arXiv preprints from January 1, 2026 through September 22, 2026 — 06:45:43 EST
The aim of this paper is to develop a framework for measure theory that avoids infinities and allows for the uniform treatment of positive and vector measures. Our approach is based on a modification of the notion of measure, which supplements the usual $σ$-additivity requirement with a suitable maximality condition. To each Hausdorff...
Let $G$ be a definable group in an NIP theory. We prove that every minimal proximal definable $G$-flow is strongly proximal. Consequently, the universal minimal proximal definable $G$-flow $Π^{\mathrm{def}}(G)$ coincides with the minimal strongly proximal definable $G$-flow $Π^{\mathrm{def}}_{\mathrm{s}}(G)$. Furthermore, for a...
We study a data-driven reflection control problem for a Brownian model with unknown drift and volatility. We first propose a learn-then-optimize (LTO) algorithm: it estimates the policy-relevant parameter during exploration, plugs the estimate into the optimality equation, and exploits the resulting policy---achieving an $O(\sqrt{T})$...
This paper is concerned with the precise asymptotics, as time goes to infinity, of a transport problem in a half plane coupled with a nonlinear nonlocal boundary condition. This system arises from a class of models for the spatial spread of epdemics, its space independent version being the classical Kermack-McKendrick model. Using...
We classify a class of abstract Bose field models in quantum field theory up to unitary equivalence. The class includes abstract free Bose field models, abstract van Hove--Miyatake models, and infrared-renormalized van Hove--Miyatake models. Moreover, as an application of our classification, we classify quadratic interaction models....
Retail supply chain operations rely on coupled decision modules that must adapt as requirements evolve. LLMs offer a natural-language interface for this task, but existing methods primarily focus on individual optimization models. Extending them to heterogeneous decision pipelines is challenging because a requirement may admit...
We study the asynchronous $\ell^p$ relaxation introduced by Amir, Nazarov, and Peres: at each step, a uniformly chosen vertex minimizes its incident $\ell^p$ energy. For the profile $f_t$ after $t$ updates, let $$ \mathsf T_p(G,1/2):= \sup_{\lVert f_0\rVert_\infty\le1} ...
We prove the following inequality for Dirichlet polynomials: \[ \int_0^1 |f(1/2+σ)|\,dσ\lesssim \lim_{T\to\infty} \frac{1}{2T} \int_{-T}^T |f(it)| \, dt. \] In particular, for a Dirichlet series $f(s) = \sum_{n\geq 1} a_n n^{-s}$ belonging to the Hardy space $\mathscr{H}^1$ of Dirichlet series, \[ \left|a_1+\sum_{n=2}^\infty...
The Schrödinger-Lohe (SL) model is a coupled system of nonlinear Schrödinger equations describing the temporal-spatial evolution of the component wave functions, and it corresponds to the infinite-dimensional counterpart of the Lohe matrix model for quantum synchronization. In this paper, we study a rigorous mean-field limit of the SL...
We disprove McKean's conjecture, which asserts that the entropy dissipation is monotone nonincreasing along solutions, or equivalently that the entropy is convex in time, for the spatially homogeneous Landau-Coulomb equation. We provide an explicit counterexample which consists of a Maxwellian equilibrium under radially symmetric,...
Autonomous robots powered by deep learning face a fundamental auditability challenge: when incidents occur, investigators cannot reconstruct why the system made specific decisions. This paper presents TRACE (Transparent Reasoning Architecture for Credible Execution), a decision framework that ensures every autonomous action can be...
Modern crop breeding demands precise organ-level analysis for trait quantification, making plant point cloud segmentation (PPCS) increasingly important. However, conventional deep learning approaches rely heavily on densely annotated datasets that are labor-intensive to acquire. Unified PPCS adaptation from distribution-shifted...
Harnessing naturally occurring feedback from user interactions offers a promising learning signal for Large Language Models (LLMs). However, recent studies suggest this feedback is inherently noisy and difficult to leverage effectively. We challenge this conception by demonstrating that user feedback is a highly actionable signal for...
The 3D center of mass (CoM) is a primary quantity in the biomechanical analysis of sport, rehabilitation, and clinical movement, yet existing 3D pose tracking, mesh recovery, and multi-view triangulation methods either optimize 3D keypoint accuracy without anatomical constraints or carry compute and capture infrastructure too heavy to...
LLMs are trained to generate natural language. However, various strands of evidence indicate that an LLM's externalized linguistic outputs and mechanistically-extracted linguistic features can be an unreliable lens for understanding internal model computation. We introduce the term ``linguistic illegibility'' to broadly refer to...
Competitive programming has become a key test of large language model reasoning, with international competitions such as IOI and ICPC representing its most challenging settings. We present an end-to-end specialization pipeline combining large-scale problem curation, synthetic reasoning traces, supervised fine-tuning (SFT), and...
Novel view synthesis from sparse inputs requires both geometric grounding from the observed views and generative priors of unobserved regions, motivating recent hybrid methods that combine reconstruction and generation. However, existing methods bridge the two with rendered images or explicit 3D representations such as point maps or...
Stable 4-bit floating-point (FP4) pretraining is difficult because the E2M1 payload represents only a narrow range of magnitudes. NVIDIA's Transformer Engine \nv{} recipe addresses this with current-tensor scaling, a randomized Hadamard transform (RHT), and bfloat16 (BF16) final layers, adding work outside the FP4 matrix...
Adverse weather conditions such as rain, haze, and snow significantly degrade image quality, posing challenges for both human perception and physical AI. Existing restoration methods require large computational budgets, struggling to process high-resolution images and handle different degradations. In this paper, we present Frequency...
Modern cameras transform RAW sensor measurements into sRGB images through an image signal processor (ISP). We benchmark two placements for blind restoration around a fixed ISP: (A) pre-ISP restoration in the RAW domain and (B) post-ISP restoration in the sRGB domain. The benchmark covers four smartphone device groups, two learned...
LiDAR-based semantic segmentation is a core perception module for autonomous vehicles and mobile robots. Despite the strong performance of recent state-of-the-art methods on standard benchmarks, existing evaluation protocols remain focused on clean, single-domain settings and fine-grained label taxonomies, leaving deployment readiness...
People increasingly use language models to support life decisions. Many such decisions involve a probabilistic forecast: How likely is a major life event, a natural disaster, or an economic outcome? Users of language models may implicitly trust that these forecasts fall out of a coherent world model. In this paper, we evaluate the...
Extending the Price-and-Choose (P&C) mechanism of Echenique and Nunez (2025), we propose the Price-Accept-and-Choose (PA&C) mechanism, which preserves efficiency while eliminating P&C's first-mover advantage. We then analyze randomized and bidding variants and show that the resulting equilibrium payoffs correspond to standard...
Large language models (LLMs) are increasingly deployed as economic agents, yet there is little evidence whether LLM agents are suited for participating in market mechanisms designed for humans, and whether these mechanisms deliver desired outcomes when faced with LLM agents. We address this question by replicating seminal economic...
We study a network formation game in which agents sponsor links at a linear cost in order to maximize centrality, defined as a weighted sum of walk counts with positive and weakly decreasing weights. This class includes Katz Bonacich centrality and total communicability and captures environments in which access decays with distance....