Vectors as Representations

An entity such as a support request, image, token, or user is not a vector. An encoder maps that entity and its context into coordinates. Those coordinates become meaningful only when paired with a representation ID that fixes the encoder revision, preprocessing, pooling, dimension order, scale, and intended uses. The same entity can have several valid representations for different decisions.

When a transform maps a higher-dimensional space into fewer coordinates, distinct source vectors can collide. That is information loss, but not automatically a defect: a projection may deliberately discard nuisance variation. The engineering obligation is to show that the lost distinctions are irrelevant to named downstream decisions on representative slices.

The reference artifact snapshots item IDs, vectors, transform rows, and source/target probe weights into immutable tuples. It rejects duplicate identities, empty or ragged shapes, booleans disguised as numbers, NaN, infinity, source-ID mismatches, and missing probes. The report compares declared linear scores, pairwise distances, and source-distinct items that collapse in the target representation.

1if __name__ == "__main__":
2    report = audit_invariance(
3        EXAMPLE_REPRESENTATIONS, EXAMPLE_ROTATION, EXAMPLE_PROBES
4    )
5    print(
6        f"representation={report.source_representation_id}"
7        f"->{report.target_representation_id}"
8    )
9    print(f"dimensions={report.source_dimension}->{report.target_dimension}")
10    print(f"max_score_drift={report.max_score_drift:.6f}")
11    print(f"max_distance_drift={report.max_distance_drift:.6f}")
12    print(f"collisions={len(report.collisions)}")

representation=support-intent-v3->support-intent-v4
dimensions=2->2
max_score_drift=0.000000
max_distance_drift=0.000000
collisions=0

1. 01Join by stable identityCompare the same canonical items across versions; row position, filenames, or arrival order are not identity contracts.
2. 02Declare behavioral probesChoose scores, neighbors, classifications, or task outputs that consumers actually depend on, and migrate each probe explicitly.
3. 03Separate intended from unintended driftA dimensional reduction may intentionally alter distance. Record the accepted property and evaluate task utility rather than forcing every numeric invariant to pass.

1. 01Keep the dimension, change the modelReject the payload unless the representation ID matches. An equal-length output from another encoder is syntactically compatible and semantically unrelated.
2. 02Rotate coordinates, keep stale weightsRaw vectors remain valid, but a downstream linear probe now asks a different question. The audit should expose score drift by item.
3. 03Project away one coordinateSearch for distinct items that become identical and inspect whether the lost distinction matters on rare, safety-critical, or high-cost slices.
4. 04Quantize near a decision boundaryAggregate error can look small while small coordinate perturbations flip high-impact decisions. Measure margin-conditioned behavior, not only mean squared drift.
5. 05Inject non-finite valuesFail before storage or scoring. NaN can poison comparisons and sorting while still occupying an otherwise valid numeric container.

• Record vector norm and invalid-value distributions by representation version and data slice.
• Keep old and new coordinates out of the same namespace unless every read is version-filtered.
• Shadow representative traffic before cutover and retain the source objects needed to rebuild either version.
• Evaluate retrieval or decision utility after approximate indexing, filtering, and thresholds—not just at the encoder boundary.
• Treat a normalization or truncation change as a representation change even when the base model name is unchanged.