Algebraic Decomposition Theory for Transformer Length Generalization 文章

arXiv:2608.13433v1 Announce Type: cross Abstract: Transformer-based language models are known to sometimes generalize to sequences longer than seen during training, but we lack a precise characterization of which tasks admit length generalization. It is not even known which regular languages transformers length-generalize on -- and this is a foundational class of languages. Our contributions are to establish the first complete characterization of which regular languages transformers length-generalize on and provide a decision algorithm running in polynomial time in the size of the language's syntactic monoid. These results rely on an effective characterization of the regular languages in C-RASP, a recently-established formalism that expresses which languages transformers length-generalize on. This characterization is challenging because classical tools like Krohn-Rhodes decomposition theory for finite semigroups are insufficient for C-RASP.