Parameter-Efficient transfer learning with Adapters have been studied in Natural Language Processing (NLP) as an alternative to full fine-tuning. Adapters are memory-efficient and scale well with downstream tasks by training small bottle-neck layers added between transformer layers while keeping the large pretrained language model (PLMs) frozen. In spite of showing promising results in NLP, these methods are under-explored in Information Retrieval. While previous studies have only experimented with dense retriever or in a cross lingual retrieval scenario, in this paper we aim to complete the picture on the use of adapters in IR. First, we study adapters for SPLADE, a sparse retriever, for which adapters not only retain the efficiency and effectiveness otherwise achieved by finetuning, but are memory-efficient and orders of magnitude lighter to train. We observe that Adapters-SPLADE not only optimizes just 2\% of training parameters, but outperforms fully fine-tuned counterpart and existing parameter-efficient dense IR models on IR benchmark datasets. Secondly, we address domain adaptation of neural retrieval thanks to adapters on cross-domain BEIR datasets and TripClick. Finally, we also consider knowledge sharing between rerankers and first stage rankers. Overall, our study complete the examination of adapters for neural IR
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