Transformers can learn broad families of tasks during pretraining and adapt to unseen tasks from a short prompt, but a rigorous understanding of this capability is limited. This paper studies how shared cross‑task structure influences the sample complexity of in‑context learning (ICL) by characterizing task‑space complexity through covering numbers, yielding a set of anchor functions that localize unseen tasks and predict responses. The authors construct a Transformer with Softmax attention to approximate this procedure and derive an error bound that separates the effects of pretraining tasks and prompt length, showing that once enough tasks are available the dependence on prompt length becomes dimension‑free.
By Zhongjie Shi, Rongjie Lai, Alexander Cloninger, Wenjing Liao
arXiv:2609.08981v1 Announce Type: cross
Abstract: A growing body of work establishes that large language models are not mere statistical memorizers, but are capable of in-context learning: performing...
By Arman Adibi, Alireza Jafari, Mohammad Ghavamzadeh, Hadi Daneshmand
arXiv:2606. 20538v1 Announce Type: new Abstract: Bayesian predictive inference provides a principled framework for uncertainty quantification, data efficiency, and robust generalization.
By Qingyang Zhu, Eric Karl Oermann, Kyunghyun Cho
arXiv:2502. 04646v2 Announce Type: replace-cross Abstract: Weighted sampling -- sampling from a probability density function (PDF) proportional to the product of a base PDF and a weight function -- is a fundamental technique with wide-ranging applications in variance reduction, biased sampling, data augmentation, and more.
By Heasung Kim, Taekyun Lee, Hyeji Kim, Gustavo de Veciana
arXiv:2610.07804v1 Announce Type: new
Abstract: Prior Fitted Networks (PFNs) such as TabPFN now rival established statistical procedures across prediction and estimation tasks. A natural explanation...
By Martin Eppert, Krishna Balasubramanian, Subhro Ghosh, Jason Klusowski, Yan Shuo Tan
The paper investigates diffusion models trained in a lazy high‑dimensional regime, extending benign overfitting theory to generative settings. By analyzing denoising score matching in a vector‑valued RKHS with an inner‑product kernel, the authors derive exact risk trajectories under gradient flow when the number of samples scales proportionally with dimensionality. These trajectories reveal three distinct phases—spectral generalization, noise‑dominated interpolation, and empirical Bayes memorization—whose interplay shapes the distribution of generated samples.
By Hugo Latourelle-Vigeant, Sinho Chewi, Aram-Alexandre Pooladian, John Sous, Theodor Misiakiewicz