Related papers: Jordan-RoPE: Non-Semisimple Relative Positional En…

6D pose estimation of rigid objects from RGB-D images is crucial for object grasping and manipulation in robotics. Although RGB channels and the depth (D) channel are often complementary, providing respectively the appearance and geometry…

We propose a novel positional encoding for learning graph on Transformer architecture. Existing approaches either linearize a graph to encode absolute position in the sequence of nodes, or encode relative position with another node using…

We expand on an idea of Vinberg to take a tensor space and the natural Lie algebra that acts on it and embed their direct sum into an auxiliary algebra. Viewed as endomorphisms of this algebra, we associate adjoint operators to tensors. We…

Let G be a quasisimple algebraic group over an algebraically closed field of characteristic p>0. We suppose that p is very good for G; since p is good, there is a bijection between the nilpotent orbits in the Lie algebra and the unipotent…

The Learning with Errors (\LWE) problem has been widely utilized as a foundation for numerous cryptographic tools over the years. In this study, we focus on an algebraic variant of the \LWE problem called \emph{Group ring} \LWE ($\GRLWE$).…

Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…

We propose a non-singular representation for a non-Hermitian operator even if the parameter space contains exceptional points (EPs), at which the operator cannot be diagonalized and the usual spectral representation ceases to exist. Our…

Accurate phase estimation -- the process of assigning phase values between $0$ and $2\pi$ to repetitive or periodic signals -- is a cornerstone in the analysis of oscillatory signals across diverse fields, from neuroscience to robotics,…

We propose Parabolic Position Encoding (PaPE), a parabola-based position encoding for vision modalities in attention-based architectures. Given a set of vision tokens-such as from videos, event camera streams, images, or point clouds-our…

We identify a core failure mode that occurs when using the usual linear interpolation on rotary positional embeddings (RoPE) for mixed-resolution denoising with Diffusion Transformers. When tokens from different spatial grids are mixed, the…

In 1934, Jordan et al. gave a necessary algebraic condition, the Jordan identity, for a sensible theory of quantum mechanics. All but one of the algebras that satisfy this condition can be described by Hermitian matrices over the complexes…

Accurate 6D object pose estimation is fundamental to robotic manipulation and grasping. Previous methods follow a local optimization approach which minimizes the distance between closest point pairs to handle the rotation ambiguity of…

Extending context window sizes allows large language models (LLMs) to process longer sequences and handle more complex tasks. Rotary Positional Embedding (RoPE) has become the de facto standard due to its relative positional encoding…

Vision-based pose estimation of articulated robots with unknown joint angles has applications in collaborative robotics and human-robot interaction tasks. Current frameworks use neural network encoders to extract image features and…

A shape invariant nonseparable and nondiagonalizable three-dimensional model with quadratic complex interaction was introduced by Bardavelidze, Cannata, Ioffe, and Nishnianidze. However, the complete hidden symmetry algebra and the…

Retrieval-based question answering systems often suffer from positional bias, leading to suboptimal answer generation. We propose LoRE (Logit-Ranked Retriever Ensemble), a novel approach that improves answer accuracy and relevance by…

This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients satisfying a Cordes condition. The construction follows the…

We propose a metallic-silicon system with a complex optical potential modulated along the length of the waveguide for a robust higher harmonic generation. For right moving fields when the strength of non-Hermiticity becomes equal to the…

Range-only (RO) pose estimation involves determining a robot's pose over time by measuring the distance between multiple devices on the robot, known as tags, and devices installed in the environment, known as anchors. The nonconvex nature…

Representational learning forms the backbone of most deep learning applications, and the value of a learned representation is intimately tied to its information content regarding different factors of variation. Finding good representations…