Putting Transformer Theories to the Test

arXiv:2610.32104v1 Announce Type: new Abstract: Several formal theories have been developed to characterize the capabilities and limitations of the transformer architecture, each employing different abstractions that capture different features of the architecture. Due to the differences in their underlying assumptions and conceptual frameworks, these theories can disagree in their predictions about what tasks transformers find easy or hard. We map out seven theories of transformer capability (Star-free, $\mathsf{AC}^0$, $\mathsf{TC}^0$, C-RASP, MPC, BAPO, and Sensitivity) and translate their results into a common matrix of predictions across a suite of tasks covering different computational structures. We provide new theoretical results to complete this matrix. We then evaluate theoretical