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arXiv:2602.05970v2 Announce Type: replace-cross Abstract: Neural scaling laws relate loss to model size in large language models (LLMs), yet depth and width may contribute to performance differently, requiring more detailed studies. Here, we quantify how depth affects loss via analysis of LLMs and toy residual networks. We find loss scales inversely proportional to depth in LLMs, probably due to functionally similar layers reducing error t..
arXiv:2602.06837v2 Announce Type: replace-cross Abstract: Hybrid modeling, the combination of machine learning models and scientific mathematical models, enables flexible and robust data-driven prediction with partial interpretability. However, the unknown parameters of the scientific model cannot necessarily be estimated properly, since the flexibility of the machine learning model might make the scientific model part effectively ignored ....
arXiv:2602.07218v2 Announce Type: replace-cross Abstract: Adaptability has been regarded as a central feature in the foundation models, enabling them to effectively acclimate to unseen downstream tasks. Parameter-efficient fine-tuning methods such as celebrated LoRA facilitate efficient adaptation of large foundation models using labeled, high-quality and generally scarce task data. To mitigate data scarcity in fine-tuning of foundation mo....
arXiv:2602.10014v3 Announce Type: replace-cross Abstract: Iterative self-improvement fine-tunes an autoregressive large language model (LLM) on reward-verified outputs generated by the LLM itself. In contrast to the empirical success of self-improvement, the theoretical foundation of this generative, iterative procedure in a practical, finite-sample setting remains limited. We make progress toward this goal by modeling each round of self-i....
arXiv:2602.10056v2 Announce Type: replace-cross Abstract: We introduce WildCat, a high-accuracy, low-cost approach to compressing the attention mechanism in neural networks. While attention is a staple of modern network architectures, it is also notoriously expensive to deploy due to resource requirements that scale quadratically with the input sequence length $n$. WildCat avoids these quadratic costs by only attending over a small weighte....
arXiv:2602.16733v3 Announce Type: replace-cross Abstract: Computational reproducibility is central to scientific credibility, yet verifying published results at scale remains costly. We develop an AI-assisted workflow for automated full-paper replication -- retrieving materials, reconstructing environments, executing code, and matching outputs to point estimates reported in regression tables. We define a universe of all empirical and quant....
arXiv:2602.19126v2 Announce Type: replace-cross Abstract: We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets. Starting from the classical equivalence between ridge-regularized RF training and Bayesian inference with Gaussian priors and likelihoods, we replace the single prior and likelihood with $\epsilon$- and $\et....
arXiv:2602.23197v2 Announce Type: replace-cross Abstract: Transformer-based large language models exhibit in-context learning, enabling adaptation to downstream tasks via few-shot prompting with demonstrations. In practice, such models are often fine-tuned to improve zero-shot performance on downstream tasks, allowing them to solve tasks without examples and thereby reducing inference costs. However, fine-tuning can degrade in-context lear....
arXiv:2603.01157v2 Announce Type: replace-cross Abstract: Risk forecasts in financial regulation and internal management are calculated through historical data. The unknown structural changes of financial data pose a substantial challenge in selecting an appropriate look-back window for risk modeling and forecasting. We develop a data-driven online learning method, called the bootstrap-based adaptive window selection (BAWS), that adaptivel....
arXiv:2603.19005v2 Announce Type: replace-cross Abstract: Data science plays a critical role in transforming complex data into actionable insights across numerous domains. Recent developments in large language models (LLMs) and artificial intelligence (AI) agents have significantly automated data science workflow. However, it remains unclear to what extent AI agents can match the performance of human experts on domain-specific data science....
arXiv:2603.23398v3 Announce Type: replace-cross Abstract: Generative modeling of discrete data, such as graphs, underpins many scientific and industrial applications, including molecular discovery and materials design. In these domains, probabilistic inference is particularly valuable, as it enables composable generation and principled incorporation of desired constraints, such as structural or functional properties. Energy-based models na....
arXiv:2604.00578v2 Announce Type: replace-cross Abstract: Marked correlation functions, in which galaxy properties such as luminosity or stellar mass are treated as marks, are widely used to test models of galaxy formation. In astronomy, however, these statistics are typically implemented as summary measures that do not preserve the joint structure of mark pairs conditioned on separation. In this work, we formulate galaxies as points $(x,m....
arXiv:2604.08149v2 Announce Type: replace-cross Abstract: We consider a linear contextual bandit model where contexts and rewards are governed by a finite hidden Markov chain. We first revisit the simplified model by Nelson et al. (2022), in which rewards are linear functions of the posterior probabilities over the hidden states given the observed contexts (called beliefs), rather than functions of the hidden states themselves. This simpli....
arXiv:2604.09041v2 Announce Type: replace-cross Abstract: AI-based weather forecasting now rivals traditional physics-based ensembles, but state-of-the-art (SOTA) models rely on specialized architectures and massive computational budgets, creating a high barrier to entry. We demonstrate that such complexity is unnecessary for frontier performance. We introduce \ours, a probabilistic forecaster built on a standard U-Net backbone trained wit....
arXiv:2604.17838v2 Announce Type: replace-cross Abstract: Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for constrained diffusion models on generic nonconvex feasible sets $\Sigma$ that simultaneously enforces equality and inequality constraints throughout the di....
arXiv:2605.12895v2 Announce Type: replace-cross Abstract: Clinical decision-support systems are expert systems whose recommendations clinicians act on directly, yet they are usually cleared on one aggregate accuracy number from a held-out test set. That number says nothing about input reliability under encoding shifts, subgroup gaps, threshold sensitivity, or operational feasibility. We present RISED, a pre-deployment evaluation framework ....
arXiv:2605.14432v2 Announce Type: replace-cross Abstract: We study far-field discrimination between one and two incoherent point sources in the singular regime of weak and closely spaced emitters. Under ideal alignment, spatial-mode demultiplexing (SPADE) attains the quantum-optimal large-sample Stein exponent, but the finite-photon behavior near the one-source boundary and the effect of realistic imperfections remain less understood. Usin....
arXiv:2605.18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process. To manage this realistic and challenging setting, new mechanisms, such as gradient clipping and gradient normalization, have been introduced to ensure the convergence of first-order algorithms. However, adaptive gradient methods, a famous class of modern optimiz..
arXiv:2605.20716v5 Announce Type: replace-cross Abstract: Random forests construct each tree with a different, randomised representation of the feature space. Their uniform voting cannot correct errors in regions where trees with incorrect representations probabilistically outnumber correct ones, even when the ensemble collectively holds enough correct information - a reducible error that this paper addresses. We propose using the structur....
arXiv:2605.21648v2 Announce Type: replace-cross Abstract: We develop a mean-field theory of dropout as a perturbation of critical signal propagation at the edge of chaos, and show that it predicts a simple, no-cost change to standard practice: \emph{front-loaded} dropout schedules cut test loss by \(18\)--\(35\%\) over constant dropout in MLPs and Vision Transformers at fixed budget. The theoretical mechanism is that dropout shifts the per....
arXiv:2605.24583v3 Announce Type: replace-cross Abstract: Comparing a model's internal activations before and after alignment is a natural way to ask what safety training changes: one forms the matrix of paired aligned-minus-base activations on safety-relevant inputs and reads off its effective rank or top direction. We show the obvious way to form this matrix is confounded. The aligned model is evaluated under a chat template the base mod....
arXiv:2605.26431v2 Announce Type: replace-cross Abstract: Structural probes train on Universal Dependencies (UD), which does not encode formal-syntactic abstractions such as phase boundaries or phase-internal cohesion. Whether large language models (LLMs) encode these remains an open question that UD-based probing cannot answer by construction. We evaluate structural probes on wh-movement stimuli where UD distances are invariant across con....
arXiv:2605.26919v2 Announce Type: replace-cross Abstract: Maintaining predictive accuracy in non-stationary environments requires online model selection to adapt autonomously to unknown distribution shifts. However, existing tuning-free algorithms face a fundamental trade-off between robustness and agility. Specifically, to ensure dynamic regret bounds, they must restrict learning rates to small constants (e.g., $O(1)$). This restriction i....
arXiv:2605.30188v2 Announce Type: replace-cross Abstract: Reliable probability estimates are critical in many machine learning applications, yet modern classifiers are often poorly calibrated. Post-hoc calibration provides a simple and widely used solution, but the large number of proposed methods, combined with small-scale and inconsistent evaluations, makes it difficult to determine which approaches are truly effective in practice. We in....
arXiv:2605.31200v2 Announce Type: replace-cross Abstract: Interpretable machine learning requires models that are accurate and structurally faithful to the data. Existing explainability methods rely heavily on additive representations (e.g., Generalized Additive Models (GAMs), SHapley Additive exPlanations (SHAP), functional ANOVA), which can suffer from signal cancellation and off-support extrapolation in the presence of strong interactio....
arXiv:2606.00233v1 Announce Type: new Abstract: Density estimation is often presented as a choice among parametric summaries, finite mixtures, and nonparametric smoothers. This review argues for a complementary view: a data set can be studied through a path of densities indexed by smoothing scale, diffusion time, model complexity, density level, or noise level. We call this perspective density evolution. Under this lens, Gaussian kernel de....
arXiv:2606.00246v1 Announce Type: new Abstract: The Fourier Entropy-Influence (FEI) conjecture states that the Fourier entropy of Boolean functions is uniformly bounded by their total influence. It has been verified for canonical examples such as disjoint tribes and for some classes of Boolean functions such as symmetric functions and read-$k$ decision trees (with a constant that depends linearly on $k$). In this note we present new classe....
arXiv:2606.00247v1 Announce Type: new Abstract: We show that Grothendieck's real constant $K_G$ can be upper bounded by projecting vectors onto a random plane through the origin and thresholding a degree five Hermite polynomial. This resolves a conjecture of Braverman-Makarychev-Makarychev-Naor from 2011, who required an extra randomization step in their rounding scheme and proved $K_G<\frac{\pi}{2\log(1+\sqrt{2})}-10^{-500}$. As a corolla..
arXiv:2606.00273v1 Announce Type: new Abstract: The goal of this work is to study the combinatorics of the lattices of higher torsion classes of the higher Auslander and Nakayama algebras of type \textbf{A}. Combinatorial descriptions of these higher torsion classes were recently obtained by August \textit{et al.} (2025), and it was observed that the lattices that they form are not semidistributive. We study in some depth these lattices, p....
arXiv:2606.00274v1 Announce Type: new Abstract: In the design of computational methods for Bayesian inverse problems, costly forward model evaluations make it difficult to sample from or compute the posterior. This motivates the need for approximate forward models that are cheaper to evaluate. We consider reduced-order forward models which exploit the lower-dimensional structure in the Bayesian inverse problem by projecting to the "likelih....
arXiv:2606.00276v1 Announce Type: new Abstract: We derive dispersive-dissipative estimates for multipliers associated to a general class of wave-type equations, in particular for the viscous Boussinesq equation. The dispersion is related to the geometric hypotheses on the phase func tion and on the degeneracies that may happen at low and high frequencies. The dissipation interacts with the dispersion, influencing the decay rate of the solu..
arXiv:2606.00283v1 Announce Type: new Abstract: We present a constructive version of the Br{\o}ndsted-Rockafellar theorem in general geodesic metric spaces. Applications include a constructive form of the Caristi theorem and quantitative relations between metric slope error bounds and the global growth of functionals.
arXiv:2606.00290v1 Announce Type: new Abstract: The inducibility constant $\lambda_{F}$ of a graph $F$ is the asymptotically maximum induced density of $F$ in a growing sequence of graphs. This paper systematically investigates the case when $F$ has 6 vertices (and there are 78 cases to consider up to isomorphism and complementation). We show that flag algebras can compute the sharp upper bound on $\lambda_F$ in 36 cases of which, as far a..
arXiv:2606.00298v1 Announce Type: new Abstract: Data-driven reduced-order modeling is an essential component in the computer-aided design of control systems. In this work, we present a novel symmetric Hermite formulation of the quadrature-based balanced truncation algorithm that constructs linear reduced-order models from evaluations of the full-order system's transfer function and its derivative. Significantly, the Hermite formulation pre..
arXiv:2606.00312v1 Announce Type: new Abstract: Over the past half-dozen years, stochastic rounding (SR) has regained significant attention as a quantization scheme for low-precision floating-point arithmetic, with applications spanning numerical analysis and modern machine learning systems. Recent work has shown that SR acts as an implicit regularizer by increasing the smallest singular value of extremely tall-and-thin (or, symmetrically,....
arXiv:2606.00316v1 Announce Type: new Abstract: We study smooth functions on Euclidean space whose Hessian is positive definite outside a bounded set, with emphasis on products of squared distance functions. More precisely, we first prove a simple convexity principle: if the superlevel region $f^{-1}([c,\infty))$ is contained in the Hessian-positive region of $f$, then the sublevel set $\{f\le c\}$ is convex. We apply this to finite produc..
arXiv:2606.00325v1 Announce Type: new Abstract: This work deals with the ergodicity for the stochastic dissipative Hasegawa-Mima equations in a bounded domain and perturbed by additive noise. The uniqueness of the invariant measure is obtained by the asymptotic coupling technique.
arXiv:2606.00330v1 Announce Type: new Abstract: We study the fluctuations of logarithmic Green singularities in the spherical ensemble, viewed as a random discretization of the two-sphere. Smooth observables exhibit the usual Sobolev or Gaussian free field fluctuations, whereas logarithmic singularities live on a larger logarithmic scale and asymptotically decouple in high-dimension, producing an explicit white-noise limit. The result give..
arXiv:2606.00335v1 Announce Type: new Abstract: Perelman's proof of the Poincare conjecture shows that every simply connected closed 3-manifold is homeomorphic to the 3-sphere. The fundamental groups of 3-manifolds attract lots of interest from mathematicians of different fields. As it was stated in a famous survey of Allen Hatcher "The classification of 3-manifolds", one would want to know exactly which groups occur as fundamental groups ....
arXiv:2606.00343v1 Announce Type: new Abstract: Motivated by the analysis of the behaviour of extremes from multivariate heavy-tailed distributions, we introduce a novel notion of statistical depth, referred to as Polar Depth. The polar depth function is naturally expressed in polar coordinates, as is the limiting distribution of a regularly varying random variable, beyond asymptotically large thresholds, once its marginals have been appro....
arXiv:2606.00347v1 Announce Type: new Abstract: We study empirical $L_p$ moments of a random vector $\pmb\varphi$ based on its i.i.d.\ copies $\pmb\varphi^1,\ldots,\pmb\varphi^m$, that is, $\frac1m\sum_{j=1}^m |\langle \pmb\varphi^j,y\rangle|^p$. Our main result is a new estimate for the expected uniform deviation \[ \mathbb{E}\sup_{y\in D}\biggl| \frac1m\sum_{j=1}^m |\langle \pmb\varphi^j,y\rangle|^p -\mathbb{E}|\langle \pmb\varphi,y\rang....
arXiv:2606.00354v1 Announce Type: new Abstract: We demonstrate that the three prevailing notions of completeness for Cartan geometries are not actually equivalent and provide methods for constructing many examples in the affine case, modernizing and extending results due to Yeaton Clifton. In an effort to rectify the folklore on the topic, we also provide detailed explanations of how specious proofs in the literature that would claim that ..
arXiv:2606.00363v1 Announce Type: new Abstract: The task of inductive logic is to develop a formal framework to analyze inductive reasoning. Historically this was accomplished by assigning probabilities to sentences of a logical language. Two natural criteria for such a system are: (i) the underlying language should be rich enough to express scientific hypotheses, and (ii) the probabilities should be, in some sense, accessible. The first c....
arXiv:2606.00375v1 Announce Type: new Abstract: Complementing a theorem of \v{S}krekovski, we characterize the $(h-1)$-critical graphs embeddable in surfaces of Euler genus at least $5$, where $h$ denotes the Heawood number of the surface. Outside of a few small cases, the bulk of our proof is determining the genus of the join of a complete graph and the 5-cycle. As a byproduct of our proof, we also provide a simpler solution to the minimu..
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