Normalization and Scaling

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Use this page when vector similarity is unstable because embeddings are not normalized or scaling factors differ between training and retrieval.
This failure often appears when cosine distance is requested but vectors are stored raw, or when IP/dot metrics exaggerate magnitude.

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Open these first

• Visual map and recovery: RAG Architecture & Recovery
• Embedding vs meaning: embedding-vs-semantic.md
• Metric mismatch: metric_mismatch.md
• Chunking checklist: chunking-checklist.md

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Core acceptance

• Vectors are L2-normalized when using cosine similarity.
• ΔS(question, retrieved) ≤ 0.45, stable across three paraphrases.
• Coverage ≥ 0.70 on the target section.
• λ remains convergent across seeds.

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Typical breakpoints and the right fix

• Cosine similarity reported but vectors not normalized
  → metric_mismatch.md

• Dot product used without rescaling (large norm vectors dominate retrieval)
  → Normalize or rescale embeddings before indexing.

• Cross-model mixing (embeddings from different checkpoints with different norms)
  → Re-normalize the corpus and queries to unit length.

• Hybrid dense + sparse weighting unstable (scale mismatch between BM25 scores and vector norms)
  → Apply explicit min-max or z-score scaling before weighted sum.

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Fix in 60 seconds

1. Check norms
   Sample 100 embeddings. Compute mean L2 norm. If not ~1.0 under cosine, normalization missing.

2. Normalize queries
   Ensure query_vector = vector / ||vector|| before retrieval when using cosine.

3. Corpus re-index
   Drop and rebuild index with normalized vectors if store does not enforce it.

4. Hybrid scaling
   Normalize dense similarity scores into the same 0–1 range as BM25 before combining.

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Copy-paste probe

import numpy as np

def check_norms(vectors):
    norms = np.linalg.norm(vectors, axis=1)
    return norms.mean(), norms.std()

mean_norm, std_norm = check_norms(sample_vectors)
print("Mean norm:", mean_norm, "Std:", std_norm)

Target: mean ≈ 1.0, std ≤ 0.05 for cosine retrieval.

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