# Out-of-Distribution Generalization

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.

On 2D halide perovskite bandgap prediction, Motif moves the large language model from emitting numbers to generating chemical taxonomies offline, which then define environments for invariant feature selection. Across six leave-one-spacer-family-out folds, mean OOD MAE falls from the kNN+GBT baseline's 0.122 eV to 0.111 eV; under a frozen dev/test protocol the deployable configuration lowers electronic bandgap error from 0.123 to 0.117 eV and optical bandgap error from 0.181 to 0.173 eV.

On 2D halide perovskite bandgap prediction, Motif moves the large language model from emitting numbers to generating chemical taxonomies offline, which then define environments for invariant feature selection. Across six leave-one-spacer-family-out folds, mean OOD MAE falls from the kNN+GBT baseline's 0.122 eV to 0.111 eV; under a frozen dev/test protocol the deployable configuration lowers electronic bandgap error from 0.123 to 0.117 eV and optical bandgap error from 0.181 to 0.173 eV.