arXiv:2510.02999v1 Announce Type: cross Abstract: Existing gradient-based jailbreak attacks on Large Language Models (LLMs), such as Greedy Coordinate Gradient (GCG) and COLD-Attack, typically optimize adversarial suffixes to align the LLM output with a predefined target response. However, by restricting the optimization objective as inducing a predefined target, these methods inherently constrain the adversarial search space, which limit their overall attack efficacy. Furthermore, existing methods typically require a large number of optimization iterations to fulfill the large gap between the fixed target and the original model response, resulting in low attack efficiency. To overcome the limitations of targeted jailbreak attacks, we propose the first gradient-based untargeted jailbreak attack (UJA), aiming to elicit an unsafe response without enforcing any predefined patterns. Specifically, we formulate an untargeted attack objective to maximize the unsafety probability of the LLM response, which can be quantified using a judge model. Since the objective is non-differentiable, we further decompose it into two differentiable sub-objectives for optimizing an optimal harmful response and the corresponding adversarial prompt, with a theoretical analysis to validate the decomposition. In contrast to targeted jailbreak attacks, UJA's unrestricted objective significantly expands the search space, enabling a more flexible and efficient exploration of LLM vulnerabilities.Extensive evaluations demonstrate that \textsc{UJA} can achieve over 80\% attack success rates against recent safety-aligned LLMs with only 100 optimization iterations, outperforming the state-of-the-art gradient-based attacks such as I-GCG and COLD-Attack by over 20\%.