  Retrieval augmentation enables large language models to take advantage of
external knowledge, for example on tasks like question answering and data
imputation. However, the performance of such retrieval-augmented models is
limited by the data quality of their underlying retrieval corpus. In this
paper, we propose an algorithm based on multilinear extension for evaluating
the data importance of retrieved data points. There are exponentially many
terms in the multilinear extension, and one key contribution of this paper is a
polynomial time algorithm that computes exactly, given a retrieval-augmented
model with an additive utility function and a validation set, the data
importance of data points in the retrieval corpus using the multilinear
extension of the model's utility function. We further proposed an even more
efficient ({\epsilon}, {\delta})-approximation algorithm. Our experimental
results illustrate that we can enhance the performance of large language models
by only pruning or reweighting the retrieval corpus, without requiring further
training. For some tasks, this even allows a small model (e.g., GPT-JT),
augmented with a search engine API, to outperform GPT-3.5 (without retrieval
augmentation). Moreover, we show that weights based on multilinear extension
can be computed efficiently in practice (e.g., in less than ten minutes for a
corpus with 100 million elements).
