The paper investigates how many data samples per domain are needed for effective learning across multiple domains. It derives criteria from learning bounds that reveal an inverse linear relationship between the number of training domains and the required samples per domain, offering theoretical guidance for dataset adequacy and construction. The study also establishes a close link between in-domain learning and out-of-domain generalization through new generalization bounds.
By Hong Zheng
arXiv:2609.36030v1 Announce Type: new
Abstract: The lack of rigorous safety and performance certificates remains a key bottleneck to the deployment of modern learning-based methods. Sample compressio...
By Dario Paccagnan, Marius Tirlea
arXiv:2606. 08638v1 Announce Type: cross Abstract: Recent research has developed practical, parallelizable first-order methods for large scale linear programming, but performance is highly dependent on hyperparameter selection.
By Siddharth Prasad, Dravyansh Sharma
arXiv:2606. 17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube.
By Jasper van Doornmalen, Mathieu Molina, Victor Verdugo, Jos\'e Verschae
arXiv:2607. 22467v1 Announce Type: new Abstract: Data scarcity poses a fundamental challenge in training generative models to produce initial guesses for parametric optimization problems that are otherwise numerically expensive to solve.
By Anjian Li, Ryne Beeson
arXiv:2601. 20970v3 Announce Type: replace-cross Abstract: The maximum-entropy remote sampling problem (MERSP) is to select a subset of $s$ random variables from a set of $n$ random variables, so as to maximize the information concerning a set of target random variables that are not directly observable.
By Gabriel Ponte, Marcia Fampa, Jon Lee
The paper investigates online linear regression with sparse comparators, focusing on feature priming techniques that reweight features using past data. It establishes sparse‑regret lower bounds that invalidate sparse‑logarithmic guarantees for univariate, Pearson, and multivariate priming rules under a past‑only Moore–Penrose protocol, showing ≥Ω(min{T,√d}) clipped regret for unit‑power rules and linear regret for powered rules in high dimensions. The authors also provide tight rank upper bounds for certain priming schemes and present algebraic constructions yielding Ω(min{T,d^{1/4}}) regret for unit‑power multivariate priming, while noting that the exact multivariate frontier remains open.
By Huibo Xu, Shi Fu, Qixin Zhang, Dacheng Tao
The paper introduces a statistical framework for post‑training hyperparameter selection, emphasizing the learn‑then‑test (LTT) paradigm. It treats hyperparameter tuning as a multiple hypothesis testing problem over a candidate set, enabling the selection of hyperparameters that meet specified reliability constraints such as risk bounds or information‑theoretic limits. The framework provides finite‑sample control of error probabilities using p‑values, e‑values, and concentration inequalities derived from first principles.
By Amirmohammad Farzaneh, Osvaldo Simeone
The paper introduces the Free Inference dimension (dFI) as a new combinatorial measure of environmental complexity for value‑mixture agents in finite meta‑reinforcement learning. It shows that dFI is smaller than the VC‑dimension and relates to the Natarajan dimension, providing PAC‑style generalization bounds. The authors also define a complementary PMS identification dimension and demonstrate that a hybrid strategy—averaging until the first collision and then selecting—achieves optimal performance, supported by grid‑world experiments.
By Luiz Carlos Castro Guedes, Edward Hermann Haeusler
arXiv:2608.30431v1 Announce Type: cross
Abstract: By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization...
By Filippo Fabiani
arXiv:2506. 21306v2 Announce Type: replace-cross Abstract: Functions that grow without bound on one side of the real line and decay to zero on the other cannot be approximated uniformly by ordinary polynomials on unbounded domains.
By Kingsley Yeon, Steven B. Damelin
arXiv:2505. 23696v2 Announce Type: replace Abstract: Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields.
By Hiroshi Kera, Nico Pelleriti, Yuki Ishihara, Max Zimmer, Sebastian Pokutta