Related papers: General adaptive rational interpolation with maxim…
A method is suggested for interpolating between small-variable and large-variable asymptotic expansions. The method is based on self-similar approximation theory resulting in self-similar root approximants. The latter are more general than…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
We present a new direction for increasing the interpretability of deep neural networks (DNNs) by promoting weight-input alignment during training. For this, we propose to replace the linear transforms in DNNs by our B-cos transform. As we…
This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calder\'on calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
Continual learning poses a fundamental challenge for modern machine learning systems, requiring models to adapt to new tasks while retaining knowledge from previous ones. Addressing this challenge necessitates the development of efficient…
A system of high-order adaptive multiresolution wavelet collocation upwind schemes are developed for the solution of hyperbolic conservation laws. A couple of asymmetrical wavelet bases with interpolation property are built to realize the…
In this study we propose a-posteriori error estimation results to approximate the precision loss in quantities of interests computed using reduced order models. To generate the surrogate models we employ Proper Orthogonal Decomposition and…
Local explanation methods, also known as attribution methods, attribute a deep network's prediction to its input (cf. Baehrens et al. (2010)). We respond to the claim from Adebayo et al. (2018) that local explanation methods lack…
When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
We present a new image scaling method both for downscaling and upscaling, running with any scale factor or desired size. The resized image is achieved by sampling a bivariate polynomial which globally interpolates the data at the new scale.…
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
We propose an efficient estimation technique for the automatic selection of locally-adaptive Total Variation regularisation parameters based on an hybrid strategy which combines a local maximum-likelihood approach estimating space-variant…
Pooling layers are essential building blocks of convolutional neural networks (CNNs), to reduce computational overhead and increase the receptive fields of proceeding convolutional operations. Their goal is to produce downsampled volumes…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
We propose a novel method for large-scale image stitching that is robust against repetitive patterns and featureless regions in the imagery. In such cases, state-of-the-art image stitching methods easily produce image alignment artifacts,…
Existing image-based rendering methods usually adopt depth-based image warping operation to synthesize novel views. In this paper, we reason the essential limitations of the traditional warping operation to be the limited neighborhood and…
Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…
The unmatched ability of Deep Neural Networks in capturing complex patterns in large and noisy datasets is often associated with their large hypothesis space, and consequently to the vast amount of parameters that characterize model…
Since DeepSeek-R1 popularized, Group Relative Policy Optimization (GRPO) has become the core part of training Reasoning LLMs. However, we find some deficiency that influences RL stability and inference efficiency, like zero-variance in…