Dense + Sparse Score Fusionmedium

Dense + Sparse Score Fusion

medium RAG & Retrieval 15 min

NumPy allowed · plain Python earns 10 bonus points

A query retrieves context

Embedding similarity ranks the documents before generation.

Open lesson →

01query

02embed

03retrieve

04context

What is RAG?→ embed →top context

retrieval.md44%

rag-systems.md33%

agents.md24%

Cosine-like similarity scores ranked before context assembly

Implement weighted score fusion between dense (embedding) and sparse (BM25-style) retrieval, the real backbone of hybrid search.

Task

Implement fuse_scores(dense_scores, sparse_scores, alpha). For every doc id in either dict, fused score is alpha*dense_scores.get(id,0) + (1-alpha)*sparse_scores.get(id,0). Return a dict of id -> fused score.

Function Signature

fuse_scores(dense_scores: dict[str, float], sparse_scores: dict[str, float], alpha: float) -> dict[str, float]

Examples

Example 1: equal weight blend
Input: dense_scores = {'a': 0.8}
sparse_scores = {'a': 0.4}
alpha = 0.5
Output: {'a': 0.6000000000000001}

Example 2: doc only in sparse
Input: dense_scores = {}
sparse_scores = {'b': 0.9}
alpha = 0.5
Output: {'b': 0.45}

Example 3: pure dense weight
Input: dense_scores = {'a': 0.7}
sparse_scores = {'a': 0.2}
alpha = 1
Output: {'a': 0.7}

Constraints

0 <= alpha <= 1

Python3Saved ✓

def fuse_scores(dense_scores, sparse_scores, alpha):

# Your implementation here

pass

Case 1: equal weight blend

Input: dense_scores = {'a': 0.8}
sparse_scores = {'a': 0.4}
alpha = 0.5

Expected: {'a': 0.6000000000000001}

Case 2: doc only in sparse

Input: dense_scores = {}
sparse_scores = {'b': 0.9}
alpha = 0.5

Expected: {'b': 0.45}

Case 3: pure dense weight

Input: dense_scores = {'a': 0.7}
sparse_scores = {'a': 0.2}
alpha = 1

Expected: {'a': 0.7}