Related papers: When do CF-approximation spaces capture sL-domains

In this work, we develop a unified framework for quasidiagonal and F\o lner-type approximations of linear operators on Hilbert spaces. These approximations (originally formulated for bounded operators and operator algebras) involve…

Continual learning (CL) aims to train models sequentially over multiple domains without forgetting previously learned knowledge. However, existing CL methods optimize for in-domain performance and are therefore prone to learning spurious,…

Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $SL_n (F)$. It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for…

In this paper, we study the lower- and upper-bounded covering (LUC) problem, where we are given a set $P$ of $n$ points, a collection $\mathcal{B}$ of balls, and parameters $L$ and $U$. The goal is to find a minimum-sized subset…

We study the complexity of approximately solving the weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, there is a classification known for the case in which the domain…

Supervised contrastive learning (SCL) frameworks treat each class as independent and thus consider all classes to be equally important. This neglects the common scenario in which label hierarchy exists, where fine-grained classes under the…

Cross-domain few-shot classification task (CD-FSC) combines few-shot classification with the requirement to generalize across domains represented by datasets. This setup faces challenges originating from the limited labeled data in each…

Closure spaces, a generalisation of topological spaces, have shown to be a convenient theoretical framework for spatial model checking. The closure operator of closure spaces and quasi-discrete closure spaces induces a notion of…

In this paper we show derivations among logarithmic space bounded counting classes based on closure properties of $\#L$ that leads us to the result that $NL=C_=L\subseteq PL$.

Long-range dependency modeling has been widely considered in modern deep learning based semantic segmentation methods, especially those designed for large-size remote sensing images, to compensate the intrinsic locality of standard…

We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data,…

By a closure space we will mean a pair $(A,\mathcal{C})$, in which $A$ is a set and $\mathcal{C}$ a set of subsets of $A$ closed under arbitrary intersections. The purpose of this paper is to initiate a development of descent theory of…

A generalisation of Scott's information systems \cite{sco82} is presented that captures exactly all L-domains. The global consistency predicate in Scott's definition is relativised in such a way that there is a consistency predicate for…

Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology…

Continual learning (CL) is the sub-field of machine learning concerned with accumulating knowledge in dynamic environments. So far, CL research has mainly focused on incremental classification tasks, where models learn to classify new…

This article introduces strongly near proximity, which represents a new kind of proximity called \emph{almost proximity}. A main result in this paper is the introduction of a hit-and-miss topology on ${CL}(X)$, the hyperspace of nonempty…

Few-shot learning (FSL) aims to learn novel visual categories from very few samples, which is a challenging problem in real-world applications. Many methods of few-shot classification work well on general images to learn global…

Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…

Given a collection S of subsets of some set U, and M a subset of U, the set cover problem is to find the smallest subcollection C of S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve,…

The given study uses the methods to identify compactifications of semigroups $S\subset L(X),$ which reside in the space $L(X).$ This method generalizes in some sense the deLeeuw-Glicksberg-Theory to a greater class of functions. The…