Q8 · Why does L2 normalisation change the relationship between cosine similarity and dot product?

Cosine is q·d / (‖q‖‖d‖). After L2 normalisation both norms are 1, so the denominator vanishes and cosine is the dot product. The rankings become identical.

The engineering consequence is the part that matters: an index configured for inner product returns the same ranking as one configured for cosine only if you normalise on write. Mix those up and every ranking silently changes — longer vectors win on inner product regardless of direction. So: normalise on write, or configure the index for cosine, and know which one you did. It is also why a similarity threshold is not portable: cosine is a relative score, not a calibrated probability, and 0.82 on one corpus is not 0.82 on another.