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Video frame interpolation can up-convert the frame rate and enhance the video quality. In recent years, although the interpolation performance has achieved great success, image blur usually occurs at the object boundaries owing to the large…

Graph neural networks (GNNs) are one of the most popular approaches to using deep learning on graph-structured data, and they have shown state-of-the-art performances on a variety of tasks. However, according to a recent study, a careful…

We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…

Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we…

Calculations of nuclei are often carried out in finite model spaces. Thus, finite-size corrections enter, and it is necessary to extrapolate the computed observables to infinite model spaces. In this work, we employ extrapolation methods…

Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…

Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature…

The detection and classification of intersections between triangles are crucial tasks in a wide range of applications within Computer Graphics and Geometry Processing, including mesh Arrangements, mesh Booleans, and generic mesh processing…

We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such…

The generalized winding number function measures insideness for arbitrary oriented triangle meshes. Exploiting this, I similarly generalize binary boolean operations to act on such meshes. The resulting operations for union, intersection,…

We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…

We obtain infinitely many boundary operators in the Brownian loop soup in the subcritical phase by analyzing the conformal block expansion of the two-point function that computes the probability of having two marked points on the upper…

We contribute NeuralSolver, a novel recurrent solver that can efficiently and consistently extrapolate, i.e., learn algorithms from smaller problems (in terms of observation size) and execute those algorithms in large problems. Contrary to…

We study the structural and statistical properties of $\mathcal{R}$-norm minimizing interpolants of datasets labeled by specific target functions. The $\mathcal{R}$-norm is the basis of an inductive bias for two-layer neural networks,…

We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable…

This paper presents a new approach of constructing $\alpha$-fractal interpolation functions (FIFs) using neural network operators, integrating concepts from approximation theory. Initially, we construct $\alpha$-fractals utilizing neural…

In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the $i$-th neuron in a…

We present a frame interpolation algorithm that synthesizes multiple intermediate frames from two input images with large in-between motion. Recent methods use multiple networks to estimate optical flow or depth and a separate network…

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators,…

Inspired by the conventional pooling layers in convolutional neural networks, many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. The great variety in the literature stems…