Provably Overwhelming Transformer Models with Designed Inputs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915302896304128 |
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| author | Stambler, Lev Nezhadi, Seyed Sajjad Coudron, Matthew |
| author_facet | Stambler, Lev Nezhadi, Seyed Sajjad Coudron, Matthew |
| contents | We develop an algorithm which, given a trained transformer model $\mathcal{M}$ as input, as well as a string of tokens $s$ of length $n_{fix}$ and an integer $n_{free}$, can generate a mathematical proof that $\mathcal{M}$ is ``overwhelmed'' by $s$, in time and space $\widetilde{O}(n_{fix}^2 + n_{free}^3)$. We say that $\mathcal{M}$ is ``overwhelmed'' by $s$ when the output of the model evaluated on this string plus any additional string $t$, $\mathcal{M}(s + t)$, is completely insensitive to the value of the string $t$ whenever length($t$) $\leq n_{free}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Provably Overwhelming Transformer Models with Designed Inputs Stambler, Lev Nezhadi, Seyed Sajjad Coudron, Matthew Machine Learning Artificial Intelligence Computational Complexity We develop an algorithm which, given a trained transformer model $\mathcal{M}$ as input, as well as a string of tokens $s$ of length $n_{fix}$ and an integer $n_{free}$, can generate a mathematical proof that $\mathcal{M}$ is ``overwhelmed'' by $s$, in time and space $\widetilde{O}(n_{fix}^2 + n_{free}^3)$. We say that $\mathcal{M}$ is ``overwhelmed'' by $s$ when the output of the model evaluated on this string plus any additional string $t$, $\mathcal{M}(s + t)$, is completely insensitive to the value of the string $t$ whenever length($t$) $\leq n_{free}$. 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. |
| title | Provably Overwhelming Transformer Models with Designed Inputs |
| topic | Machine Learning Artificial Intelligence Computational Complexity |
| url | https://arxiv.org/abs/2502.06038 |