What adjustments need to be made to an ANN algorithm when switching from Euclidean to cosine similarity? (Consider that cosine similarity can be achieved via normalized vectors and Euclidean distance.)

When switching an artificial neural network (ANN) algorithm from Euclidean distance to cosine similarity, the primary adjustments involve preprocessing the data, modifying the distance metric, and potentially reconfiguring the indexing structure. Cosine similarity measures the angle between vectors, which is equivalent to the Euclidean distance between L2-normalized vectors. This means vectors must be normalized to unit length before indexing and querying. Additionally, the ANN implementation must use a distance metric aligned with cosine similarity—often achieved by leveraging inner product calculations on normalized vectors.

Data Normalization and Preprocessing The first step is to normalize all input vectors to have an L2 norm (Euclidean length) of 1. This ensures that the Euclidean distance between two normalized vectors directly corresponds to their cosine similarity. For example, if your ANN indexes embeddings from a neural network, you’ll need to divide each vector by its L2 norm before adding it to the index. Similarly, query vectors must also be normalized before searching. Failure to normalize either the indexed data or queries will break the equivalence between Euclidean distance and cosine similarity. For instance, in Python, you could normalize a vector v using v_normalized = v / np.linalg.norm(v).

Distance Metric and Algorithm Configuration Most ANN libraries (e.g., FAISS, Annoy, or HNSW) allow specifying the distance metric. After normalization, Euclidean distance can be used, but switching to inner product (dot product) is often more efficient and interpretable. For example, FAISS provides IndexFlatIP for inner product, which matches cosine similarity when vectors are normalized. If your library doesn’t support inner product, you can still use Euclidean distance, but ensure the index is built on normalized vectors. Some libraries, like Annoy, offer a dedicated “angular” distance mode, which internally normalizes vectors and computes cosine similarity. Always verify the library’s documentation to ensure the metric aligns with your preprocessing steps.

Performance and Indexing Considerations Normalizing vectors changes their distribution, potentially affecting how the ANN partitions the data. For example, hierarchical navigable small world (HNSW) graphs or k-d trees optimized for Euclidean distance might require parameter adjustments (e.g., search depth or the number of neighbors) when working with normalized vectors on a unit hypersphere. Additionally, indexing time and memory usage may increase slightly due to normalization overhead. Testing is critical: after switching, validate recall and latency using a subset of queries. For example, if using FAISS with inner product, compare results against a brute-force cosine similarity search to ensure consistency. Libraries like Scikit-learn’s cosine_similarity function can help verify correctness during testing.