When and How Unlabeled Data Provably Improve In-Context Learning

Recent research shows that in-context learning (ICL) can be effective even when demonstrations have missing or incorrect labels. To shed light on this capability, we examine a canonical setting where the demonstrations are drawn according to a binary Gaussian mixture model (GMM) and a certain fraction of the demonstrations have missing labels. We provide a comprehensive theoretical study to show that: (1) The loss landscape of one-layer linear attention models recover the optimal fully-supervised estimator but completely fail to exploit unlabeled data; (2) In contrast, multilayer or looped transformers can effectively leverage unlabeled data by implicitly constructing estimators of the form $\sum_{i\ge 0} a_i (X^\top X)^iX^\top y$ with $X$ and $y$ denoting features and partially-observed labels (with missing entries set to zero). We characterize the class of polynomials that can be expressed as a function of depth and draw connections to Expectation Maximization, an iterative pseudo-labeling algorithm commonly used in semi-supervised learning. Importantly, the leading polynomial power is exponential in depth, so mild amount of depth/looping suffices. As an application of theory, we propose looping off-the-shelf tabular foundation models to enhance their semi-supervision capabilities. Extensive evaluations on real-world datasets show that our method significantly improves the semisupervised tabular learning performance over the standard single pass inference.

@article{li2025_2506.15329,
  title={ When and How Unlabeled Data Provably Improve In-Context Learning },
  author={ Yingcong Li and Xiangyu Chang and Muti Kara and Xiaofeng Liu and Amit Roy-Chowdhury and Samet Oymak },
  journal={arXiv preprint arXiv:2506.15329},
  year={ 2025 }
}