Editing Information Retrieval (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Hybrid BM25 + dense retrieval pipeline:'''
<syntaxhighlight lang="python">
from rank_bm25 import BM25Okapi
from sentence_transformers import SentenceTransformer, util
import numpy as np

docs = [
    "Machine learning is a subset of artificial intelligence.",
    "Neural networks are computational models inspired by the brain.",
    "Gradient descent optimizes model parameters by following the loss gradient.",
    "Transformers use self-attention mechanisms to process sequences.",
]
tokenized = [d.lower().split() for d in docs]
bm25 = BM25Okapi(tokenized)
embedder = SentenceTransformer("BAAI/bge-small-en-v1.5")
doc''embeddings = embedder.encode(docs, normalize''embeddings=True)

def hybrid''retrieve(query: str, top''k: int = 3, alpha: float = 0.5) -> list:
    """alpha: weight for dense scores (1-alpha for BM25)."""
    # BM25 scores (sparse)
    bm25''scores = np.array(bm25.get''scores(query.lower().split()))
    bm25''norm = (bm25''scores - bm25''scores.min()) / (bm25''scores.max() - bm25_scores.min() + 1e-10)
    # Dense scores
    q''emb = embedder.encode(query, normalize''embeddings=True)
    dense''scores = util.dot''score(q''emb, doc''embeddings).numpy().flatten()
    dense''norm = (dense''scores - dense''scores.min()) / (dense''scores.max() - dense_scores.min() + 1e-10)
    # Combine
    combined = alpha * dense''norm + (1 - alpha) * bm25''norm
    top''idx = combined.argsort()[-top''k:][::-1]
    return [(docs[i], combined[i]) for i in top_idx]

results = hybrid_retrieve("How do neural networks learn?")
for doc, score in results:
    print(f"Score: {score:.3f} | {doc}")
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