Maximum Inner Product Search (MIPS)

An efficient distance approximation technique where database vectors are compressed via quantization while the query vector remains in full precision. This asymmetry yields higher accuracy than symmetric computation because the query—the most critical component—suffers no quantization distortion. In MIPS, ADC preserves the query's magnitude information, which is essential for correct inner product ranking. The approach reduces memory bandwidth requirements while maintaining near-exact search quality.

A critical distinction in vector search: cosine similarity measures orientation only (angle between vectors), normalizing magnitudes to unit length. Inner product preserves magnitude information, making it sensitive to both direction and vector length. In recommendation systems using matrix factorization, user and item vectors with larger magnitudes indicate stronger latent factors—information lost by cosine normalization. MIPS explicitly optimizes for this magnitude-aware scoring.

A technique that transforms the MIPS problem into a standard Nearest Neighbor Search (NNS) problem by appending an additional dimension to vectors. By concatenating a scaled norm term, the Euclidean distance in the augmented space becomes equivalent to the negative inner product in the original space. This allows MIPS to leverage existing ANN libraries like FAISS without native MIPS support, though careful scaling is required to avoid precision loss.

The distortion introduced when mapping continuous vectors to discrete codebook representations. In MIPS, quantization error disproportionately impacts high-magnitude vectors because small relative errors in large dot products translate to large absolute ranking errors. Standard Product Quantization optimized for Euclidean distance may perform poorly on inner product ranking. MIPS-specific quantization schemes like norm-explicit quantization separate magnitude encoding from direction encoding to preserve ranking fidelity.

The exact retrieval method that computes the dot product between the query and every database vector, guaranteeing perfect recall at O(N * D) time complexity. While computationally prohibitive for large-scale production systems, brute-force MIPS serves as the ground truth baseline for evaluating approximate methods. It remains practical for small datasets (<100K vectors) or as a verification step in re-ranking pipelines where a candidate set is re-scored with full precision.