A new theoretical framework explains the emergence of inductive reasoning abilities in Transformer language models by studying a generalized class of inductive tasks that unifies synthetic tasks like in-context n-grams and multi-hop reasoning.

  • Training dynamics of attention models are confined to a highly interpretable, low-dimensional invariant manifold.
  • Learning dynamics on this manifold are captured by a handful of interpretable coordinates rather than millions of parameters.
  • The framework characterizes how data statistics govern the competition between in-context and in-weights learning.
  • Random initializations determine the 'winning' circuit when multiple solutions are possible.
  • The coordinate frame associated with the manifold can be used to automatically detect which circuits have been learned in trained models.

By casting circuit formation as a low-dimensional dynamical phenomenon, this work takes a step toward a predictive theory of how Transformers learn.