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At least 1,567 records · Page 87Linked to original sources
arXiv2026

Near-Optimal Bounds for Testing k-Colorability

We study the sample complexity of testing $k$-colorability in the dense graph model. A graph is $\varepsilon$-far from being $k$-colorable if at least $\varepsilon n^2$ edge deletions are required to make it $k$-colorable. We prove that, for every integer $k\ge 2$, a uniformly random induced subgraph on \[ O\!\left(\frac{k\log k}{\varepsilon}\right) \] vertices is non-$k$-colorable with probability at least $2/3$ whenever the original graph is $\varepsilon$-far from $k$-colorable. The proof introduces a trial coloring process based on nested palette systems and iteratively selected pivots. This yields an upper bound of $O(k\log k/\varepsilon)$, which is no worse than the previous state of the art $O(k\log(1/\varepsilon)/\varepsilon)$ throughout the nonvacuous parameter range, and is an improvement whenever $1/\varepsilon$ is superpolynomial in $k$. Moreover, for every fixed $k$, our bound matches the known lower bound, thereby establishing the optimal $Θ(1/\varepsilon)$ dependence on $\varepsilon$ and, to the best of our knowledge, achieving this optimal dependence for the first time.

cs.DM↗
arXiv2026

Self-Supervised Multibeam Sonar Restoration via Coherent Forward Modeling

Multibeam imaging sonar produces intensity images degraded by coherent speckle and system-induced blur, while clean reflectivity targets are rarely available. Existing despeckling methods often rely on simplified intensity-domain noise models, synthetic clean targets, or blind-spot self-supervision, and typically do not jointly model deblurring and speckle suppression. We propose a physics-consistent self-supervised framework for joint despeckling and deblurring of multibeam imaging sonar. A stochastic coherent image-formation model yields a conditional-mean forward operator that relates latent scene reflectivity to expected intensity through the squared magnitude of the system point spread function. We then use registered multi-frame sonar sequences to train without clean ground truth images, showing that, under an idealized inter-frame conditional-mean condition, the expected paired loss equals the corresponding forward-prediction loss up to a network-independent constant. To stabilize the ill-conditioned inverse problem, we further adapt robust equivariant imaging using stochastic coherent simulation and introduce a paired forward prediction error metric for ground-truth-free evaluation. Experiments on two real multibeam sonar datasets demonstrate a favourable balance between forward-prediction agreement, homogeneous-region speckle suppression, and preservation of visible structural boundaries compared with representative baselines.

eess.IV↗
arXiv2026

Coresets for $k$-Means: When Does Uniform Sampling Suffice?

Data summarization techniques, such as coresets, are essential for scaling clustering algorithms to massive datasets. We study uniform sampling, which is an extremely simple and ultra-efficient method to construct coresets, in the context of weak, stable, and strong coresets for the $k$-means problem in Hilbert space. We begin with the fundamental case $k=1$, and establish matching upper and lower bounds on the sample complexity of stable and weak coresets, finding that the two notions require different sample complexities. As a consequence, we obtain tight bounds for stable $1$-median coresets in $\ell_1$ and $\ell_2$ (and thus also Kendall--tau and Jaccard metrics), removing the dimension dependence of Carmel and Krauthgamer (ICLR 2026). Our analysis is substantially simpler than prior work and reduces to bounding the deviation of the sample mean. For the general $k$-means problem on $ρ$-separated instances, a well-studied structural assumption on the input, we show that uniform sampling yields a stable coreset for all $O(1)$-approximate solutions, and a strong coreset if the instance additionally has bounded kurtosis. In all these results, the sample complexity is independent of the dimension and the instance size.

cs.DS↗
arXiv2026

A Headwind-like Helium Outflow from TOI-3884b

Constraining atmospheric loss is crucial for understanding the evolution of planetary atmospheres. We report the detection of an evaporating exosphere from TOI-3884b, a super-Neptune in a polar orbit around an M4 dwarf star. We infer this evaporation from a 6.8$\pm$0.27\% excess transit depth in the He I 10830 Å\, line, observed during five transits of TOI-3884b with the Habitable Zone Planet Finder spectrometer. While we observe outflow signatures starting as early as 5 hours before the onset of the planet's optical transit, no significant post-transit tail is detected. Hitherto, such a pre-transit headwind without a significant post-transit tail has only been detected from HAT-P-67b, a hot Saturn orbiting an F-type star. This asymmetric outflow morphology supports irradiation-driven mass loss over core-heated mass loss, and we explore whether this could be caused by sub-Alfvén star-planet interaction. The detection of such complex outflow morphologies is now opening a new window, enabling us to test theories of star-planet interactions and planetary magnetic fields with observations.

astro-ph.EP↗
arXiv2026

Improved Bounds for the Entropic Central Limit Theorem in the Log-Concave Case

Let $μ$ be a log-concave isotropic probability measure on $R^d$ , and let $μ^n$ denote the law of the normalized sum of $n$ independent random vectors with law $μ$. We prove that \[ H(μ^n|γ)\leq \frac{C}{n} \min\left\{1+\log(ed)^2H(μ|γ)\ ,\ d\right\}. \] Compared to the previous best known bound, our estimate replaces the polynomial dependence on the dimension by a polylogarithmic one. The proof relies on a new combination of the De Bruijn identity with Eldan's stochastic localization process.

cs.IT↗
arXiv2026

AgentVQA: A Unified Benchmark for Agentic Visual Understanding

Vision-language models (VLMs) can perform a broad range of tasks across diverse settings, yet their performance in agentic contexts remains poorly understood. Although online evaluations in simulators and real-world environments are essential for measuring interactive agent performance, they are costly and challenging to scale. Complementary offline VQA benchmarks can enable faster and more reliable comparisons across agentic domains, yet existing benchmarks remain limited and fragmented. To address this gap, we introduce AgentVQA, an offline benchmark for evaluating VLMs on realistic agentic scenarios across five agent domains: Web Agents, Robotics, Egocentric Videos, Games, and Spatial Planning. We build AgentVQA by manually selecting 1000 challenging, real-world agent examples from 23 source datasets and adapting them for reliable offline evaluation. The resulting benchmark preserves realistic scenarios from interactive environments across diverse domains, and its model rankings track those from corresponding online evaluations. Across the 22 evaluated models, the best achieves only 58.5% accuracy. Our cross-domain analysis shows that errors are driven primarily by failures to ground and maintain accurate representations of the current and evolving visual state, including localizing relevant UI elements, interpreting motion, tracking state changes over time, and inferring 3D spatial relationships, rather than by task misinterpretation or downstream logical reasoning.

cs.CV↗
arXiv2026

SABLE: Scalable Affine Bayesian Latent-space Exploration

Complex objects such as engineering designs and proteins are often difficult to optimise because their design spaces exhibit high-dimensional structure and objective evaluations are expensive. Generative models provide continuous latent representations, but their latent spaces can have thousands to tens of thousands of dimensions, creating a regime where the latent dimension $D$ greatly exceeds the evaluation budget. We introduce SABLE, a Bayesian optimisation method for high-dimensional latent spaces with an isotropic distribution and limited budget. SABLE uses a Bayesian affine surrogate for prediction and acquisition, treating higher-order structure as surrogate discrepancy. After $N$ observations, the slope update has dimension at most $N-1$, yielding a decomposition of each query into an in-span component optimised by expected improvement (EI) in at most $N$ dimensions and an off-span component governed by a scalar norm. We show that the off-span norm implicitly selected by affine EI can lead to underexploration, and SABLE instead prescribes it using a finite-horizon schedule, without restricting search to a learned subspace. A recompression scheme reduces information to $\mathcal O(M)$ pseudo-observations, bounding refitting cost by $\mathcal O(M^2D+M^3)$ while keeping parameter inference, prediction, and acquisition decisions to tens of milliseconds. Across synthetic benchmarks and latent-space optimisation tasks, SABLE achieves high sample efficiency and reduces decision time by several orders of magnitude at large budgets.

cs.LG↗
arXiv2026

Mixed-Precision Coalesced Matrix-Free Multigrid with Vertex-Patch Smoothing

I present a geometric multigrid solver for the Poisson equation with continuous cubic elements in three dimensions, smoothed by a multiplicative vertex-patch Schwarz method with exact local solves. All fields are kept in persistent cell-wise storage, where every cell holds its own copy of each shared degree of freedom. The patch smoother yields a continuous solution without any exchange between cells. On the GPU, the patch update is computed in registers, one cell per thread, and the cells of a patch exchange data by warp shuffles, so shared memory is avoided almost entirely. Despite the low occupancy that this design implies, the arithmetic of the patch update runs close to the FP32 peak. Fast diagonalization, merged transforms, and a reflection symmetry of the patch then reduce the arithmetic until a sweep moves its data at $87\%$ of the bandwidth of a plain device copy. The hierarchy therefore runs in single precision inside a double-precision outer iteration. Rounding the unassembled residual destroys the cancellation between opposite-sign copies of shared degrees of freedom; exchanging the copies between cells in double precision performs this cancellation before rounding, without changing the dual vector they represent. With this \emph{rebalancing}, the cycle converges as in double precision and independently of the mesh size, the error converges at the optimal rate down to the precision of the solve, and the solver reaches over $400$ million degrees of freedom per second on a single NVIDIA A100 GPU.

math.NA↗
arXiv2026

A semiampleness result for hyperkähler fourfolds and smoothings of Lagrangian subvarieties

We give a geometric proof of the following statement: let $X$ be a smooth hyperkähler fourfold such that the Picard group is generated by a line bundle $L$ that is nef, non-trivial, and not big. If the Kodaira dimension of $L$ is non-negative, some positive multiple defines a Lagrangian fibration. The proof requires a number of tools which are of independent interest, including an analogue of Voisin's unobstructedness result and a smoothing result for singular Lagrangian subvarieties.

math.AG↗
arXiv2026

Observation of Polarization Topology in Magneto-Optical BICs

Polarization topology in momentum space is a fundamental characteristic of photonic bound states in the continuum (BICs), where the winding of far-field polarization defines a quantized topological charge. Although magneto-optical (MO) BICs combine polarization topology with magnetically tunable chirality, experimental characterization remains challenging because time-reversal symmetry (TRS) breaking complicates eigenpolarization extraction. Here, we experimentally resolve the momentum-space polarization topology of an MO BIC by reconstructing its two-dimensional far-field eigenpolarization texture. We extract the resonant output polarization using singular value decomposition of the polarization-resolved angle-resolved reflection matrix without invoking reciprocity. The reconstructed polarization azimuth winds counterclockwise by 2$π$ around the $Γ$-point singularity, yielding a topological charge of q = +1. Moreover, the polarization handedness can be reversed solely by varying the magnetic-bias strength, while the field direction and the measured topological charge remain unchanged. A non-Hermitian coupled-mode model traces this reversal to hybridization between the BIC mode and a leaky mode. This work establishes experimental access to momentum-space polarization topology in nonreciprocal photonics, opening a route to explore topological singularities and their evolution under active TRS breaking.

physics.optics↗
arXiv2026

Water Transport on 3-Spiders: Unbounded Lengths of Shortest Optimal Strategies

Let $G$ be a finite simple graph. An averaging operation selects a nonempty connected vertex set and replaces the weights of its vertices by their arithmetic mean. For a nonnegative initial weight function $ω:V(G)\to\mathbb R_{\ge0}$ and a target vertex $x$, let $t(G,x,ω)$ denote the minimum number of averaging operations needed to attain the maximum reachable weight at $x$. Gollin et al.[1] proved, using the Axiom of Choice, that a finite optimal strategy exists for every finite graph, every nonnegative initial weight function and every target vertex; see Tao [2] for a simplified proof. We prove that the lengths of shortest optimal strategies on $3$-spiders have no uniform finite bound. In particular, these lengths cannot be bounded in terms of the maximum degree of the graph.

math.CO↗
arXiv2026

The Impact of Markovian Errors on Random Circuits

Randomized benchmarking (RB) returns a single decay parameter or gate error rate, but when the noise is gate-dependent that parameter is notoriously difficult to interpret. We study RB and related random-circuit benchmarks under small gate-local Markovian noise by factorizing each noisy gate into its ideal action followed by the exponential of a small error generator and then perturbing the RB $\mathscr{L}$ matrix, which models the RB decay. For any low-error gate set that satisfies the requirements of RB (it is a sequence-asymptotic unitary 2-design), we show that Pauli-stochastic error rates contribute linearly to the RB decay parameter, while Hamiltonian error rates contribute through a gauge-invariant quadratic form. Pauli-correlation and active generators are absent from the linear term and enter only at higher order. For the single-qubit native gate set $\{X_{π/2},Y_{π/2}\}$ we derive this quadratic form explicitly in terms of three first-order gauge-invariant (FOGI) coordinates: the two intrinsic over-rotations and one relational axis-tilt error. The resulting formula explains the dependence of DRB on the sampling distribution and the compilation dependence of CRB. These results turn RB decay rates into interpretable functions of experimentally meaningful elementary error rates.

quant-ph↗
arXiv2026

One-shot entanglement generation and distillation via Petz recovery and binary hypothesis testing

How much entanglement can two distant laboratories share when their connection is noisy? We relate this question to deciding which of two quantum hypotheses is present. Our one-shot bounds apply to entanglement generation over a quantum channel and to one-way entanglement distillation from a shared state. We use Cheng's trace inequality to bound the infidelity of a Petz decoder in terms of a binary hypothesis testing cost. Applying the inequality before averaging over codes reduces the error analysis to computing a second moment of random subspaces. The proof covers every integer target dimension and treats rank-deficient states explicitly. A corollary expresses the achievable entanglement through hypothesis-testing coherent information, with a single logarithmic error slack and exact integer rounding. We also prove an error-preserving conversion from entanglement generation codes to entanglement transmission codes: the target dimension decreases by only a constant factor at fixed error, and the decoder is the original decoder followed by local processing. Consequently, for both entanglement generation and entanglement transmission, arbitrary pure reference-input states yield the same coherent-information rate, second-order Gaussian correction at the original error tolerance, and explicit achievable logarithmic remainder. For commuting testing hypotheses, the logarithmic remainder improves to a constant. These results give a direct route from binary distinguishability to explicit recovery guarantees and finite-resource quantum communication rates.

quant-ph↗
arXiv2026

Douglas-Rachford splitting method for nonconvex stochastic optimal control

Motivated by the numerical resolution of stochastic optimal control problems, particularly those involving nonlinear dynamics, we investigate the convergence properties of the Douglas-Rachford splitting algorithm in a nonconvex and infinite-dimensional setting. We introduce an extension of the method that applies when one component of the objective function is continuously differentiable with a locally Lipschitz gradient, while the other is weakly lower semicontinuous with a bounded domain.

math.OC↗
arXiv2026

Maximum Likelihood Estimation and Likelihood Ratio Tests for the Power Spherical Distribution

The Power Spherical distribution has been proposed as a computationally efficient alternative to the von Mises-Fisher distribution for data on the unit sphere, with reduced computational cost for simulation and a simpler normalizing constant. Despite these advantages, its statistical inference properties remain underdeveloped. In this paper, we develop a likelihood-based framework for estimation and inference for the Power Spherical distribution. Within this framework, we develop maximum likelihood estimation procedures for both the central direction and concentration parameter. Building on these estimators, we formulate likelihood ratio tests for hypotheses involving known and unknown parameters, study their asymptotic behavior, and evaluate finite-sample performance through simulation studies. The results demonstrate accurate Type I error control and good power when the asymptotic chi-square approximation is appropriate, while the parametric bootstrap provides reliable inference in small-sample settings or those where the dimension is large relative to the sample size. The findings also highlight nontrivial dependence of the power of tests for the central direction on the concentration parameter.

stat.ME↗
arXiv2026

Structure-preserving reduced-order models of thin panels in supersonic and hypersonic flow

We build structure-preserving reduced-order models for both challenge problems of the AePW-4 High-Speed Working Group. They are a clamped thin panel at Mach 1.92 (RC-19) and a cantilever plate at Mach 5.85 (HyMAX). The published data for each case hold no time-resolved response and no repeated runs. The physics must therefore be carried by the form of the model. One construction gives two models per problem. A Ritz-Galerkin reference model describes the plate. A learned model keeps the reference model's exact potential, fits the remaining generalized forces, and trains only a dissipation that cannot add energy. Its energy balance holds for any weights by construction. On the trained model the worst relative residual is 2.2e-15. On RC-19, shock relations predict a pressure ratio of 1.521 across the panel. Pressure-sensitive paint measured the same value. Thirty runs of the learned model place the mean dominant frequency within 1.0% of the measured 236 Hz. At one periodic and one chaotic condition, the learned model reproduces the response regime of a published reduced-order model in all sixteen runs. It does so without that model's 113 Hz spectral peak, which the measurements do not show. Measured displacements can also correct the chaotic response through one more force that respects the energy balance. We tested this on synthetic data at the experiment's 5 kHz sampling rate. The state error is 1.25% of the panel thickness without noise and 3.5% with 10 micrometers of noise. On HyMAX the learned model follows the reference model's trailing-edge displacement for 65 ms with a relative error of 3.7%. These results show that a model whose structure carries the physics can match measured flutter behavior when the available data cannot train it.

cs.CE↗
arXiv2026

FairFRESH: A Neuro-Symbolic Framework for Fair and Explainable Household Food Recommendation

Recommender systems typically serve one user at a time. However, in households, members share a finite pantry and follow different dietary rules, making independent recommendations prone to resource conflicts and dietary violations. We formulate household food recommendation as constrained fair division and present FairFRESH, a neuro-symbolic framework that learns per-member utilities, allocates foods under explicit welfare objectives, enforces dietary rules through a deterministic filter, and explains recommendations using Shapley and Banzhaf attributions. Theoretically, we show that no finite penalty guarantees compliance near a dietary-rule threshold, establish approximation guarantees for greedy allocation under utilitarian and smoothed Nash objectives in the stock-free model before filtering, and characterize the scale invariance of Nash welfare. We also use the minimax theorem to analyze rotating shared meals. On NHANES-derived data, the learned utility model achieves Recall@20 of 0.293, outperforming five learned recommenders (at most 0.244) but not a previous-day repetition heuristic (0.321). On held-out four-person households, Nash allocation reduces Gini disparity by 42% relative to conflict resolution while improving Recall@20 from 0.180 to 0.197. It comes within 2% of an upper bound on the smoothed Nash optimum, and rescaling one member's utilities changes at most 1.5% of assignments. All recommendations satisfy the encoded dietary rules, while attribution scores correlate with utility loss upon component removal (r = 0.76). In simulation, shared meals reduce pantry use by about one-third, and weekly rotation increases the worst-off member's utility by 38% over the best fixed meal.

cs.AI↗
arXiv2026

Macroscopic Nuclear Resonance Energy Transfer Mediated by Coherent Magnons

Phonon-mediated nuclear Resonance Energy Transfer (RET) in metal deuterides is severely constrained by inertial rest-mass dilution, lattice fracture limits, and thermal nuclear spin cancellation. Extending the generalized nuclear Dicke model to Ferromagnetic Resonance (FMR) magnons eliminates mass dilution via hyperfine-amplified M1 coupling while unlocking relativistic Dirac M2 coupling via Overhauser spin polarization. We derive a Suhl-clamped FMR scaling law predicting 14.2 MeV (Pd-106) and 11.4 MeV (Ni-58) breakup neutrons, 19.9 MeV alpha particles, and reconciled sub-keV fusion anomalies.

nucl-ex↗