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Provably Overwhelming Transformer Models with Designed Inputs

9 February 2025
Lev Stambler
Seyed Sajjad Nezhadi
Matthew Coudron
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Abstract

We develop an algorithm which, given a trained transformer model M\mathcal{M}M as input, as well as a string of tokens sss of length nfixn_{fix}nfix​ and an integer nfreen_{free}nfree​, can generate a mathematical proof that M\mathcal{M}M is ``overwhelmed'' by sss, in time and space O~(nfix2+nfree3)\widetilde{O}(n_{fix}^2 + n_{free}^3)O(nfix2​+nfree3​). We say that M\mathcal{M}M is ``overwhelmed'' by sss when the output of the model evaluated on this string plus any additional string ttt, M(s+t)\mathcal{M}(s + t)M(s+t), is completely insensitive to the value of the string ttt whenever length(ttt) ≤nfree\leq n_{free}≤nfree​. Along the way, we prove a particularly strong worst-case form of ``over-squashing'', which we use to bound the model's behavior. Our technique uses computer-aided proofs to establish this type of operationally relevant guarantee about transformer models. We empirically test our algorithm on a single layer transformer complete with an attention head, layer-norm, MLP/ReLU layers, and RoPE positional encoding. We believe that this work is a stepping stone towards the difficult task of obtaining useful guarantees for trained transformer models.

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@article{stambler2025_2502.06038,
  title={ Provably Overwhelming Transformer Models with Designed Inputs },
  author={ Lev Stambler and Seyed Sajjad Nezhadi and Matthew Coudron },
  journal={arXiv preprint arXiv:2502.06038},
  year={ 2025 }
}
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