Dense retrievers are widely used in information retrieval and have also been successfully extended to other knowledge intensive areas such as language models, e.g., Retrieval-Augmented Generation (RAG) systems. Unfortunately, they have recently been shown to be vulnerable to corpus poisoning attacks in which a malicious user injects a small fraction of adversarial passages into the retrieval corpus to trick the system into returning these passages among the top-ranked results for a broad set of user queries. Further study is needed to understand the extent to which these attacks could limit the deployment of dense retrievers in real-world applications. In this work, we propose Approximate Greedy Gradient Descent (AGGD), a new attack on dense retrieval systems based on the widely used HotFlip method for efficiently generating adversarial passages. We demonstrate that AGGD can select a higher quality set of token-level perturbations than HotFlip by replacing its random token sampling with a more structured search. Experimentally, we show that our method achieves a high attack success rate on several datasets and using several retrievers, and can generalize to unseen queries and new domains. Notably, our method is extremely effective in attacking the ANCE retrieval model, achieving attack success rates that are 17.6\% and 13.37\% higher on the NQ and MS MARCO datasets, respectively, compared to HotFlip. Additionally, we demonstrate AGGD's potential to replace HotFlip in other adversarial attacks, such as knowledge poisoning of RAG systems.\footnote{Code can be find in \url{https://github.com/JinyanSu1/AGGD}}
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