Long-Tail Crisis in Nearest Neighbor Language Models

The $k$-nearest-neighbor language model ($k$NN-LM), one of the retrieval-augmented language models, improves the perplexity for given text by directly accessing a large datastore built from any text data during inference. A widely held hypothesis for the success of $k$NN-LM is that its explicit memory, i.e., the datastore, enhances predictions for long-tail phenomena. However, prior works have primarily shown its ability to retrieve long-tail contexts, leaving the model's performance remain underexplored in estimating the probabilities of long-tail target tokens during inference. In this paper, we investigate the behavior of $k$NN-LM on low-frequency tokens, examining prediction probability, retrieval accuracy, token distribution in the datastore, and approximation error of the product quantization. Our experimental results reveal that $k$NN-LM does not improve prediction performance for low-frequency tokens but mainly benefits high-frequency tokens regardless of long-tail contexts in the datastore.