The paper extends prior work on volume sampling by providing a Loewner envelope for the centered coefficient covariance in least‑squares regression with a fixed pool of features and responses. It characterizes when this envelope is tight, linking tightness to strict spectral properties of residuals, and introduces a residual‑augmented change of measure to derive a one‑sided slack bound. The results also offer geometric insights at the boundary and demonstrate non‑vacuous certificates through frozen‑feature examples, focusing on conditional centered, full‑Gram‑whitened covariance rather than population generalization.
By Kihun Rhee
arXiv:2607. 21999v1 Announce Type: new Abstract: Long-tailed learning couples two sources of poor generalization: head classes dominate training exposure, while under-represented classes often converge to sharper regions of the loss landscape.
By Jiaxin Deng, Junbiao Pang
The paper investigates restricted eigenvalue (RE) bounds for norm‑regularized estimators under heavy‑tailed designs. It shows that the previously conjectured sample‑size law based on Gaussian width fails for heavy‑tailed measurements, due to a phenomenon called simultaneous threshold occupancy. The authors provide explicit counterexamples, derive worst‑case sample‑complexity bounds, and compare the behavior of heavy‑tailed versus Gaussian designs on constant‑width polyhedral descent cones.
By Shi Fu, Huibo Xu, Qixin Zhang, Dacheng Tao
The paper investigates the geometry of full conformal prediction (FullCP) regions produced by an empirical energy‑form pairwise score. It shows that convexity of the candidate score alone does not ensure connected FullCP regions, and establishes conditions under which comparison regions share a common minimizer, making the exact conformal region star‑shaped. For power distances with exponent β≥1 the geometry is deterministic, and for β between 1 and 2 explicit Lipschitz bounds allow certified inner and outer radial envelopes with Hausdorff guarantees.
By Yiheng Feng
arXiv:2607. 07206v2 Announce Type: replace Abstract: Optimizer experiments observe responses to algorithmic configurations without uniquely revealing hidden mechanisms.
By Zavier Li
arXiv:2607. 22935v1 Announce Type: new Abstract: Minimum-exposure constraints arise in recommendation, content curation, and regulated allocation when each provider, arm, or group must receive guaranteed exposure inside a period rather than only in aggregate.
By Ibne Farabi Shihab, Joyanta Jyoti Mondal, Anuj Sharma
The paper introduces Resolution-Aware Experimental Design (RAED), a method that selects experiments by minimizing the expected size of the nonempty structural candidate set while controlling false-exclusion rates. RAED is shown to preserve expected ordering under a composite Blackwell comparison and is implemented via a learned score-based approach with finite-sample nuisance-average and positive-tail calibration. Experiments on subsurface-flow, fluvial, and methane-oxidation benchmarks demonstrate RAED’s ability to resolve structural ambiguities and provide finite-sample guarantees for tail-sensitive nuisance risk.
By Sofianos Panagiotis Fotias
arXiv:2511. 13592v2 Announce Type: replace-cross Abstract: The existing method of GS-PowerOpt solves the non-convex optimization problem of the form $\max_{\boldsymbol{x} \in \mathbb{R}^d} f(\boldsymbol{x})$ through maximizing a Gaussian-smoothed surrogate $F_{N,\sigma}(\boldsymbol{\mu}) = \mathbb{E}_{\boldsymbol{x}\sim\mathcal{N}(\boldsymbol{\mu},\sigma^2 I_d)}[e^{N f(\boldsymbol{x})}]$.
By Chen Xu
arXiv:2606.14636v3 Announce Type: replace
Abstract: Many two-stage estimators assess the first-stage learner by prediction error, even when the next stage uses its residual. In control-function instr...
By Rui Wu, Zongyuan Chen, Hong Xie, Defu Lian, Enhong Chen
arXiv:2607. 05815v1 Announce Type: new Abstract: The Minkowski functionals of a field's excursion sets -- area, boundary measure, and Euler characteristic -- describe its level-set morphology; the Euler characteristic is the cheapest handle on topology.
By Gunner Levi Howe
The paper introduces Resolution-Aware Experimental Design (RAED), a method that selects experiments by minimizing the expected size of the nonempty structural candidate set while controlling false exclusions. RAED is shown to align with a composite Blackwell comparison and is implemented via a learned score-based approach with finite-sample calibration. Experiments on subsurface-flow, fluvial, and methane-oxidation benchmarks demonstrate that RAED can diverge from expected-information-gain selections, yielding clearer resolution and explicit ambiguity handling.
arXiv:2606. 01883v1 Announce Type: new Abstract: Open-set recognition (OSR) requires a classifier to reject inputs from unseen classes which is essential in safety-critical settings such as medical imaging.
By Mayank Sharma, Rohit Kumar Mourya