Compositional Generalization in Autoregressive Models via Logit Composition

Composing autoregressive models remains a core challenge in understanding how large language models can combine behaviors or skills learned across tasks. We introduce a new and principled composition strategy for autoregressive systems, inspired by composition methods developed for diffusion models. Under a factorized-conditionals assumption, we show that the resulting composition is projective: each component model preserves control over its own designated subspace of the output distribution avoiding interference between models. This property is further preserved under smooth reparameterizations of the output space, yielding a feature-space theorem. Finally, we show that composition inherits length generalization: if the constituent autoregressive models generalize to longer sequences individually, the composed model does so on the combined task as well. These results provide a principled understanding of when model composition and merging succeed in autoregressive systems and identify conditions under which their interactions remain stable.