Large vision-language models (LVLMs) have demonstrated their incredible capability in visual question answering. However, this rich visual interaction also makes LVLMs vulnerable to adversarial examples. In this paper, we formulate a novel and practical targeted attack scenario that the adversary knows only the vision encoder of the victim LVLM, without the knowledge of its prompts and its underlying large language model. This practical setting poses challenges to the cross-prompt and cross-model transferability of targeted adversarial attack, which aims to confuse the LVLM to output a response that is semantically similar to the attacker's chosen target text. To this end, we propose an instruction-tuned targeted attack (dubbed InstructTA) to deliver the targeted adversarial attack on LVLMs with high transferability. Initially, we utilize a public text-to-image generative model to reverse the target response into a target image, and employ GPT-4 to infer a reasonable instruction $\boldsymbol{p}^\prime$ from the target response. We then form a local surrogate model (sharing the same vision encoder with the victim LVLM) to extract instruction-aware features of an adversarial image example and the target image, and minimize the distance between these two features to optimize the adversarial example. To further improve the transferability with instruction tuning, we augment the instruction $\boldsymbol{p}^\prime$ with instructions paraphrased from GPT-4. Extensive experiments on 6 victim LVLMs demonstrate the superiority of our proposed method in targeted attack performance and transferability. In particular, InstructTA achieves an attack success rate of 51.9% on BLIP-2, outperforming the strongest baseline by 10.5%, and consistently yields the highest attack success rates across all evaluated models. The code is available at https://github.com/xunguangwang/InstructTA.

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