למידה לא פרמטרית בהקשר של סיבוכיות גאומטרית גדלה

תקציר מקורי באנגליתarXiv:2609.31458v1 Announce Type: cross Abstract: Transformers have become a central architecture for in-context learning (ICL), particularly through their state-of-the-art performance in large language models. This success motivates understanding how transformers exploit task-relevant structure in geometrically heterogeneous data. However, existing nonparametric ICL theory has largely focused on Euclidean domains or single-manifold models. To address this gap, we study the prediction problem under unknown local geometry, modeled by sample size-dependent mixtures of manifolds with heterogeneous dimensions, smoothness, and sampling masses. Under local separation and small-perturbation conditions, we establish a minimax lower bound capturing the aggregate difficulty of the components and con