Transformer learning dynamics for reasoning tasks can be reduced to a low-dimensional invariant manifold, making it possible to predict and interpret which circuits the model will learn from data statistics and initialization alone.
This paper explains how Transformers learn inductive reasoning by showing that their training dynamics stay confined to a low-dimensional manifold with interpretable coordinates. Rather than tracking millions of parameters, the authors prove that learning can be captured by a handful of meaningful variables, allowing them to predict which reasoning circuits emerge and why.