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

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

Parallel LLM test-time scaling techniques (e.g., best-of-$N$) require drawing $N>1$ sequences conditioned on the same input prompt. These methods boost accuracy while exploiting the computational efficiency of batching $N$ generations.…

Dynamic Data Driven Applications Systems (DDDAS) motivate the development of optimization approaches capable of adapting to streaming, heterogeneous, and asynchronous data from sensor networks. Many established optimization solvers, such as…

Most existing latent-space models for dynamical systems require fixing the latent dimension in advance, they rely on complex loss balancing to approximate linear dynamics, and they don't regularize the latent variables. We introduce RRAEDy,…

For finite p-groups P of class 2 and exponent p the following are invariants of fully refined central decompositions of P: the number of members in the decomposition, the multiset of orders of the members, and the multiset of orders of…

A relativistic analogue of the quantum adiabatic approximation is developed for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an arbitrary scalar potential. The corresponding adiabatic dynamical and geometrical…

Using derivatives of primary fields (null or not) with respect to the conformal dimension, we build infinite families of non-trivial logarithmic representations of the conformal algebra at generic central charge, with Jordan blocks of…

In this paper we find a representative of each orbit of the adjoint action of a real affine classical group of its Lie algebra. These orbits are not determined by the usual Jordan invariants of eigenvalues and block sizes, but require a…

The aim of this article is to introduce the concept of centrally-extended Jordan endomorphisms and proving that if $R$ is a non-commutative prime ring of characteristic not two, and $G$ is a CE- Jordan epimorphism such that $[G(x), x] \in…

Transformers have demonstrated outstanding performance in many applications of deep learning. When applied to time series data, transformers require effective position encoding to capture the ordering of the time series data. The efficacy…

We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$ \emph{exact}…

Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded noise gain is typically proven. In recent work it has been shown, in both the pole placement…

Atom loss is a major error source in neutral-atom quantum computers, accounting for over 40% of the total physical errors in recent experiments. Its nonlinear and correlated nature poses significant challenges: current syndrome extraction…

Rule-based systems must solve complex matching problems within tight time constraints to be effective in real-time applications, such as planning and reactive control for AI agents, as well as low-latency relational database querying.…

The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…

We establish a local rigidity theorem for quasi--Lie brackets on quaternionic Banach right modules. Under quantitative control of antisymmetry and Jacobi defects, we construct an explicit bilinear correction that preserves right…

We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework.…

Explaining closed-source Large Language Model (LLM) outputs is challenging because API access prevents gradient-based attribution, while perturbation methods are costly and noisy when they depend on regenerated text. We introduce…

We present a new algorithm for the numerical evaluation of five-point conformal blocks in $d$-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in…

Sampling low-energy molecular conformations, spatial arrangements of atoms in a molecule, is a critical task for many different calculations performed in the drug discovery and optimization process. Numerous specialized equivariant networks…