Transformers Can Learn Multiclass Classification In-Context: Isotropy Governs Generalization

In-context learning plays a central role in transformer-based large language models, yet its theoretical understanding remains limited. In this work, we study multiclass in-context classification under more realistic settings, including anisotropic class centers and label imbalance, by introducing a spectral data generation framework that constructs class-center matrices with a prescribed singular spectrum. We first show that the isotropy of class-center vectors, as quantified by the stable rank, improves ICL generalization performance. From a meta-learning perspective, our theorem shows that linear transformers can learn multiclass in-context classification with near-optimal per-label sample complexity, extending prior guarantees beyond the binary setting. In the test label imbalance regime, our analysis reveals that queries from majority classes are easier to classify, while those from minority classes are more error-prone; moreover, robustness to this bias improves with the stable rank. Finally, we empirically demonstrate that our theory is consistent with observations on transformers and pretrained large language models.