  Most dense retrieval models contain an implicit assumption: the training
query-document pairs are exactly matched. Since it is expensive to annotate the
corpus manually, training pairs in real-world applications are usually
collected automatically, which inevitably introduces mismatched-pair noise. In
this paper, we explore an interesting and challenging problem in dense
retrieval, how to train an effective model with mismatched-pair noise. To solve
this problem, we propose a novel approach called Noisy Pair Corrector (NPC),
which consists of a detection module and a correction module. The detection
module estimates noise pairs by calculating the perplexity between annotated
positive and easy negative documents. The correction module utilizes an
exponential moving average (EMA) model to provide a soft supervised signal,
aiding in mitigating the effects of noise. We conduct experiments on
text-retrieval benchmarks Natural Question and TriviaQA, code-search benchmarks
StaQC and SO-DS. Experimental results show that NPC achieves excellent
performance in handling both synthetic and realistic noise.
