arXiv preprints from January 1, 2026 through July 28, 2026 — 19:58:50 EST
A holographic entropy inequality (HEI) is a linear inequality obeyed by Ryu-Takayanagi holographic entanglement entropies, or equivalently by the minimum cut function on weighted graphs. We establish a new combinatorial framework for studying HEIs, and use it to prove several properties they share, including two majorization-related...
This paper presents several efficient decision procedures for trace equivalence of GKAT automata, which make use of on-the-fly symbolic techniques via SAT solvers. To demonstrate applicability of our algorithms, we designed symbolic derivatives for CF-GKAT, a practical system based on GKAT designed to validate control-flow...
Approximate Nearest-Neighbor Search (ANNS) is a key technique in retrieval-augmented generation (RAG), enabling rapid identification of the most relevant high-dimensional embeddings from massive vector databases. Modern ANNS engines accelerate this process using prebuilt indexes and store compressed vector-quantized representations in...
Lymphovascular invasion (LVI) is an important prognostic marker for head and neck squamous cell carcinoma (HNSC), but the true effect of LVI on survival may be distorted by endogeneity arising from unmeasured confounding. Conventional one-stage conditional models and instrument-based two-stage estimators are prone to bias under...
We sketch the proof of an effective equidistribution theorem for one-parameter unipotent subgroups in $S$-arithmetic quotients arising from $\mathbf K$-forms of $\mathrm{SL}_2^{\mathsf n}$ where $\mathbf K$ is a number field. This gives an effective version of equidistribution results of Ratner and Shah with a polynomial rate. The...
Neural Machine Translation (NMT) models for low-resource languages suffer significant performance degradation under domain shift. We quantify this challenge using Dhao, an indigenous language of Eastern Indonesia with no digital footprint beyond the New Testament (NT). When applied to the unseen Old Testament (OT), a standard NMT...
Reasoning segmentation is an emerging vision-language task that requires reasoning over intricate text queries to precisely segment objects. However, existing methods typically suffer from overthinking, generating verbose reasoning chains that interfere with object localization in multimodal large language models (MLLMs). To address...
In this work we explore the performance and behavior of reasoning large language models to autonomously optimize atomic layer deposition (ALD) processes. In the ALD process optimization task, an agent built on top of a reasoning LLM has to find optimal dose times for an ALD precursor and a coreactant without any prior knowledge on the...
We introduce \emph{in-context operator learning on probability measure spaces} for optimal transport (OT). The goal is to learn a single solution operator that maps a pair of distributions to the OT map, using only few-shot samples from each distribution as a prompt and \emph{without} gradient updates at inference. We parameterize the...
Enhancing future wireless networks presents a significant challenge for networking systems due to diverse user demands and the emergence of 6G technology. While reinforcement learning (RL) is a powerful framework, it often encounters difficulties with high-dimensional state spaces and complex environments, leading to substantial...
The proliferation of connected devices and privacy-sensitive applications has accelerated the adoption of Federated Learning (FL), a decentralized paradigm that enables collaborative model training without sharing raw data. While FL addresses data locality and privacy concerns, it does not inherently support data deletion requests...
Photon statistics plays a governing role in multi-photon interference. While interference visibility in the standard two-photon case, known as Hong-Ou-Mandel interference, monotonically degrades with higher intensity correlation functions, we show that this monotonicity does not hold for three-photon interference in symmetric...
We present a unified operator-theoretic framework for stochastic calculus based on the factorization (Id - E)F = δ_X Π_X D_X F, valid for F_T^X-measurable F in L^2(Ω) when the driving process X has the representation property. For a square-integrable process X with stochastic integral δ_X, we define the operator-covariant derivative...
There exist conformally invariant, higher-derivative, variational analogs of the Yang-Mills condition for connections on vector bundles over a conformal manifold of even dimension greater than or equal to six. We give a compact formula for these analogs and prove that they are a strict weakening of the Yang-Mills condition with...
Personalizing Large Language Models typically relies on static retrieval or one-time adaptation, assuming user preferences remain invariant over time. However, real-world interactions are dynamic, where user interests continuously evolve, posing a challenge for models to adapt to preference drift without catastrophic forgetting....
An algebraic telic problem is a decision problem in $\textsf{NP}_\mathbb{R}$ formalizing finite-time reachability questions for one-dimensional dynamical systems. We prove that the existence of "natural" mapping reductions between algebraic telic problems coming from distinct dynamical systems implies the two dynamical systems exhibit...
Recent advances in large language models (LLMs) have led to substantial progress in domain-specific applications, particularly within the legal domain. However, general-purpose models such as GPT-4 often struggle with specialized subdomains that require precise legal knowledge, complex reasoning, and contextual sensitivity. To address...
Time series classification (TSC) is a core machine learning problem with broad applications. Recently there has been growing interest in repurposing large language models (LLMs) for TSC, motivated by their strong reasoning and generalization ability. Prior work has primarily focused on alignment strategies that explicitly map time...
Magnetoelectric multiferroics, materials with intrinsically coupled electric polarization and magnetic order, promise ultralow-power switching, nonvolatile memory, and energy-efficient signal transduction. Yet practical deployment demands ultrathin films down to the atomic limit, where both orders typically degrade. Maintaining both...
Interface circuits are the key components that enable the hybrid integration of superconductor and semiconductor digital electronics. The design requirements of superconductor-semiconductor interface circuits vary depending on the application, such as high-performance classical computing, superconducting quantum computing, and digital...
This paper presents the exact mathematical derivation of the mean and variance properties for the Exponentially Weighted Moving Average (EWMA) statistic applied to binomial proportion monitoring in Multiple Stream Processes (MSPs). We develop a Cumulative Standardized Binomial EWMA (CSB-EWMA) formulation that provides adaptive control...
We develop an operator-theoretic formulation of stochastic calculus for fractional Brownian motion with Hurst parameter H in (0, 1/2). The approach is based on adjointness between stochastic integration and differentiation in the Cameron-Martin space of the driving process. For Gaussian Volterra processes, we establish a canonical...
We argue that the machine learning value chain is structurally unsustainable due to an economic data processing inequality: each state in the data cycle from inputs to model weights to synthetic outputs refines technical signal but strips economic equity from data generators. We show, by analyzing seventy-three public data deals, that...
This exploratory study examines the classroom deployment of aiPlato, an AI-enabled homework platform, in a large introductory physics course at the University of Texas at Arlington. Designed to support open-ended problem solving, aiPlato provides step-wise feedback and iterative guidance through tools such as "Evaluate My Work" and...
Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures unify several classical and probabilistic families, including those of Stirling, Lah, Bell and...