Logicbreaks: A Framework for Understanding Subversion of Rule-based Inference

TL;DR

This paper introduces Logicbreaks, a formal framework using propositional Horn logic to analyze how large language models can be subverted from following prompt-specified rules, revealing vulnerabilities and attack strategies.

Contribution

It formalizes rule-following in LLMs using logic, proves their susceptibility to adversarial prompts, and connects theoretical insights with practical attack algorithms.

Findings

Small transformers can follow rules faithfully

Malicious prompts can mislead models and theory

Attack algorithms find adversarial prompts aligned with theory

Abstract

We study how to subvert large language models (LLMs) from following prompt-specified rules. We first formalize rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form "if $P$ and $Q$, then $R$" for some propositions $P$, $Q$, and $R$. Next, we prove that although small transformers can faithfully follow such rules, maliciously crafted prompts can still mislead both theoretical constructions and models learned from data. Furthermore, we demonstrate that popular attack algorithms on LLMs find adversarial prompts and induce attention patterns that align with our theory. Our novel logic-based framework provides a foundation for studying LLMs in rule-based settings, enabling a formal analysis of tasks like logical reasoning and jailbreak attacks.