When and How Unlabeled Data Provably Improve In-Context Learning

• URL: http://arxiv.org/abs/2506.15329v1
• Date: Wed, 18 Jun 2025 10:01:17 GMT
• Title: When and How Unlabeled Data Provably Improve In-Context Learning
• Authors: Yingcong Li, Xiangyu Chang, Muti Kara, Xiaofeng Liu, Amit Roy-Chowdhury, Samet Oymak,
• Abstract summary: In-supervised learning can be effective even when demonstrations have missing or incorrect labels.<n>We show that multilayer or looped transformers can effectively leverage unlabeled data by implicitly constructing estimators of the form $sum_ige 0 a_i (Xtop X)iXtop y$ with $X$ and $y$ denoting features and partially-observed labels.
• Score: 31.201385551730926
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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