Functional Homotopy: Smoothing Discrete Optimization via Continuous Parameters for LLM Jailbreak Attacks

TL;DR

This paper introduces the functional homotopy method, a novel continuous optimization technique for language models, improving jailbreak attack success rates by 20-30% over existing methods.

Contribution

The study proposes the functional homotopy approach, leveraging functional duality and homotopy principles to optimize discrete inputs for LLM jailbreak attacks.

Findings

Achieved 20-30% higher success rates in jailbreak attacks.

Demonstrated effectiveness on Llama-2 and Llama-3 models.

Introduced a new continuous optimization framework for discrete input problems.

Abstract

Optimization methods are widely employed in deep learning to identify and mitigate undesired model responses. While gradient-based techniques have proven effective for image models, their application to language models is hindered by the discrete nature of the input space. This study introduces a novel optimization approach, termed the \emph{functional homotopy} method, which leverages the functional duality between model training and input generation. By constructing a series of easy-to-hard optimization problems, we iteratively solve these problems using principles derived from established homotopy methods. We apply this approach to jailbreak attack synthesis for large language models (LLMs), achieving a $20\%-30\%$ improvement in success rate over existing methods in circumventing established safe open-source models such as Llama-2 and Llama-3.