Provably Overwhelming Transformer Models with Designed Inputs

2025-02-09

AI Summary

This work investigates output invariance of Transformer models under suffix perturbations given a fixed prefix—termed “prefix domination”: when inputs consist of a constant prefix concatenated with an arbitrary suffix of length ≤ L, the model’s output remains unchanged. To address this, we propose the first verifiable formal definition and constructive proof framework for such invariance, grounded in rigorous bounds derived from strong over-squashing. Our methodology integrates RoPE position encoding modeling, theoretical analysis of attention sensitivity, and computer-assisted formal verification. We establish quasi-polynomial-time certifiably invariant behavior for single-layer Transformers incorporating self-attention, LayerNorm, MLP (with ReLU), and RoPE. This is the first work to provide a constructive, formally verifiable mathematical proof technique for local input robustness in Transformers.

Technology Category

• Natural Language Processing: Safety and Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

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.

Problem

• Generate proof transformer overwhelmed by input
• Establish worst-case over-squashing bounds
• Provide operational guarantees for transformer models

Innovation

• Algorithm for transformer model analysis
• Computer-aided mathematical proofs
• Empirical testing on transformer architecture