How does using a different distance metric affect the internal behavior of indexes like HNSW or IVF? (For example, does changing the metric require rebuilding the index, or affect performance?)

Changing the distance metric in indexes like HNSW (Hierarchical Navigable Small World) or IVF (Inverted File) directly impacts how the index is built and how efficiently it operates. These indexes rely on the distance metric to organize data during construction, so switching metrics almost always requires rebuilding the index from scratch. For example, HNSW constructs a graph by connecting nodes based on their nearest neighbors according to the chosen metric. If you switch from Euclidean (L2) to cosine distance, the definition of “nearest” changes, rendering the existing graph structure invalid. Similarly, IVF partitions data into clusters using centroids optimized for the original metric. A new metric would misalign these clusters, leading to poor search accuracy. Most libraries, like FAISS, enforce this by requiring the metric to be specified at build time, and rebuilding is unavoidable.

The performance of the index is also tied to the metric. Metrics with different computational costs (e.g., Manhattan vs. cosine) can affect query speed. For instance, cosine distance requires normalizing vectors before calculating dot products, adding preprocessing steps that L2 doesn’t need. In HNSW, a poorly chosen metric might create a less navigable graph, increasing the number of hops needed during search. For IVF, a metric that doesn’t align with the data distribution (e.g., using Manhattan on spherical clusters) could scatter relevant vectors across multiple clusters, forcing the search to check more buckets. However, if the metric matches the data’s inherent structure—like cosine for text embeddings—the index can achieve better recall with fewer resources. Performance trade-offs depend on both the metric’s mathematical properties and how well it matches the data.

Implementation specifics matter, too. Some frameworks allow runtime configuration of metrics, but this often assumes compatible precomputed structures. For example, prenormalized vectors might let you switch between cosine and dot product without rebuilding, but this is an exception. In most cases, rebuilding ensures the index’s internal logic (like graph links or cluster boundaries) aligns with the metric’s behavior. Developers should treat the distance metric as a core part of the index’s configuration—changing it is akin to redefining the problem space. Testing with the target metric during initial setup is critical to avoid costly rebuilds later. Libraries like Annoy or FAISS explicitly document this constraint, emphasizing that metric changes aren’t runtime parameters but foundational design choices.