Related papers: Boundary Interpolation on Triangles via Neural Net…
We address the problem of accurately interpolating measured anechoic steering vectors with a deep learning framework called the neural field. This task plays a pivotal role in reducing the resource-intensive measurements required for…
Deep learning based methods have penetrated many image processing problems and become dominant solutions to these problems. A natural question raised here is "Is there any space for conventional methods on these problems?" In this paper,…
Video prediction is an extrapolation task that predicts future frames given past frames, and video frame interpolation is an interpolation task that estimates intermediate frames between two frames. We have witnessed the tremendous…
The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of…
In the era of deep learning, understanding over-fitting phenomenon becomes increasingly important. It is observed that carefully designed deep neural networks achieve small testing error even when the training error is close to zero. One…
When using recurrent neural networks (RNNs) it is common practice to apply trained models to sequences longer than those seen in training. This "extrapolating" usage deviates from the traditional statistical learning setup where guarantees…
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by…
We theoretically demonstrate that the generalization error of interpolators for machine learning models under teacher-student settings becomes 0 once the number of training samples exceeds a certain threshold. Understanding the high…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the…
Monotonic linear interpolation (MLI) - on the line connecting a random initialization with the minimizer it converges to, the loss and accuracy are monotonic - is a phenomenon that is commonly observed in the training of neural networks.…
We are interested in assessing the use of neural networks as surrogate models to approximate and minimize objective functions in optimization problems. While neural networks are widely used for machine learning tasks such as classification…
Based on the variable Hilbert scale interpolation inequality bounds for the error of regularisation methods are derived under range inclusions. In this context, new formulae for the modulus of continuity of the inverse of bounded operators…
Recurrent neural networks (RNNs) are effective at emulating the non-linear, stateful behavior of analog guitar amplifiers and distortion effects. Unlike the case of direct circuit simulation, RNNs have a fixed sample rate encoded in their…
Super-resolution of LiDAR range images is crucial to improving many downstream tasks such as object detection, recognition, and tracking. While deep learning has made a remarkable advances in super-resolution techniques, typical…
In general, matrix or tensor-valued functions are approximated using the method developed for vector-valued functions by transforming the matrix-valued function into vector form. This paper proposes a tensor-based interpolation method to…
We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…
An upper bound for the Lebesgue constant (the supremum norm) of the operator of interpolation of a function in equally spaced points of a triangle by a polynomial of total degree less than or equal to n is obtained. Earlier, the rate of…
The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…