Two-tower retrieval requires matching representations and the exact search metric

Let a query tower produce q from the request context and an item tower produce v_i from item features. A dot-product score enables precomputation when the item representation does not depend on request-specific features omitted from its tower. Rich cross-features between a particular user and item may need a later ranker instead of a precomputed item vector. Preserve the distinction between a model architecture that permits separate encoding and an arbitrary scoring network whose item side cannot be cached independently without changing its function.

For a fixed nonzero query, maximum inner product depends on item-vector norm as well as direction. Normalizing only the query multiplies all dot products by the same positive factor and preserves ordering, but normalizing each item generally changes an unnormalized dot-product ranking. Cosine similarity divides by both norms. If training used magnitude as part of the learned score, silently replacing it with cosine is a model change requiring evaluation. Zero vectors have no defined cosine direction and need an explicit fallback or exclusion policy before normalization.

For unit-length query and item vectors, squared Euclidean distance equals two minus twice their inner product. Exact minimization of that distance then gives the same ordering as exact maximum inner product or cosine, subject to ties. Without unit norms, the general squared-distance identity includes separate norm terms and can produce a different ranking. Some libraries report squared distances, so do not interpret their numeric outputs as unsquared lengths. Check normalization and the documented metric at both index construction and query time.

Equivalent exact scores do not guarantee two approximate index configurations return identical neighbors. Quantization, pruning, search effort, and stale or missing vectors can change results. Evaluate approximate recall against exact top neighbors under the same score, then evaluate relevance coverage separately. Sampled training negatives introduce another distribution choice: a training correction for sampled items is not automatically a correction for logged exposure bias or a proof that retrieval scores estimate click probability. Keep score meaning, training sampling, and online feedback identification separate.

Track query-tower, item-tower, feature-schema, ID mapping, normalization, and index versions together. Updating one tower while retaining old item vectors can change compatibility even when dimensions match. A rollout needs a validated compatible pair or an explicitly tested transition, not only a successful deserialization. Record the snapshot used for each request and define how new, removed, or modified items enter it. Compare exact probes, relevance cohorts, latency, and resource cost before switching a production index generation.

The vector lab illustrates a two-dimensional projection rather than a retriever. Reset, set both angle 0° and magnitude 1, predict components (1,0), then Play or Step. Reset and set both angle 90° and magnitude 1 for (0,1), within numerical display precision. Reset and set both angle 0° and magnitude 2 for (2,0). The graph uses Cartesian projections of one vector and playback traces its selected angle; it has no item index, query tower, learned score, or nearest-neighbor algorithm. Use the explicit vectors in the worked example to compare actual metrics.