arXiv preprints from January 1, 2026 through September 22, 2026 — 00:31:24 EST
Although probabilistic statements are ubiquitous, foundational disagreements persist about their understanding, as exemplified by debates between Bayesians and frequentists; moreover, it is unclear when and why acting on them actually leads to desirable outcomes. Here, we argue that every probability is the output of a...
This paper develops estimator-level asymptotic theory for maximum Diaconis-Ylvisaker prior penalised likelihood for logistic regression with a jointly fitted intercept and nonzero prior slope direction in the proportional-limit regime. For $\mathrm{N}(\mathbf{0}_p, p^{-1}\mathbf{I}_p)$ Gaussian covariates and $p/n\toκ\in(0,1)$, a...
Muon replaces matrix momentum with an approximately orthogonal polar direction, but its geometry depends on the matrix representation. For convolution, standard unfolding describes a local patch map rather than the convolution operator. We introduce Muon-C, an operator-aligned optimizer that represents kernel momentum as...
We identify a diagonal saturation principle in modal inverse problems: when truncation noise is isotropic, the Bayes-optimal Tikhonov shape is a closed-form power law Gamma_k proportional to lambda_k^|s| set by the prior alone, independent of the domain. Berry's random-wave conjecture decorrelates the truncation noise across modes,...
A popular class of causal inference methods addresses confounding through weighting, which reweights treated and control groups to balance their covariate distributions without using outcome information, thereby preserving a design-based perspective. In this paper, we propose sliced $L^p$ distributional balancing (SLDB), a family...
The orthogonal factor model has been a very useful tool in uncovering covariance structures in a set of variables through a smaller set of underlying factors. This old model is suitable for continuous variables with unbounded support, since the most common assumption for the observables and the factors is multivariate normality. In...
Time series foundation models (TSFMs) are increasingly pre-trained on synthetically generated time series trajectories, where the data generating process is known. Current pre-training recipes are based on loss objectives which compare TSFM outputs to realized future values of each trajectory. We instead propose loss objectives which...
Odor quality is commonly represented using high dimensional descriptor profiles, yet their low dimensional organization remains unclear. We investigated whether a two-dimensional hyperbolic embedding can provide an interpretable representation of this structure. We applied hyperbolic metric multidimensional scaling to two...
Synthetic data has become a promising way to scale model training beyond limited human-generated data but it may also induce strong model collapse (Dohmatob et al., 2024), where any fixed fraction of synthetic data prevents model performance from improving under data scaling, leaving a non-vanishing excess risk floor. In this paper,...
Neural networks can leverage feature superposition to encode more concepts than dimensions, but cross-feature interference constrains the linear accessibility of simultaneously active features. By framing linear accessibility as a compressed sensing problem, we derive high-probability bounds for fixed supports under subgaussian noise,...
We recast statistical significance as a choice between making an immediate policy recommendation and deferring it until further evidence is collected. We show that the welfare-optimal decision corresponds, under minimax regret, to a statistical test whose level depends on the cost and precision of additional evidence. Inverting this...
Average treatment effect (ATE) estimation in observational studies is a fundamental statistical tool used frequently in social science, medicine, and other fields. These fields often work with sensitive data where privacy protections are important, so a differentially private mechanism for ATE estimation is highly desirable. Here we...
We study the oracle complexity of computing a point with small fixed-point residual $\|T(x)-x\| \leq ε$, for a general norm $\|\cdot\|$ and a self-map $T$ of a compact convex set. We study this problem in the setting where $T$ is nonexpansive with respect to the same norm $\|\cdot\|$ and accessed via an unbiased stochastic oracle with...
We prove that, for every smooth complex del Pezzo surface of degree at most four, the enhanced right orthogonal to the structure sheaf determines the surface up to isomorphism. In degrees one, two, and three, we recover the anticanonical equation from intrinsic pieces of the Hochschild-Serre algebra via graded matrix factorizations;...
Let H be a subgroup of a finite group G, and put n = [G:H] > 1. If p is the least prime divisor of n, we prove that the number of subgroups K with H <= K <= G is less than c(p) n^((log_p n)/4). Here c(p) is the product of (1 - p^(-j))^(-1) over all positive integers j, multiplied by the sum of p^(-z^2) over all integers z. The...
We introduce a new type of $p$-adic hypergeometric function, which satisfies congruence relations similar to Dwork's $p$-adic hypergeometric function. Also, we prove that the syntomic regulators of the Hesse cubic curves are expressed in terms of the special values of our new $p$-adic hypergeometric functions. We also show that there...
We develop a family of weakly symmetric and pointwise traceless tangential--normal tensor finite elements in arbitrary space dimension and for all polynomial orders. Symmetry is imposed through local cell moments, while the only globally coupled stress degrees of freedom are tangential--normal facet moments; no vertex degrees of...
A graph $G$ is $n$-existentially closed or $n$-e.c. if, for all subsets $S\subseteq V(G)$ with $|S|=n$ and for all partitions $S=A\sqcup B$, there exists a vertex in $V(G)\sm S$ adjacent to all vertices in $A$ and no vertices in $B$. We study the minimum number of edges $m(v,n)$ of a $v$-vertex $n$-e.c. graph, and show that...
We prove the strict positivity conjectured by Chenevier for the critical vectors in the unconditional part of his automorphic Hermite--Minkowski theorem. The proof establishes strict negativity of all Verblunsky coefficients of a circle measure associated with the weight $(\arcsin x)/x$ on $(-1,1)$. A positive-kernel formula and the...
In this paper, we count the number of (almost) extremally stretched closed geodesics for a pair of (non-conjugate) Fuchsian representations of a closed surface group, and show that it has subexponential growth. We then deduce that, as a discrete subgroup of $\mathsf{PO}(2, 1) \times \mathsf{PO}(2, 1)$, the growth indicator of the...
We establish sharp local estimates for smooth numbers. Corollaries are derived, including optimal estimates for square-free smooth numbers.
We give counterexamples to Yau's question on normalized scalar curvature integrals in every dimension $n\geq4$. For each such $n$, there exists a smooth complete Riemannian metric $g$ on $\mathbb{R}^n$ with nonnegative Ricci curvature and a pole such that \[ \lim_{R\to\infty}R^{2-n}\int_{B_q(R)}\mathrm{Scal}_g\,\mathrm dV_g=+\infty...
In this paper, we prove that, under suitable conditions on the generating profile, every connected, compact embedded minimal capillary hypersurface supported on a one-ended rotational hypersurface in the Euclidean space is a horizontal slice. We also construct a smooth one-ended rotational support carrying a non-horizontal planar...
We study convex quadratic minimization over the unit $L_1$ ball in which the maximum eigenvalue of the Hessian matrix is bounded by a positive constant $L$. We propose a novel first-order algorithm with objective value error bounded by $O(L/T^3)$ after $T$ gradient evaluations, assuming that the subproblems involved in the algorithm...
We develop an algebraic framework for the quasi-modularity of symmetric multiple $q$-zeta values. We identify natural classes of symmetric quasi-shuffles whose $q$-zeta values exhaust the algebra of level-one quasi-modular forms, and further classes whose $q$-zeta values are quasi-modular forms of finite level. We also obtain explicit...