Related papers: Function Extrapolation with Neural Networks and It…
We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while…
One of the most common problems preventing the application of prediction models in the real world is lack of generalization: The accuracy of models, measured in the benchmark does repeat itself on future data, e.g. in the settings of real…
We study the applicability of a Deep Neural Network (DNN) approach to simulate one-dimensional non-relativistic fluid dynamics. Numerical fluid dynamical calculations are used to generate training data-sets corresponding to a broad range of…
Generalizing skill policies to novel conditions remains a key challenge in robot learning. Imitation learning methods, while data-efficient, are largely confined to the training region and consistently fail on input data outside it, leading…
Traditional approaches to interpolate/extrapolate frames in a video sequence require accurate pixel correspondences between images, e.g., using optical flow. Their results stem on the accuracy of optical flow estimation, and could generate…
Appropriately evaluating the discrepancy between domains is essential for the success of unsupervised domain adaptation. In this paper, we first point out that existing discrepancy measures are less informative when complex models such as…
A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an…
Domain adaptation is a sub-field of machine learning that involves transferring knowledge from a source domain to perform the same task in the target domain. It is a typical challenge in machine learning that arises, e.g., when data is…
We introduce a new procedure for training of artificial neural networks by using the approximation of an objective function by arithmetic mean of an ensemble of selected randomly generated neural networks, and apply this procedure to the…
The feasibility of extrapolation of completely monotone functions can be quantified by examining the worst case scenario, whereby a pair of completely monotone functions agree on a given interval to a given relative precision, but differ as…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
Neural networks allow us to model complex relationships between variables. We show how to efficiently find extrema of a trained neural network in regression problems. Finding the extremizing input of an approximated model is formulated as…
While the basic laws of Newtonian mechanics are well understood, explaining a physical scenario still requires manually modeling the problem with suitable equations and estimating the associated parameters. In order to be able to leverage…
Due to the heterogeneity of the global distribution of ecological and hydrological ground-truth observations, machine learning models can have limited adaptability when applied to unknown locations, which is referred to as weak…
Neural network models and deep models are one of the leading and state of the art models in machine learning. Most successful deep neural models are the ones with many layers which highly increases their number of parameters. Training such…
We develop a minimax rate analysis to describe the reason that deep neural networks (DNNs) perform better than other standard methods. For nonparametric regression problems, it is well known that many standard methods attain the minimax…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
Neural networks are often utilised in critical domain applications (e.g. self-driving cars, financial markets, and aerospace engineering), even though they exhibit overconfident predictions for ambiguous inputs. This deficiency demonstrates…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
As function approximators, deep neural networks have served as an effective tool to represent various signal types. Recent approaches utilize multi-layer perceptrons (MLPs) to learn a nonlinear mapping from a coordinate to its corresponding…