arXiv preprints from January 1, 2026 through September 10, 2026 — 18:21:55 EST
Machine learning procedures are commonly evaluated in terms of predictive accuracy and computational efficiency. However, their achievable performance is fundamentally constrained by structural properties of the underlying data-generating process, which are formalized in terms of informational bounds. In this work we examine intrinsic...
In this paper, we extend the classical problem of studying the distribution of $k$-free integers in arithmetic progressions to the setting of arbitrary number fields. Using the language of ray class groups, we establish asymptotic formulas, together with error terms, for the number of $k$-free ideals of bounded norm lying in a given...
In this short note, we show that $H$-minor-free graphs have a tree cover with $3$ trees and constant stretch for any fixed graph $H$. The number of trees matches the recent lower bound by Chen, Tan, and Xu who showed that a toroidal grid requires at least $3$ trees for constant stretch. Our result is obtained by establishing a...
We study safety-critical control for teams of quadrotor UAVs driven by decentralized navigation functions under learned model uncertainty. These functions generate fully actuated translational reference forces, while quadrotors can only produce thrust along their body-fixed vertical axes. We construct a thrust-attitude implementation...
Liquids exhibit collective behavior that depends sensitively on thermodynamic conditions, interfaces and confinement, yet predicting each new state commonly requires a separate atomistic simulation. Classical density functional theory offers a reusable variational description, but its central excess free-energy functional is generally...
Scientific discovery increasingly requires AI systems that can reason over scientific evidence of heterogeneous modalities, interact with scientific tools and environments, and sustain progress across long task horizons. We present Intern-S2-Preview, a series of scientific agentic foundation models designed to support multimodal...
We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data. SORT estimates expansion coefficients directly from observations using L1-regularized regression, avoiding explicit quadrature or analytic inner-product...
Complex multipath environments are usually avoided in wave-based information processing because repeated scattering creates many interfering propagation paths, obscuring controllability and generating extreme sensitivity to perturbations. The addition of nonlinear mechanisms fundamentally alters the wave-control landscape by breaking...
Snapshot Compressive Imaging (SCI) offers an efficient solution for high-speed video acquisition and, under exposure-time camera--scene relative motion, multi-view scene capture by compressing temporal or spatial information into a single 2D measurement. While recent studies have explored SCI for 3D scene reconstruction, existing...
In the transversal achievement game on the $n\times n$ board, two players alternately claim cells, and the first to own a transversal---a set of $n$ cells of which no two share a row or column---wins. Ranđelović showed that the first player wins for every $n\ge4$, while the game is a draw for $n=2,3$. We give an independent proof that...
We describe a mechanism of affine symmetry emergence in the maximal density regime of the prototypical model of self-organized criticality when the inverse square of the mesh of the underlying lattice is much larger than the number of random perturbation points distributed according to a prescribed probability measure supported in the...
Achieving cost efficiency while meeting strict user-facing SLOs (e.g., time-to-first-token) remains a fundamental challenge for cloud GPU clusters serving large language models (LLMs). Autoscaling is the key mechanism for cluster resource management, yet a basic system design question is open for serving LLMs: what should be the unit...
We investigate the quadratic-order effective energy--momentum tensor (2EMT) of scalar cosmological perturbations on uniform-density hypersurfaces during slow-roll inflation. The 2EMT is constructed from terms quadratic in the linear metric and inflaton perturbations, and is therefore a gauge-fixed effective source rather than a...
We prove that for every integer $N\geq 3$ and $α\geq \frac{1}{2}$, Beckner's inequality \[ \fracα{2}\int_{\mathbb{S}^N}u(P_{N}u) dw+(N-1)!\int_{\mathbb{S}^N}u dw-\frac{(N-1)!}{N}\log\int_{\mathbb{S}^N}e^{Nu} dw\geq 0 \] holds for every $u\in H^{\frac{N}{2}}(\mathbb{S}^N)$ whose center of mass is at the origin. The proof is mainly...
Secure, private multi-tenant execution spanning processors, memory, and accelerators remains one of the most significant challenges in modern edge computing systems. Simultaneously, processing-in-memory (PIM) has emerged as an effective approach for reducing the Von Neumann bottleneck by moving computation closer to data. Existing...
Efficiently retrieving relevant clips from large-scale driving logs is essential for data curation, model development, and safety analysis. Structured and rule-based retrieval systems can explicitly target driving events, but typically require expert-defined rules, auxiliary data, and multi-stage perception pipelines. Multimodal...
AI weather emulators benefit from clear objectives and metrics, which have led to the rapid development of models that outperform traditional benchmarks. In contrast, long-term climate emulators must reliably reproduce forced responses over months to centuries, while relying on training objectives that span a small number of model...
We study the distribution of quantum correlations and basis-independent coherence in a pair of massive particles confined in a double-well potential and coupled through their mutual Newtonian gravitational interaction. Non-classical correlations are characterized using Bures distance of entanglement and quantum discord, while...
This report presents an improved version of AlayaWorld. While the backbone architecture, chunk-wise autoregressive generation scheme, and training data remain unchanged from the previous release, we substantially revise how conditioning signals are represented and integrated into the model. The new design is guided by a simple...
Unitary designs provide finite-moment approximations to Haar-random unitaries, with wide-ranging applications across physics and quantum information, from scrambling and black-hole dynamics to foundational primitives in quantum algorithms. Strong unitary designs capture a more demanding operational notion of approximation, requiring...
Deep learning surrogates for RANS flow prediction around airfoils face two persistent bottlenecks. A single neural architecture cannot simultaneously resolve sharp near-wall boundary layers and smooth far-field potential flow. Additionally, force prediction is undermined by the numerical instability of computing wall-normal velocity...
We present \textbf{DreamX-Phi 1.0}, an action-conditioned video world model for robotic manipulation that, given an observed frame, a language instruction, and a prescribed action sequence comprising end-effector poses and gripper states, predicts the resulting future observations. Yet realism alone does not guarantee faithfulness: a...
Motivated by recent DESI results suggesting dynamical dark energy, we investigate the thawing scenario in quintessence with an exponential potential, $V=V_0e^{-λφ/m_{\mathrm{pl}}}$, by analytically expanding the deviation of the equation of state parameter $w_φ$ from $-1$ in powers of $λ$. In addition to the previously known...
Let $K\subset\mathbb{R}^n$ be an isotropic convex body. We prove that the hit-and-run walk, started from any $M$-warm distribution, reaches total-variation distance $\varepsilon$ from the uniform distribution on $K$ in $O\!\left(n^2ψ_n^{-2}\log^3(M/\varepsilon)\right)$ steps, where $ψ_n^{-1}$ is the Kannan-Lovász-Simonovits (KLS)...
We give the first theoretical characterization, and the first algorithm, for continuous monitoring of a distributed Cyber-Physical System (CPS) against a dense-time temporal logic specification. A distributed CPS is composed of multiple agents, each with a local clock; these clocks drift from each other, so there is no well-defined...