How Transformers Learn Causal Structures In-Context: Explainable Mechanism Meets Theoretical Guarantee

Transformers have demonstrated remarkable in-context learning abilities, adapting to new tasks from just a few examples without parameter updates. However, theoretical understanding of this phenomenon typically assumes fixed dependency structures, while real-world sequences exhibit flexible, context-dependent relationships. We address this gap by investigating whether transformers can learn causal structures -- the underlying dependencies between sequence elements -- directly from in-context examples. We propose a novel framework using Markov chains with randomly sampled causal dependencies, where transformers must infer which tokens depend on which predecessors to make accurate predictions. Our key contributions are threefold: (1) We prove that a two-layer transformer with relative position embeddings can implement Bayesian Model Averaging (BMA), the optimal statistical algorithm for causal structure inference; (2) Through extensive experiments and parameter-level analysis, we demonstrate that transformers trained on this task learn to approximate BMA, with attention patterns directly reflecting the inferred causal structures; (3) We provide information-theoretic guarantees showing how transformers recover causal dependencies and extend our analysis to continuous dynamical systems, revealing fundamental differences in representational requirements. Our findings bridge the gap between empirical observations of in-context learning and theoretical understanding, showing that transformers can perform sophisticated statistical inference over structural uncertainty.