Maximal marginal relevance

Balance relevance and diversity to reduce redundancy in search results

MMR (Maximal Marginal Relevance) balances relevance with diversity by penalizing documents too similar to those already selected. The result set covers more aspects of a topic instead of repeating similar content.

How it works

MMR iteratively selects documents by balancing query relevance against redundancy with already-selected documents.

MMR algorithm

MMR iteratively selects documents by scoring each candidate with:

MMR(d) = λ × sim(d, query) - (1-λ) × max_sim(d, selected)

Where:

• λ (lambda_param) - Trade-off between relevance and diversity (0.0-1.0)
• sim(d, query) - Cosine similarity between document and query embeddings
• max_sim(d, selected) - Maximum similarity to any already-selected document

Selection process

1. First document - Select most relevant to query
2. Iterative selection - For remaining slots:
   • Calculate relevance to query for each candidate
   • Calculate redundancy (max similarity to selected docs)
   • Compute MMR score with lambda weighting
   • Select document with highest MMR score
3. Repeat - Until k documents selected

Lambda parameter guidelines

lambda_param · float

Controls the relevance-diversity trade-off:

• λ = 1.0 - Pure relevance ranking (no diversity penalty)
• λ = 0.7-0.8 - Emphasize relevance, mild diversity (recommended for precision)
• λ = 0.5 - Balanced relevance and diversity (good default)
• λ = 0.3-0.4 - Emphasize diversity (recommended for exploratory search)
• λ = 0.0 - Pure diversity (minimum redundancy, ignores relevance)

Key features

• Tune relevance vs diversity to fit the task
• Uses cosine similarity for both relevance and diversity scoring
• Particularly useful for summarization and exploratory search
• Greedy algorithm ensures efficiency

Implementation

LangChain MMR helper

from vectordb.langchain.utils import MMRHelper

# Generate embeddings for documents and query
doc_embeddings = embedder.embed_documents([doc.page_content for doc in documents])
query_embedding = embedder.embed_query(query)

# Apply MMR reranking
reranked = MMRHelper.mmr_rerank(
    documents=documents,
    embeddings=doc_embeddings,
    query_embedding=query_embedding,
    lambda_param=0.5,
    k=10,
)

# Returns list of (Document, MMR_score) tuples
for doc, score in reranked:
    print(f"MMR Score: {score:.3f} - {doc.page_content[:100]}")

Use cases

Exploratory search

When users need to understand different aspects of a topic:

# Lower lambda for more diversity
results = MMRHelper.mmr_rerank(
    documents=candidates,
    embeddings=embeddings,
    query_embedding=query_emb,
    lambda_param=0.3,  # Emphasize diversity
    k=10,
)

Multi-document summarization

Provide diverse context to LLMs:

# Balanced approach
diverse_docs = MMRHelper.mmr_rerank_simple(
    documents=retrieved_docs,
    embeddings=doc_embeddings,
    query_embedding=query_embedding,
    k=5,
    lambda_param=0.5,
)

# Use diverse docs for summarization
summary = llm.summarize(diverse_docs)

Reducing near-duplicates

When search returns many similar results:

# High diversity to remove redundancy
unique_results = MMRHelper.mmr_rerank_simple(
    documents=search_results,
    embeddings=result_embeddings,
    query_embedding=query_emb,
    k=10,
    lambda_param=0.4,  # Favor diversity
)

High-precision search

When relevance is critical:

# High lambda for relevance focus
precise_results = MMRHelper.mmr_rerank(
    documents=candidates,
    embeddings=embeddings,
    query_embedding=query_emb,
    lambda_param=0.8,  # Emphasize relevance
    k=5,
)

Lambda parameter tuning

Task-specific recommendations

Task type	Recommended λ	Rationale
Q&A systems	0.7-0.8	Prioritize relevant answers
Exploratory search	0.3-0.4	Show diverse perspectives
Summarization	0.4-0.6	Balance coverage and relevance
Deduplication	0.2-0.4	Maximize uniqueness
Fact verification	0.6-0.7	Relevant but diverse sources

Tuning guidelines

1. Start with default

   Begin with lambda_param=0.5 (balanced)

2. Evaluate results

   Check for redundancy or missing relevant docs

3. Adjust based on metrics

   • Too much redundancy? Decrease lambda (more diversity)
   • Missing relevant results? Increase lambda (more relevance)
4. A/B test

   Compare user engagement across lambda values

Example with full pipeline

from vectordb.langchain.semantic_search import PineconeSemanticSearchPipeline
from vectordb.langchain.utils import MMRHelper, EmbedderHelper

# Initial retrieval
pipeline = PineconeSemanticSearchPipeline("config.yaml")
candidates = pipeline.search(
    query="climate change mitigation strategies",
    top_k=50,  # Over-fetch for MMR
)

# Generate embeddings
doc_texts = [doc.page_content for doc in candidates["documents"]]
doc_embeddings = embedder.embed_documents(doc_texts)
query_embedding = embedder.embed_query(candidates["query"])

# Apply MMR for diversity
diverse_results = MMRHelper.mmr_rerank_simple(
    documents=candidates["documents"],
    embeddings=doc_embeddings,
    query_embedding=query_embedding,
    k=10,
    lambda_param=0.5,
)

print(f"Retrieved {len(diverse_results)} diverse documents")
for i, doc in enumerate(diverse_results, 1):
    print(f"{i}. {doc.page_content[:100]}...")

Performance characteristics

Time complexity

• First selection: O(n) to find most relevant
• Subsequent selections: O((k-1) × n) for k selections from n candidates
• Overall: O(k × n)

For typical values (k=10, n=100), this is very fast (~ms).

Space complexity

• O(n × d) for storing embeddings (n docs, d dimensions)
• Cosine similarity computed on-demand

Optimization tips

Pre-compute and cache embeddings for retrieved documents to avoid repeated embedding calls. Only re-embed when document content changes.

Comparison with other diversity methods

Method	Approach	Speed	Use case
MMR	Query-aware greedy selection	Fast	General diversity with relevance
Clustering	K-means + sampling	Moderate	Topic coverage
Threshold filtering	Similarity cutoff	Fastest	Simple deduplication
Graph-based	Community detection	Slow	Complex relationships

Integration with diversity filtering

MMR is one of the diversity methods available in the diversity filtering pipeline:

from vectordb.langchain.diversity_filtering import PineconeDiversityFilteringSearchPipeline

pipeline = PineconeDiversityFilteringSearchPipeline({
    "pinecone": {"api_key": "...", "index_name": "..."},
    "diversity": {
        "method": "mmr",
        "lambda_param": 0.5,
        "max_documents": 10,
        "candidate_multiplier": 3,
    },
})

results = pipeline.search(query="machine learning", top_k=10)

See Diversity filtering for more details.

Related features

Diversity filtering

Complete diversity pipeline with MMR and clustering

Semantic search

Initial retrieval before MMR

Reranking

Cross-encoder scoring alternative

Contextual compression

Reduce retrieved context