Related papers: The E$\Delta$-MHC-Geo Transformer: Adaptive Geodes…

Transformers empirically perform precise probabilistic reasoning in carefully constructed ``Bayesian wind tunnels'' and in large-scale language models, yet the mechanisms by which gradient-based learning creates the required internal…

Noncommutative K\"ahler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a \emph{compact quantum homogeneous…

We conduct a systematic robustness analysis of the hybrid machine learning framework \texttt{USmorph}, which integrates unsupervised and supervised learning for galaxy morphological classification. Although \texttt{USmorph} has already been…

Leaf-lesion segmentation is topology-sensitive: small merges, splits, or false holes can be biologically meaningful descriptors of biochemical pathways, yet they are weakly penalized by standard pixel-wise losses in Euclidean latents. I…

A new multiplication-free transform derived from DHT is introduced: the RHT. Investigations on the properties of the RHT led us to the concept of weak-inversion. Using new constructs, we show that RHT is not involutional like the DHT, but…

Let M be a hypercomplex Hermitian manifold, (M,I) the same manifold considered as a complex Hermitian with a complex structure I induced by the quaternions. The standard linear-algebraic construction produces a canonical nowhere degenerate…

In the first part, Hyperkaehler Embeddings and Holomorphic symplectic Geometry I, we prove the following. Let $N$ be a closed analytic subvariety of a generic deformation of a holomorphically symplectic compact manifold $M$. Then the…

Dimensionality reduction (DR) plays a crucial role in various fields, including data engineering and visualization, by simplifying complex datasets while retaining essential information. However, achieving both high DR accuracy and strong…

Further studies on the corner singularity of GS reconstruction are are compiled in this paper. It's focused on solution of the Data Completion (DC) problem with the Extended Hilbert Transform (EHT) over plane rectangular region. Optimal…

Deep-learning electronic structure calculations show great potential for revolutionizing the landscape of computational materials research. However, current neural-network architectures are not deemed suitable for widespread general-purpose…

Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified…

We propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer…

Recent progress in geometric deep learning has drawn increasing attention from the machine learning community toward domain adaptation on symmetric positive definite (SPD) manifolds, especially for neuroimaging data that often suffer from…

In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Formulations are given for the geodesic…

We present a hybrid transformer architecture that replaces discrete middle layers with a continuous-depth Neural Ordinary Differential Equation (ODE) block, enabling inference-time control over generation attributes via a learned steering…

This paper presents a novel hybrid approach for modeling the voltage gain of LLC resonant converters by combining deep-learning neural networks with the polynomial based Group Method of Data Handling (GMDH). While deep learning offers high…

Let $\mathcal M= (M,\mathcal O_\mathcal M)$ be a smooth supermanifold with connection $\nabla$ and Batchelor model $\mathcal O_\mathcal M\cong\Gamma_{\Lambda E^\ast}$. From $(\mathcal M,\nabla)$ we construct a connection on the total space…

This note contains two remarks. The first remark concerns the extension of the well-known Cayley representation of rotation matrices by skew symmetric matrices to rotation matrices admitting -1 as an eigenvalue and then to all orthogonal…

We consider locally conformal Kaehler geometry as an equivariant (homothetic) Kaehler geometry: a locally conformal Kaehler manifold is, up to equivalence, a pair (K,\Gamma) where K is a Kaehler manifold and \Gamma a discrete Lie group of…

Let ${\mathbb H}_g$ and ${\mathbb D}_g$ be the Siegel upper half plane and the generalized unit disk of degree $g$ respectively. Let ${\mathbb C}^{(h,g)}$ be the Euclidean space of all $h\times g$ complex matrices. We present a partial…