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arXiv · 2603.02238

Length Generalization Bounds for Transformers

Andy Yang·Pascal Bergsträßer·Georg Zetzsche·David Chiang·Anthony W. Lin
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Abstract

Length generalization is a key property of a learning algorithm that enables it to make correct predictions on inputs of any length, given finite training data. To provide such a guarantee, one needs to be able to compute a length generalization bound, beyond which the model is guaranteed to generalize. This paper concerns the open problem of the computability of such generalization bounds for C-RASP, a class of languages which is closely linked to transformers. A positive partial result was recently shown by Chen et al. for C-RASP with only one layer and, under some restrictions, also with two layers. We provide complete answers to the above open problem. Our main result is the non-existence of computable length generalization bounds for C-RASP (already with two layers) and hence for transformers. To complement this, we provide a computable bound for the positive fragment of C-RASP, which we show equivalent to fixed-precision transformers. For both positive C-RASP and fixed-precision transformers, we show that the length complexity is exponential, and prove optimality of the bounds.

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BibTeXRIS

Andy Yang, Pascal Bergsträßer, Georg Zetzsche, David Chiang, Anthony W. Lin. 2026-02-13. Length Generalization Bounds for Transformers. https://arxiv.org/abs/2603.02238

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