The Information Bottleneck (IB) principle facilitates effective representation learning by preserving label-relevant information while compressing irrelevant information. However, its strong reliance on accurate labels makes it inherently vulnerable to label noise, prevalent in real-world scenarios, resulting in significant performance degradation and overfitting. To address this issue, we propose LaT-IB, a novel Label-Noise ResistanT Information Bottleneck method which introduces a "Minimal-Sufficient-Clean" (MSC) criterion. Instantiated as a mutual information regularizer to retain task-relevant information while discarding noise, MSC addresses standard IB's vulnerability to noisy label supervision. To achieve this, LaT-IB employs a noise-aware latent disentanglement that decomposes the latent representation into components aligned with to the clean label space and the noise space. Theoretically, we first derive mutual information bounds for each component of our objective including prediction, compression, and disentanglement, and moreover prove that optimizing it encourages representations invariant to input noise and separates clean and noisy label information. Furthermore, we design a three-phase training framework: Warmup, Knowledge Injection and Robust Training, to progressively guide the model toward noise-resistant representations. Extensive experiments demonstrate that LaT-IB achieves superior robustness and efficiency under label noise, significantly enhancing robustness and applicability in real-world scenarios with label noise.

Foundation models have emerged as a dominant paradigm in machine learning, enabling broad generalization and efficient adaptation across diverse tasks and domains. While this paradigm has achieved remarkable success in language and vision data, its extension to structured data remains far less understood. Foundation models for structured data are an emerging yet highly impactful research area with a rapidly growing body of literature. In this survey, we provide a systematic analysis of foundation models for structured data, focusing on tabular, time series, and graph data, covering over 150 representative methods. We analyze the intrinsic properties and inductive biases of structured data, clarify the core concepts of foundation models, and conduct an in-depth analysis of the key challenges that hinder the development of foundation models for structured data. Building on these insights, we organize existing approaches into a coherent taxonomy based on tokenization, architectures, pre-training objectives, and adaptation strategies. Finally, we discusse merging research directions and open problems, aiming to provide guidance toward more principled and scalable foundation models for structured data.