Combine vector and keyword search for improved retrieval. Use when implementing RAG systems, building search engines, or when neither approach alone provides sufficient recall.
from typing import List, Dict, Tuple
from collections import defaultdict
def reciprocal_rank_fusion(
result_lists: List[List[Tuple[str, float]]],
k: int = 60,
weights: List[float] = None
) -> List[Tuple[str, float]]:
"""
Combine multiple ranked lists using RRF.
Args:
result_lists: List of (doc_id, score) tuples per search method
k: RRF constant (higher = more weight to lower ranks)
weights: Optional weights per result list
Returns:
Fused ranking as (doc_id, score) tuples
"""
if weights is None:
weights = [1.0] * len(result_lists)
scores = defaultdict(float)
for result_list, weight in zip(result_lists, weights):
for rank, (doc_id, _) in enumerate(result_list):
# RRF formula: 1 / (k + rank)
scores[doc_id] += weight * (1.0 / (k + rank + 1))
# Sort by fused score
return sorted(scores.items(), key=lambda x: x[1], reverse=True)
def linear_combination(
vector_results: List[Tuple[str, float]],
keyword_results: List[Tuple[str, float]],
alpha: float = 0.5
) -> List[Tuple[str, float]]:
"""
Combine results with linear interpolation.
Args:
vector_results: (doc_id, similarity_score) from vector search
keyword_results: (doc_id, bm25_score) from keyword search
alpha: Weight for vector search (1-alpha for keyword)
"""
# Normalize scores to [0, 1]
def normalize(results):
if not results:
return {}
scores = [s for _, s in results]
min_s, max_s = min(scores), max(scores)
range_s = max_s - min_s if max_s != min_s else 1
return {doc_id: (score - min_s) / range_s for doc_id, score in results}
vector_scores = normalize(vector_results)
keyword_scores = normalize(keyword_results)
# Combine
all_docs = set(vector_scores.keys()) | set(keyword_scores.keys())
combined = {}
for doc_id in all_docs:
v_score = vector_scores.get(doc_id, 0)
k_score = keyword_scores.get(doc_id, 0)
combined[doc_id] = alpha * v_score + (1 - alpha) * k_score
return sorted(combined.items(), key=lambda x: x[1], reverse=True)
Template 2: PostgreSQL Hybrid Search
import asyncpg
from typing import List, Dict, Optional
import numpy as np
class PostgresHybridSearch:
"""Hybrid search with pgvector and full-text search."""
def __init__(self, pool: asyncpg.Pool):
self.pool = pool
async def setup_schema(self):
"""Create tables and indexes."""
async with self.pool.acquire() as conn:
await conn.execute("""
CREATE EXTENSION IF NOT EXISTS vector;
CREATE TABLE IF NOT EXISTS documents (
id TEXT PRIMARY KEY,
content TEXT NOT NULL,
embedding vector(1536),
metadata JSONB DEFAULT '{}',
ts_content tsvector GENERATED ALWAYS AS (
to_tsvector('english', content)
) STORED
);
-- Vector index (HNSW)
CREATE INDEX IF NOT EXISTS documents_embedding_idx
ON documents USING hnsw (embedding vector_cosine_ops);
-- Full-text index (GIN)
CREATE INDEX IF NOT EXISTS documents_fts_idx
ON documents USING gin (ts_content);
""")
async def hybrid_search(
self,
query: str,
query_embedding: List[float],
limit: int = 10,
vector_weight: float = 0.5,
filter_metadata: Optional[Dict] = None
) -> List[Dict]:
"""
Perform hybrid search combining vector and full-text.
Uses RRF fusion for combining results.
"""
async with self.pool.acquire() as conn:
# Build filter clause
where_clause = "1=1"
params = [query_embedding, query, limit * 3]
if filter_metadata:
for key, value in filter_metadata.items():
params.append(value)
where_clause += f" AND metadata->>'{key}' = ${len(params)}"
results = await conn.fetch(f"""
WITH vector_search AS (
SELECT
id,
content,
metadata,
ROW_NUMBER() OVER (ORDER BY embedding <=> $1::vector) as vector_rank,
1 - (embedding <=> $1::vector) as vector_score
FROM documents
WHERE {where_clause}
ORDER BY embedding <=> $1::vector
LIMIT $3
),
keyword_search AS (
SELECT
id,
content,
metadata,
ROW_NUMBER() OVER (ORDER BY ts_rank(ts_content, websearch_to_tsquery('english', $2)) DESC) as keyword_rank,
ts_rank(ts_content, websearch_to_tsquery('english', $2)) as keyword_score
FROM documents
WHERE ts_content @@ websearch_to_tsquery('english', $2)
AND {where_clause}
ORDER BY ts_rank(ts_content, websearch_to_tsquery('english', $2)) DESC
LIMIT $3
)
SELECT
COALESCE(v.id, k.id) as id,
COALESCE(v.content, k.content) as content,
COALESCE(v.metadata, k.metadata) as metadata,
v.vector_score,
k.keyword_score,
-- RRF fusion
COALESCE(1.0 / (60 + v.vector_rank), 0) * $4::float +
COALESCE(1.0 / (60 + k.keyword_rank), 0) * (1 - $4::float) as rrf_score
FROM vector_search v
FULL OUTER JOIN keyword_search k ON v.id = k.id
ORDER BY rrf_score DESC
LIMIT $3 / 3
""", *params, vector_weight)
return [dict(row) for row in results]
async def search_with_rerank(
self,
query: str,
query_embedding: List[float],
limit: int = 10,
rerank_candidates: int = 50
) -> List[Dict]:
"""Hybrid search with cross-encoder reranking."""
from sentence_transformers import CrossEncoder
# Get candidates
candidates = await self.hybrid_search(
query, query_embedding, limit=rerank_candidates
)
if not candidates:
return []
# Rerank with cross-encoder
model = CrossEncoder('cross-encoder/ms-marco-MiniLM-L-6-v2')
pairs = [(query, c["content"]) for c in candidates]
scores = model.predict(pairs)
for candidate, score in zip(candidates, scores):
candidate["rerank_score"] = float(score)
# Sort by rerank score and return top results
reranked = sorted(candidates, key=lambda x: x["rerank_score"], reverse=True)
return reranked[:limit]