MMR

MMR — Maximal Marginal Relevance

Note: MMR (Maximal Marginal Relevance) is a diversity metric and reranking strategy. Do not confuse with MRR (Mean Reciprocal Rank), a ranking quality metric.

A reranking method that balances relevance and novelty. Instead of ranking purely by relevance, MMR penalizes results that are similar to already-selected results — reducing redundancy while preserving quality.

Formula

$\text{MMR}=\arg {\max }_{d_i\in R\setminus S}\left[\lambda \cdot {\text{Sim}}_1(d_i,q)-(1-\lambda )\cdot {\max }_{d_j\in S}{\text{Sim}}_2(d_i,d_j)\right]$

Where:

• $R$ = candidate result set
• $S$ = already-selected results
• $q$ = query
• ${\text{Sim}}_1$ = query-document relevance (e.g., cosine similarity)
• ${\text{Sim}}_2$ = document-document similarity
• $\lambda$ = tradeoff parameter (0 = pure diversity, 1 = pure relevance)

Algorithm

Greedy iterative selection:

1. Select the most relevant document as the first result
2. For each subsequent position, pick the document that maximizes the MMR score — highest relevance minus penalty for similarity to already-chosen documents
3. Repeat until the result list is full

Properties

• Tunable: λ controls the relevance/diversity tradeoff
• Greedy: not globally optimal, but O(n) per step — practical for reranking
• Similarity-agnostic: works with any similarity function (BM25 score, embedding cosine, etc.)

Use Cases

• Search result diversification: reduce ten near-duplicate product results in favor of different categories
• Keyphrase extraction: select diverse keyphrases from a document rather than all from the same topic cluster
• RAG context selection: choose diverse passages for LLM context to avoid redundant information
• Facet result pages: ensure different facet values are represented in top results

Tradeoffs

Relevance-focused (λ→1)	Diversity-focused (λ→0)
Top results are most relevant	Top results cover more aspects
May show redundant content	May surface lower-relevance items
Better for known-item search	Better for exploratory / ambiguous queries

Related

• APD — Average Pairwise Distance, a passive diversity measurement (vs MMR’s active reranking)
• Diversity Metrics — overview of diversity approaches
• Reranking — MMR is applied as a post-retrieval reranking step