MMR: Diversify Search Results with Maximal Marginal Relevance

The Redundancy Problem

Standard similarity search returns similar documents - often too similar:

Query: "How does photosynthesis work?"

Top 5 results:
1. "Photosynthesis converts light to energy..."
2. "Photosynthesis is how plants make energy..."  ← Redundant
3. "Plants use photosynthesis to create..."      ← Redundant
4. "Chlorophyll enables photosynthesis..."       ← Different aspect!
5. "Photosynthesis occurs in chloroplasts..."    ← Different aspect!

You waste context on repetition.

Maximal Marginal Relevance (MMR)

MMR balances relevance to query and diversity from already-selected docs.

Formula:

MMR = argmax[λ * Sim(Di, Q) - (1-λ) * max Sim(Di, Dj)]
         Di              ↑                    ↑
                   relevance to query    similarity to selected

λ = 0.7 typical (70% relevance, 30% diversity)

Implementation

DEVELOPERpython
import numpy as np
from sklearn.metrics.pairwise import cosine_similarity

def mmr_search(query_embedding, doc_embeddings, documents, k=10, lambda_param=0.7):
    """
    MMR retrieval
    
    Args:
        query_embedding: Query vector
        doc_embeddings: All document vectors
        documents: Original documents
        k: Number of results
        lambda_param: Relevance vs diversity (0-1)
    """
    # Calculate similarity to query
    query_sim = cosine_similarity([query_embedding], doc_embeddings)[0]
    
    selected_indices = []
    remaining_indices = list(range(len(documents)))
    
    # Select first document (most similar to query)
    first_idx = np.argmax(query_sim)
    selected_indices.append(first_idx)
    remaining_indices.remove(first_idx)
    
    # Iteratively select k-1 more documents
    for _ in range(k - 1):
        mmr_scores = []
        
        for idx in remaining_indices:
            # Relevance to query
            relevance = query_sim[idx]
            
            # Max similarity to already selected docs
            selected_embeddings = doc_embeddings[selected_indices]
            diversity = max(cosine_similarity([doc_embeddings[idx]], selected_embeddings)[0])
            
            # MMR score
            mmr_score = lambda_param * relevance - (1 - lambda_param) * diversity
            mmr_scores.append((idx, mmr_score))
        
        # Select doc with highest MMR score
        best_idx = max(mmr_scores, key=lambda x: x[1])[0]
        selected_indices.append(best_idx)
        remaining_indices.remove(best_idx)
    
    return [documents[i] for i in selected_indices]

LangChain Built-in MMR

DEVELOPERpython
from langchain.vectorstores import Chroma
from langchain.embeddings import OpenAIEmbeddings

vectorstore = Chroma.from_documents(documents, OpenAIEmbeddings())

# MMR search
results = vectorstore.max_marginal_relevance_search(
    query="photosynthesis",
    k=5,
    fetch_k=20,  # Fetch 20 candidates, return diverse 5
    lambda_mult=0.7  # Relevance weight
)

When to Use MMR

Use MMR when:

• Documents have high overlap
• Context window is limited
• You need broad coverage
• Multi-aspect queries ("tell me about X, Y, and Z")

Skip MMR when:

• Documents already diverse
• Speed is critical (MMR is slower)
• Single-aspect queries

Tuning Lambda

DEVELOPERpython
# Test different lambda values
lambdas = [0.3, 0.5, 0.7, 0.9]

for lam in lambdas:
    results = mmr_search(query, embeddings, docs, lambda_param=lam)
    
    # Measure diversity
    diversity = measure_diversity(results)
    relevance = measure_relevance(results, query)
    
    print(f"λ={lam}: Relevance={relevance:.2f}, Diversity={diversity:.2f}")

Recommendations:

• High redundancy domain: λ = 0.5-0.6
• General purpose: λ = 0.7
• Precision critical: λ = 0.8-0.9

Performance Optimization

MMR is O(k²) - slow for large k:

DEVELOPERpython
# Faster: Fetch candidates first
def fast_mmr(query, vectordb, k=10, fetch_k=100, lambda_param=0.7):
    # 1. Get fetch_k candidates (fast vector search)
    candidates = vectordb.search(query, k=fetch_k)
    
    # 2. Apply MMR on smaller set
    return mmr_search(
        query_embedding=query,
        doc_embeddings=[c['embedding'] for c in candidates],
        documents=[c['doc'] for c in candidates],
        k=k,
        lambda_param=lambda_param
    )

Combining with Reranking

Pipeline: Retrieval → MMR → Reranking

DEVELOPERpython
# 1. Initial retrieval
candidates = vector_search(query, k=100)

# 2. Diversify with MMR
diverse_docs = mmr_search(query, candidates, k=20)

# 3. Rerank for precision
final_results = cross_encoder_rerank(query, diverse_docs, k=10)

MMR ensures your LLM sees varied, non-redundant context. Essential for high-quality RAG.