The paper investigates fundamental limits of algorithmic principles in multiclass learning, specifically proper learning and regularization. It shows that learning cannot always be reduced to proper learning even with an enlarged hypothesis class, that proper learners may need a sublinear number of errors that can be arbitrarily large, and that regularization (SRM or local) is not universally sufficient. The authors also provide a positive theory giving sufficient conditions for SRM learnability and a characterization via integrability of revealed preferences.
By Julian Asilis, Shaddin Dughmi, Vatsal Sharan, Alec Sun, Shang-Hua Teng, Chang Wang
arXiv:2608. 25326v1 Announce Type: new Abstract: In transductive classification, an adversary fixes a labeled population, one label is hidden uniformly, and the learner sees all remaining labels.
By Pahan Dewasurendra
arXiv:2606. 28309v1 Announce Type: cross Abstract: Binary classification from positive-only samples is a variant of PAC learning in which the learner receives i.
By Shai Ben-David, Farnam Mansouri, Anay Mehrotra, Manolis Zampetakis
arXiv:2608.30246v1 Announce Type: cross
Abstract: The fundamental theorem of statistical learning states that, under suitable measurability assumptions, finite Vapnik--Chervonenkis (VC) dimension gua...
By Mateus Jesus de Arruda Campos, Gabriel Fernandes, Vinicius de Oliveira Rodrigues
arXiv:2607. 07423v1 Announce Type: new Abstract: We prove that, in the realizable PAC setting, the sample complexity of exact-trace learning for full autoregressive Chain-of-Thought traces is upper bounded by the standard multiclass rate of the local next-token class, where this rate is governed by the Daniely--Shalev-Shwartz dimension.
By Zhiyuan Li
arXiv:2604. 24749v2 Announce Type: replace Abstract: While the optimal sample complexity of binary classification in terms of the VC dimension is well-established, determining the optimal sample complexity of multiclass classification has remained open.
By Chirag Pabbaraju
The paper investigates learning with monotone adversarial corruptions, extending previous binary classification results to multiclass and partial binary settings. It shows that even a small number of strategically inserted corrupted examples can render a learnable multiclass problem with DS dimension 2 completely unlearnable, and provides matching upper bounds when the adversary’s budget is sublinear. The work also demonstrates that classic error rates remain attainable under bounded or limited‑view adversaries.
By Julian Asilis, Shaddin Dughmi, Chirag Pabbaraju
arXiv:2608. 06337v1 Announce Type: cross Abstract: A monotone adversary observes an i.
By Anay Mehrotra
arXiv:2608. 14020v1 Announce Type: new Abstract: Adding data known to be correct ought to be safe.
By Joseph Sankoorikal Johny
arXiv:2607. 15467v1 Announce Type: new Abstract: Knowledge distillation enables an adversary to replicate a proprietary classifier by querying its prediction interface and training a surrogate on the returned probability vectors.
By Khawaja Abaid Ullah, Mohammad Javad Khojasteh
arXiv:2511. 02644v2 Announce Type: replace Abstract: We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions.
By David Kattermann, Lothar Sebastian Krapp
We revisit the problem of learning predictors robust to adversarial examples at test-time. We prove that VC classes are adversarially robustly learnable with sample complexity linear in the VC dimension $d$, providing an exponential improvement over the previous upper bound of Montasser, Hanneke, and Srebro (2019).