Abstract: Given its effectiveness on knowledge-intensive natural language processing tasks, dense retrieval models have become increasingly popular. Specifically, the de-facto architecture for open-domain question answering uses two isomorphic encoders that are initialized from the same pretrained model but separately parameterized for questions and passages. This biencoder architecture is parameter-inefficient in that there is no parameter sharing between encoders. Further, recent studies show that such dense retrievers underperform BM25 in various settings. We thus propose a new architecture, Task-Aware Specialization for dEnse Retrieval (TASER), which enables parameter sharing by interleaving shared and specialized blocks in a single encoder. Our experiments on five question answering datasets show that TASER can achieve superior accuracy, surpassing BM25, while using about 60\% of the parameters as bi-encoder dense retrievers. In out-of-domain evaluations, TASER is also empirically more robust than bi-encoder dense retrievers. Our code is available at {https://github.com/microsoft/taser}.