Related papers: Jordan-RoPE: Non-Semisimple Relative Positional En…
Deep Learning Reduced Order Models (ROMs) are becoming increasingly popular as surrogate models for parametric partial differential equations (PDEs) due to their ability to handle high-dimensional data, approximate highly nonlinear…
Reinforcement learning with verifiable rewards, particularly Group Relative Policy Optimization (GRPO), has significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, in complex tasks, GRPO frequently…
We construct via Fra\"iss\'e amalgamation an $\omega$-categorical structure whose automorphism group is an infinite oligomorphic Jordan primitive permutation group preserving a `limit of $D$-relations'. The construction is based on a…
We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at…
We consider Artinian algebras $A$ over a field $\mathsf{k}$, both graded and local algebras. The Lefschetz properties of graded Artinian algebras have been long studied, but more recently the Jordan type invariant of a pair $(\ell,A)$ where…
Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing and data analysis. The existing methods require a guess of the ranks of matrices that represent images or involve…
Transformers are increasingly prevalent for multi-view computer vision tasks, where geometric relationships between viewpoints are critical for 3D perception. To leverage these relationships, multi-view transformers must use camera geometry…
Retrieval-Augmented Generation (RAG) systems are widely adopted in knowledge-intensive NLP tasks, but current evaluations often overlook the structural complexity and multi-step reasoning required in real-world scenarios. These benchmarks…
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for \textit{ab initio} calculations of electronic correlation energies in solids and molecules. The method is an extension of the…
Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying…
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
The purpose of this note is to prove the following. Suppose $\R$ is a semiprime unity ring having an idempotent element e $\left(e \neq 0, e \neq 1\right)$ which satisfies mild conditions. It is shown that every additive generalized Jordan…
Conventional mobile tensegrity robots constructed with straight links offer mobility at the cost of locomotion speed. While spherical robots provide highly effective rolling behavior, they often lack the stability required for navigating…
Transformer architecture has enabled recent progress in speech enhancement. Since Transformers are position-agostic, positional encoding is the de facto standard component used to enable Transformers to distinguish the order of elements in…
Robot grasping of desktop object is widely used in intelligent manufacturing, logistics, and agriculture.Although vision-language models (VLMs) show strong potential for robotic manipulation, their deployment in low-level grasping faces key…
Object shape and pose estimation is a foundational robotics problem, supporting tasks from manipulation to scene understanding and navigation. We present a fast local solver for shape and pose estimation which requires only category-level…
Let $G$ be a connected reductive algebraic group with simply connected derived subgroup. Over the complex numbers there exists a local method to study the geometric properties of a point $g$ in the closure of a Jordan class of $G$ in terms…
Understanding intraventricular hemodynamics requires compact and physically interpretable representations of the underlying flow structures, as characteristic flow patterns are closely associated with cardiovascular conditions and can…
Let $\mathbb{K}$ be a field of characteristic different from $2$, and let $M_n(\mathbb{K})$ be the algebra of all $n\times n$ matrices over $\mathbb{K}$. We consider the corresponding special Jordan algebra $\mathcal{A}:=M_n(\mathbb{K})^+$…
We investigate the fine properties of harmonic measure and boundary rotation. By focusing on quasidisks and, in particular, on connected Jordan Repellers arising from conformal expanding dynamical systems, we explore those using the deep…