Introduction

• In the [Basic RAG post]({% post_url 2025-04-26-BasicRAG %}), retrieval relied on vector search: find chunks whose embeddings are close to the question.
• Vector search is strong at meaning (synonyms, paraphrases), but it can miss exact keywords (for example a chemical formula, an ID, or a rare acronym).
• BM25 is a classic keyword ranker: great at exact terms, weak on semantics.
• Fusion retrieval runs both, normalizes their scores, and blends them so you get meaning and keywords.

Why fuse vector search and BM25?

Method	Strengths	Weaknesses
Vector search (FAISS)	Meaning, synonyms, paraphrases	May miss exact keyword matches
BM25 (keyword)	Exact term matching	No semantic understanding
Fusion	Both meaning and keywords	Slightly more setup

How it works (high level)

Query
  |---> BM25 scores  ----\
  |                       --> normalize --> alpha * vector + (1-alpha) * BM25 --> top-k
  |---> Vector scores ---/

1. Run both vector search and BM25 on the same query.
2. Normalize both score lists to the range [0, 1].
3. Combine with a weighted average: alpha * vector_score + (1 - alpha) * bm25_score.
4. Rank by the combined score and return top-k chunks.

• alpha controls the balance:
  • alpha = 1.0 → pure vector search
  • alpha = 0.0 → pure BM25
  • alpha = 0.5 → equal weight

Models / libraries used

• Embeddings: mxbai-embed-large:335m via [Ollama]({% post_url 2024-01-15-ollama %})
• BM25: rank_bm25 (statistical; no neural model)

Step by Step Coding guide

• Make sure Ollama is running and the embedding model is pulled (ollama pull mxbai-embed-large:335m).
• Install helpers such as langchain-community, langchain-ollama, faiss-cpu, rank-bm25, and numpy.

Step 0: Import packages

import numpy as np
from rank_bm25 import BM25Okapi
from langchain_community.document_loaders import PyPDFLoader
from langchain_text_splitters import RecursiveCharacterTextSplitter
from langchain_community.vectorstores import FAISS
from langchain_ollama.embeddings import OllamaEmbeddings

Step 1: Set up the embedding model

embedding_model = OllamaEmbeddings(model="mxbai-embed-large:335m")
print("Embedding model ready")

Step 2: Load PDF, chunk, and build the vector store

• Same ingest path as Basic RAG: load → chunk → FAISS.

path = "data/Understanding_Climate_Change.pdf"

loader = PyPDFLoader(path)
documents = loader.load()

text_splitter = RecursiveCharacterTextSplitter(
    chunk_size=1000, chunk_overlap=200, length_function=len
)
chunks = text_splitter.split_documents(documents)

for chunk in chunks:
    chunk.page_content = chunk.page_content.replace("\t", " ")

vectorstore = FAISS.from_documents(chunks, embedding_model)

print(f"Loaded {len(documents)} pages, split into {len(chunks)} chunks")
print("FAISS vector store created")

Step 3: Build the BM25 index

• BM25 (Best Matching 25) scores a chunk by how often query terms appear, adjusted for document length.
• Build it from the same chunks used in the vector store so both methods rank the same candidate set.

tokenized_docs = [chunk.page_content.split() for chunk in chunks]
bm25 = BM25Okapi(tokenized_docs)

print(f"BM25 index created from {len(tokenized_docs)} chunks")

Step 4: Perform fusion retrieval

• Core steps:
  1. Score all chunks with BM25
  2. Score all chunks with vector similarity
  3. Normalize both to [0, 1] (invert vector distance so higher = better)
  4. Combine with alpha
  5. Sort and keep top-k

query = "What are the impacts of climate change on the environment?"
k = 5
alpha = 0.5  # 0.5 = equal weight to vector and BM25
epsilon = 1e-8  # avoid division by zero

print(f"Query: {query}")
print(f"alpha = {alpha} (0 = pure BM25, 1 = pure vector, 0.5 = equal)\n")

# A) All documents in index order
all_docs = vectorstore.similarity_search("", k=vectorstore.index.ntotal)

# B) BM25 scores
bm25_scores = bm25.get_scores(query.split())
print(f"BM25 scores range: [{bm25_scores.min():.4f}, {bm25_scores.max():.4f}]")

# C) Vector similarity scores (FAISS distance: lower is better)
vector_results = vectorstore.similarity_search_with_score(query, k=len(all_docs))
vector_scores = np.array([score for _, score in vector_results])
print(f"Vector scores range: [{vector_scores.min():.4f}, {vector_scores.max():.4f}]")

# D) Normalize to [0, 1]
vector_scores = 1 - (vector_scores - vector_scores.min()) / (
    vector_scores.max() - vector_scores.min() + epsilon
)
bm25_scores = (bm25_scores - bm25_scores.min()) / (
    bm25_scores.max() - bm25_scores.min() + epsilon
)

print(f"\nNormalized vector scores range: [{vector_scores.min():.4f}, {vector_scores.max():.4f}]")
print(f"Normalized BM25 scores range:   [{bm25_scores.min():.4f}, {bm25_scores.max():.4f}]")

# E) Combine
combined_scores = alpha * vector_scores + (1 - alpha) * bm25_scores

# F) Rank and take top-k
sorted_indices = np.argsort(combined_scores)[::-1]
top_docs = [all_docs[i] for i in sorted_indices[:k]]

print(f"\nTop {k} combined scores: {[f'{combined_scores[i]:.4f}' for i in sorted_indices[:k]]}")

Step 5: Display the retrieved documents

for i, doc in enumerate(top_docs):
    print(f"Result {i}:")
    print(f"Content: {doc.page_content[:300]}...")
    print(f"Source: page {doc.metadata.get('page', 'N/A')}")
    print("=" * 80)

Step 6 (optional): Compare different alpha values

• See how the top hit shifts when you favor BM25 vs vector search.

for test_alpha in [0.0, 0.25, 0.5, 0.75, 1.0]:
    scores = test_alpha * vector_scores + (1 - test_alpha) * bm25_scores
    best_idx = np.argmax(scores)
    print(
        f'alpha={test_alpha:.2f}: top result = "{all_docs[best_idx].page_content[:80]}..."'
    )

Summary

• Fusion retrieval = vector search + BM25, score-normalized and blended with alpha.
• It can catch documents that either method alone might miss. A query like “CO2 emissions impact” benefits from BM25 (exact term CO2) and vector search (semantic “impact” ≈ consequences).
• Tune alpha per use case: more keywords → lower alpha; more paraphrases → higher alpha.
• Next: plug top_docs into the Generate step from [Basic RAG]({% post_url 2025-04-26-BasicRAG %}), or explore graph expansion in [GraphRAG]({% post_url 2025-08-27-GraphRAG %}).