arXiv preprints from January 1, 2026 through September 22, 2026 — 12:44:36 EST
Classical chaining controls an indexed stochastic process through a single worst-case bound, which can obscure substantial variation across the index set. We establish the first simultaneous pointwise majorization theory for Banach-valued processes with sub-Weibull or two-metric mixed-tail increments. For an anchored sub-Weibull...
Feature-based newsvendor models use observable covariates to tailor inventory decisions, aiming to balance holding and shortage costs under demand uncertainty. However, high-dimensional feature sets often hinder interpretability and inflate data collection and implementation costs. This paper studies variable selection for the...
Historically, retrieving rainfall data from satellite imagery has been the domain of space agencies. However, in recent years, the development of cheaper, more compact satellites (SmallSats) capable of detecting rainfall proxies has led to a significant increase in private-sector initiatives for satellite launch and surface...
We introduce a statistical framework for Gaussian fields indexed at arbitrary edge locations on general compact directed metric graphs. The construction is based on a stochastic differential equation with a first-order operator and conditions at the vertices. We characterise well-posedness and identify the covariance reproducing...
Generative data augmentation is widely used to mitigate class imbalance, yet its theoretical effect on downstream generalization remains poorly understood. In this work, we develop a statistical framework for conditional generative augmentation and analyze its impact on classification risk. We formalize augmentation as a...
The Rashomon effect is a machine learning phenomenon where equally accurate models produce different predictions for the same inputs (predictive multiplicity). Existing work primarily focuses on multiplicity within individual models, but in more complex decision systems, the impact of the Rashomon effect is less well understood. In...
At a junction, a score field can reveal weighted tangent rays, yet these first-order quantities do not determine how individual branches bend or how their densities change away from the center. Recovering this missing information is necessary for describing local continuation beyond a single point, but finite observations must...
We extend recent work establishing an equivalence between one-layer transformers and nearest-neighbor classifiers in the binary setting to the multiclass case. By leveraging the simplex encoding, we show that one-layer transformers with an argmax classification head behave identically to a one-nearest-neighbor classifier in the...
We prove that a multi-head scaled dot product attention can be viewed as a parameter identification strategy. The ratio of unidentified parameters to the total number of parameters scales like the reciprocal of the number of heads ($1/2 \to 1/(2H)$), meaning models with more heads are structurally more identified. A subtle side effect...
The present research is devoted to the nonparametric estimation of a density-dependent drift coefficient in a multivariate McKean--Vlasov diffusion from independent observations at a common time, as well as the stationary density. Under certain assumptions on the (known) potential, we reduce the problem to the one-dimensional one and...
While unified multimodal models (UMMs) jointly perform visual understanding and generation within a single model, functional unification does not guarantee learning synergy: the two objectives may reinforce each other, compete for capacity, or merely coexist. We investigate their relationship at the representation, task, and system...
Prethermalization describes long-lived intermediate regimes that precede equilibrium and can dominate experimentally accessible dynamics. Here, we show that a separation of spectral energy scales, despite giving rise to a hierarchy of dynamical timescales, does not by itself guarantee the appearance of a prethermal plateau. Under the...
We construct a constant-degree and constant-gap quantum expander on $n$ qubits where each unitary can be implemented by a depth-$1$ and 1D circuit of Pauli or CNOT gates. We provide two applications of this expander. First, we use it to construct a family of frustration-free 1D Hamiltonians whose ground states obey the...
LLM-based evaluators of natural language generation (NLG) quality are widely deployed as scoring tools and as automated training signals, yet the internal procedure by which they assign a rating remains poorly understood. We investigate this procedure mechanistically through an eight-attack perturbation taxonomy across the Readability...
Evaluating software engineering agents on realistic benchmarks is costly, since each task may require multi-step code exploration, modification, and test execution. Existing efficient evaluation methods select representative subsets to estimate full-benchmark performance, but are largely result-only: they fit historical pass/fail...
In a bulk 3D type-II superconductor, the lower critical field at which an isolated vortex becomes thermodynamically favorable is a size-independent material property. We show that the situation is different in 2D superconductors: the larger the superconductor, the weaker the field needed to create its first vortex. The lower critical...
The repository-level code generation task requires synthesizing code that satisfies task requirements while remaining consistent with the target repository context. Since real-world repositories often exceed the input length limits of LLMs, existing approaches commonly adopt retrieval-augmented generation (RAG) to provide...
Dynamic agent harnesses let language models change the software that shapes their own execution. This flexibility brings a new reasoning burden: a local plugin change can propagate through dependencies and cleanup. We introduce CordisBench, a 1,200-question benchmark of this lifecycle reasoning. It combines a controlled formal setting...
Warm Jupiters are an intriguing class of planets with uncertain origins. Their planetary obliquities could help distinguish between different formation pathways: planet-planet scattering and migration across resonances can excite large obliquities, whereas in-situ formation would more naturally produce low obliquities. We searched for...
Accurate segmentation of vascular structures in digital subtraction angiography (DSA) images remains challenging due to the thin, elongated, and branching nature of blood vessels. Pixel-wise deep learning approaches such as U-Net achieve strong general-purpose segmentation performance but often produce fragmented or discontinuous...
Natural language is emerging as a primary feedback channel for improving language agents, capable of conveying intent, preferences, and causal structure in forms interpretable by both humans and modern language models. We call this paradigm Verbal Reinforcement Learning (VRL) and offer the first unified account of it. We organize the...
Real-world robotic assembly at sub-millimeter tolerances demands spatial precision, compliant interaction, and robustness to contact failures. We present Facet-0, a robotic foundation model that predicts and values the contact consequences of its actions. Facet-0 unifies multimodal representation learning and reinforcement learning...
We develop a framework for mechanism design with AI agents whose alignment (preferences) and capabilities (feasible actions and information) are unknown. We want such agents to act on our behalf so mechanisms must incentivize both honesty and obedience. A one-sided imitation structure---capabilities can be concealed but not...
Hilbert's Tenth Problem over the integers was solved negatively by Y. Matiyasevich in 1970. In this paper, we prove that there is no algorithm to determine for any polynomial equation $P(z_1,\ldots,z_{10})=0$ (with integer coefficients and ten unknowns) whether it has integer solutions. This improves the previous 11 unknowns theorem.
Superconductor-semiconductor hybrids host emergent states of matter and offer a platform for new qubits, but the superconducting metal shunts electrical transport, which rules out conventional semiconductor characterization and leaves the hybrid parameters to speculation. Here we determine density, mass, $g$-factor, mobility and...