In such conditions, if x is a nearest neighbor to q, x is often onerous to search out, as a result of although ⟨q, x⟩ is excessive, ⟨q, r⟩ can be excessive, ensuing within the query-center similarity ⟨q, c⟩ being low, so this specific cluster is prone to be pruned and never searched additional. There are a selection of the way to mitigate this downside. For instance, computing a higher-quality clustering tends to lower the magnitude of r, which lowers the typical estimation error, whereas anisotropic vector quantization (AVQ) “shapes” the error such that it tends to be largest when the question is dissimilar to x, and due to this fact much less prone to impression outcomes.
SOAR addresses this concern by taking a totally completely different method: permitting vectors to be assigned to a couple of cluster. Intuitively, that is efficient by the precept of redundancy: secondary assignments could act as “backup clusters” that facilitate environment friendly, correct vector search when the first project performs poorly (when q is extremely parallel with r of the first project).
This redundancy arises from the truth that the second project supplies a brand new vector-center distinction r’. So long as this r’ isn’t near-parallel with q when r is near-parallel with q, this secondary heart ought to assist ScaNN find the closest neighbors to q. Nevertheless, SOAR goes a step additional than this naïve redundancy, and modifies the project loss operate for secondary assignments to explicitly optimize for unbiased, efficient redundancy: it goals to search out secondary clusters whose r’ are perpendicular to r, in order that when q is near-parallel to r and the first heart has excessive error, q can be near-orthogonal to r’ and the secondary heart could have low error. The impact of SOAR’s modified loss is visualized beneath: