# TF-IDF and BM25 Are Exact KL Divergences

arXiv: https://arxiv.org/abs/2609.14016 · HTML: https://mlsanity.com/paper/2609.14016/

## Key facts

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- First posted on arXiv 12 Sep 2026.

## Abstract (arXiv)

TF-IDF and BM25 are two of the most widely used methods for scoring query-document relevance, yet neither has a standard probabilistic derivation that justifies it as a statistical method within a unified framework. We address this gap by showing that both scoring methods admit an exact interpretation as Kullback-Leibler divergences between two probability models. We treat the BM25 variant that includes the plus 1 correction in the IDF term, which is the one used in practice, and also discuss the original BM25 formulation without that correction. The resulting framework provides a common theoretical basis for TF-IDF and BM25, clarifies what they measure, and allows them to be compared theoretically with other information retrieval methods rather than only experimentally.