Related papers: Complex Interpolation of Matrices with an applicat…
Machine learning models have been progressively used for predicting materials properties. These models can be built using pre-existing data and are useful for rapidly screening the physicochemical space of a material, which is…
We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an…
Let $(X, Y)$ be a couple of quasi-Banach lattices of measurable functions on $\mathbb T \times \Omega$ satisfying some additional assumptions. The K-closedness of a couple of Hardy-type spaces $(X_A, Y_A)$ in $(X, Y)$ and the stability of…
We study cross-modal alignment between independently pretrained vision (DINOv2) and language (all-MiniLM-L6-v2) encoders using the functional map framework from computational geometry, which represents correspondence between representation…
We prove a generalization of Maehara's lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig's interpolation property. As a…
Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…
The relationship between interpolation and separation properties of hypersurfaces in Bargmann-Fock spaces over $\mathbb{C} ^n$ is not well-understood except for $n=1$. We present four examples of smooth affine algebraic hypersurfaces that…
Given two different self-adjoint extensions of the same symmetric operator, we analyse the intersection of their point spectra. Some simple examples are provided.
The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges-Rovnyak spaces H (b) where the defining function b is a general non-extreme rational function. Our results carry over to recently…
When a matrix A with n columns is known to be well approximated by a linear combination of basis matrices B_1,..., B_p, we can apply A to a random vector and solve a linear system to recover this linear combination. The same technique can…
A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets…
For a topological space $X$ we study continuous maps $f : X\to \mathbb R^m$ such that images of every pairwise distinct $k$ points are affinely (linearly) independent. Such maps are called affinely (linearly) $k$-regular embeddings. We…
Matrix completion has received vast amount of attention and research due to its wide applications in various study fields. Existing methods of matrix completion consider only nonlinear (or linear) relations among entries in a data matrix…
A modular proof-theoretic framework was recently developed to prove Craig interpolation for normal modal logics based on generalizations of sequent calculi (e.g., nested sequents, hypersequents, and labelled sequents). In this paper, we…
Maps between manifolds $M^m\to N^{m+\ell}$ ($\ell>0$) have multiple points, and more generally, multisingularities. The closure of the set of points where the map has a particular multisingularity is called the multisingularity locus. There…
It is common in machine learning and statistics to use symmetries derived from expert knowledge to simplify problems or improve performance, using methods like data augmentation or penalties. In this paper we consider the unsupervised and…
We study spectral properties of unbounded Jacobi matrices with periodically modulated or blended entries. Our approach is based on uniform asymptotic analysis of generalized eigenvectors. We determine when the studied operators are…
A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…
Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$…
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…