinforcement learning agents faster and to better solutions on simple manipulation tasks.
[EX A]: We propose a stochastic differentiable forward dynamics predictor that is able to sample multiple physically plausible trajectories under the same initial input state and show that it can be used to train model-free policies more efficiently.

[EX Q]: This work provides theoretical and empirical evidence that invariance-inducing regularizers can increase predictive accuracy for worst-case spatial transformations (spatial robustness). Evaluated on these adversarially transformed examples, we demonstrate that adding regularization on top of standard or adversarial training reduces the relative error by 20% for CIFAR10 without increasing the computational cost. This outperforms handcrafted networks that were explicitly designed to be spatial-equivariant. Furthermore, we observe for SVHN, known to have inherent variance in orientation, that robust training also improves standard accuracy on the test set.
[EX A]: for spatial transformations robust minimizer also minimizes standard accuracy; invariance-inducing regularization leads to better robustness than specialized architectures

[EX Q]: Kronecker-factor Approximate Curvature (Martens & Grosse, 2015) (K-FAC) is a 2nd-order optimization method which has been shown to give state-of-the-art performance on large-scale neural network optimization tasks (Ba et al., 2017). It is based on an approximation to the Fisher information matrix (FIM) that makes assumptions about the particular structure of the network and the way it is parameterized. The original K-FAC method was applicable only to fully-connected networks, although it has been recently extended by Grosse & Martens (2016) to handle convolutional networks as well. In this work we extend the method to handle RNNs by introducing a novel approximation to the FIM for RNNs. This approximation works by modelling the covariance structure between the gradient contributions at different time-steps using a chain-structured linear Gaussian graphical model, summing the various cross-covariances, and computing the inverse in closed form. We demonstrate in experiments that our method significantly outperforms general purpose state-of-the-art optimizers like SGD with momentum and Adam on several challenging RNN training tasks.
[EX A]:
We extend the K-FAC method to RNNs by developing a new family of Fisher approximations.