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