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.

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.
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.

The vast majority of natural sensory data is temporally redundant. For instance, video frames or audio samples which are sampled at nearby points in time tend to have similar values.   Typically, deep learning algorithms take no advantage of this redundancy to reduce computations.   This can be an obscene waste of energy.   We present a variant on backpropagation for neural networks in which computation scales with the rate of change of the data - not the rate at which we process the data.   We do this by implementing a form of Predictive Coding wherein neurons communicate a combination of their state, and their temporal change in state, and quantize this signal using Sigma-Delta modulation.   Intriguingly, this simple communication rule give rise to units that resemble biologically-inspired leaky integrate-and-fire neurons, and to a spike-timing-dependent weight-update similar to Spike-Timing Dependent Plasticity (STDP), a synaptic learning rule observed in the brain.   We demonstrate that on MNIST, on a temporal variant of MNIST, and on Youtube-BB, a dataset with videos in the wild, our algorithm performs about as well as a standard deep network trained with backpropagation, despite only communicating discrete values between layers.  
An algorithm for training neural networks efficiently on temporally redundant data.

We study the statistical properties of the endpoint of stochastic gradient descent (SGD). We approximate SGD as a stochastic differential equation (SDE) and consider its Boltzmann Gibbs equilibrium distribution under the assumption of isotropic variance in loss gradients.. Through this analysis, we find that three factors – learning rate, batch size and the variance of the loss gradients – control the trade-off between the depth and width of the minima found by SGD, with wider minima favoured by a higher ratio of learning rate to batch size. In the equilibrium distribution only the ratio of learning rate to batch size appears, implying that it’s invariant under a simultaneous rescaling of each by the same amount. 
We experimentally show how learning rate and batch size affect SGD from two perspectives: the endpoint of SGD and the dynamics that lead up to it. For the endpoint, the experiments suggest the endpoint of SGD is similar under simultaneous rescaling of batch size and learning rate, and also that a higher ratio leads to flatter minima, both findings are consistent with our theoretical analysis. We note experimentally that the dynamics also seem to be similar under the same rescaling of learning rate and batch size, which we explore showing that one can exchange batch size and learning rate in a cyclical learning rate schedule. Next, we illustrate how noise affects memorization, showing that high noise levels lead to better generalization. Finally, we find experimentally that the similarity under simultaneous rescaling of learning rate and batch size breaks down if the learning rate gets too large or the batch size gets too small.

Three factors (batch size, learning rate, gradient noise) change in predictable way the properties (e.g. sharpness) of minima found by SGD.