Nuojing Liang

Chain-of-thought out-of-distribution generalization is framed as compositional generalization: training supplies only single-step atomic transitions, while the target task requires composing many steps. Theory bounds target risk by the sum of step risks times a depth-independent coefficient, and shows that sharing one predictor makes the estimation term shrink as the inverse square root of depth rather than grow linearly. Atom-Task and GSM8K experiments support short-to-long and unseen-combination transfer, and show explicit state tracking is essential.

Chain-of-thought out-of-distribution generalization is framed as compositional generalization: training supplies only single-step atomic transitions, while the target task requires composing many steps. Theory bounds target risk by the sum of step risks times a depth-independent coefficient, and shows that sharing one predictor makes the estimation term shrink as the inverse square root of depth rather than grow linearly. Atom-Task and GSM8K experiments support short-to-long and unseen-combination transfer, and show explicit state tracking is essential.