相关论文: InfoMod: A visual and computational approach to Ga…
Algorithmic methods for the explicit inversion of the indefinite double covering maps are proposed. These are based on either the Givens decomposition or the polar decomposition of the given matrix in the proper, indefinite orthogonal group…
Multimodal Recommendation (MMR) systems are crucial for modern platforms but are often hampered by inherent noise and uncertainty in modal features, such as blurry images, diverse visual appearances, or ambiguous text. Existing methods…
We propose an explicit and practical algorithm for computing Galois conjugates and irreducible polynomials for special values of modular functions evaluated at CM points associated with imaginary quadratic orders. Our approach builds upon…
CylindricalAlgebraicDecomposition.m2 is the first implementation of Cylindrical Algebraic Decomposition (CAD) in Macaulay2. CAD decomposes space into 'cells' where input polynomials are sign-invariant. This package computes an Open CAD…
Knowledge Graphs, such as Wikidata, comprise structural and textual knowledge in order to represent knowledge. For each of the two modalities dedicated approaches for graph embedding and language models learn patterns that allow for…
In this paper, we present a modern version of Gordan's algorithm on binary forms. Symbolic method is reinterpreted in terms of $\mathsf{SL}_2(\mathbb{C})$--equivariant homomorphisms defined upon Cayley operator and polarization operator. A…
Geolocating precise locations from images presents a challenging problem in computer vision and information retrieval.Traditional methods typically employ either classification, which dividing the Earth surface into grid cells and…
Interval type-2 fuzzy logic systems (IT2 FLSs) have a wide range of applications due to their abilities to handle uncertainties compared to their type-1 counterparts. This paper discusses the representation of IT2 FLSs in closed…
The category $\mathbf{XSq}$ of crossed squares is equivalent to the category $\mathbf{Cat2}$ of cat$^2$-groups. Functions for computing with these structures have been developed in the package $\mathsf{XMod}$ written using the…
Visual Question Answering (VQA) presents a unique challenge as it requires the ability to understand and encode the multi-modal inputs - in terms of image processing and natural language processing. The algorithm further needs to learn how…
Unsupervised (or self-supervised) graph representation learning is essential to facilitate various graph data mining tasks when external supervision is unavailable. The challenge is to encode the information about the graph structure and…
We introduce a notion of $R$-quadratic maps between modules over a commutative ring $R$ which generalizes several classical notions arising in linear algebra and group theory. On a given module $M$ such maps are represented by $R$-linear…
This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric objects are defined over supercommutative rings of coefficients, and we consider an integral ring with exactly two odd variables. In this case the…
This paper studies learning the representations of whole graphs in both unsupervised and semi-supervised scenarios. Graph-level representations are critical in a variety of real-world applications such as predicting the properties of…
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems to do with polynomial systems over the reals, but known to have worst-case computational…
Informational parsimony provides a useful inductive bias for learning representations that achieve better generalization by being robust to noise and spurious correlations. We propose \textit{information gating} as a way to learn…
A new predictor-corrector type incremental algorithm is proposed for the exact construction of weighted straight skeletons of 2D general planar polygons of arbitrary complexity based on the notion of deforming polygon. In the proposed…
Multimodal semantic communication has gained widespread attention due to its ability to enhance downstream task performance. A key challenge in such systems is the effective fusion of features from different modalities, which requires the…
Gradual semantics (GS) have demonstrated great potential in argumentation, in particular for deploying quantitative bipolar argumentation frameworks (QBAFs) in a number of real-world settings, from judgmental forecasting to explainable AI.…
This is a study of algebras with involution that become isomorphic over a separable closure of the base field to a tensor product of two composition algebras. We classify these algebras, provide criteria for isomorphism and isotopy, and…