mlsanityData to 14 Oct 2026

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

arXiv 2410.04234 ↗First posted 5 Oct 2024cs.LG cs.AI cs.CRcited by 4

On the map: LLM safety and security → Jailbreaking

Abstract (arXiv)

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 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.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Placed in Jailbreaking, one of 12 directions in LLM safety and security. Builds on 20 of its 33 references that are in the map. First posted on arXiv 5 Oct 2024.

Builds on

20 of 33 references.

Closest ancestors · 8

Same direction, newest first

  1. 2024Efficient LLM Jailbreak via Adaptive Dense-to-sparse Constrained Optimization15 May
  2. 2024AmpleGCG: Learning a Universal and Transferable Generative Model of Adversarial Suffixes for Jailbreaking Both Open and Closed LLMs11 Apr
  3. 2024Jailbreaking Leading Safety-Aligned LLMs with Simple Adaptive Attacks2 Apr
  4. 2024Soft Prompt Threats: Attacking Safety Alignment and Unlearning in Open-Source LLMs through the Embedding Space14 Feb
  5. 2023Tree of Attacks: Jailbreaking Black-Box LLMs Automatically4 Dec
  6. 2023Jailbreaking Black Box Large Language Models in Twenty Queries12 Oct
  7. 2023AutoDAN: Generating Stealthy Jailbreak Prompts on Aligned Large Language Models3 Oct
  8. 2023Universal and Transferable Adversarial Attacks on Aligned Language Models27 Jul

Other references · 12

  1. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,380
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  3. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  4. 2013Intriguing properties of neural networkscited by 5,155
  5. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,998
  6. 2021Convex optimizationcited by 2,515
  7. 2024HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusalcited by 1,429
  8. 2022Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learnedcited by 729
  9. 2024Automatic and Universal Prompt Injection Attacks against Large Language Modelscited by 119
  10. 2020Interval Universal Approximation for Neural Networkscited by 14
  11. 2023Rethinking Diversity in Deep Neural Network Testingcited by 2
  12. 2020TOFU: Target-Oriented FUzzercited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 1.

4 papers.

  1. 2025DREAM: Scalable Red Teaming for Text-to-Image Generative Systems via Distribution Modelingcited by 5
  2. 2025SoK: Systematizing LLM Prompt Security: Taxonomies, Datasets, and Unified Evaluation of Attacks and Defensescited by 5
  3. 2024Topological Data Analysis Applications in Natural Language Processing: A Surveycited by 2
  4. 2026LLM Security and Safety: Insights from Homotopy-Inspired Prompt Obfuscationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Gradient Cuff: Detecting Jailbreak Attacks on Large Language Models by Exploring Refusal Loss Landscapes
  2. 2026TAO-Attack: Toward Advanced Optimization-Based Jailbreak Attacks for Large Language Models
  3. 2025Efficient Jailbreaking of Large Models by Freeze Training: Lower Layers Exhibit Greater Sensitivity to Harmful Content
  4. 2026SoK: Robustness in Large Language Models against Jailbreak Attacks
  5. 2024Defending Large Language Models Against Jailbreak Attacks via Layer-specific Editing
  6. 2024AttnGCG: Enhancing Jailbreaking Attacks on LLMs with Attention Manipulation
  7. 2025Adversarial Attack on Large Language Models using Exponentiated Gradient Descent
  8. 2025Guiding not Forcing: Enhancing the Transferability of Jailbreaking Attacks on LLMs via Removing Superfluous Constraints