Related papers: Feature-Based Interpolation and Geodesics in the L…
Latent flow matching for image generation usually transports Gaussian noise to variational autoencoder latents along linear paths. Both endpoints, however, concentrate in thin spherical shells, and a Euclidean chord leaves those shells even…
It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…
Capturing data from dynamic processes through cross-sectional measurements is seen in many fields, such as computational biology. Trajectory inference deals with the challenge of reconstructing continuous processes from such observations.…
Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…
When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…
Bayesian Model Mixing (BMM) is a statistical technique that can be used to combine models that are predictive in different input domains into a composite distribution that has improved predictive power over the entire input space. We…
We introduce and discuss shape-based models for finding the best interpolation data in the compression of images with noise. The aim is to reconstruct missing regions by means of minimizing a data fitting term in the $L^2$-norm between the…
Large-scale structure of the universe is a useful cosmological probe of the primordial non-Gaussianity and the expansion history of the universe because its topology does not change with time in the linear regime in the standard paradigm of…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and…
The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do…
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering…
In the feature space, the collapse between features invokes critical problems in representation learning by remaining the features undistinguished. Interpolation-based augmentation methods such as mixup have shown their effectiveness in…
Many promising applications of supervised machine learning face hurdles in the acquisition of labeled data in sufficient quantity and quality, creating an expensive bottleneck. To overcome such limitations, techniques that do not depend on…
A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals.…
In this work we develop a dynamically adaptive sparse grids (SG) method for quasi-optimal interpolation of multidimensional analytic functions defined over a product of one dimensional bounded domains. The goal of such approach is to…
Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the…
Deep generative models can automatically create content of diverse types. However, there are no guarantees that such content will satisfy the criteria necessary to present it to end-users and be functional, e.g. the generated levels could…
We study the problem of transfer learning, observing that previous efforts to understand its information-theoretic limits do not fully exploit the geometric structure of the source and target domains. In contrast, our study first…