Scaling Laws for Grid-Based Approximate Nearest Neighbor Search in High Dimensions

Approximate Nearest-Neighbor Search (ANNS) pipelines for high-dimensional neural embeddings spend the bulk of their query time in candidate verification, making it the primary bottleneck in the search process. In this paper, we present PANORAMA, a state-of-the-art refinement technique that accelerates verification by exploiting the inherent spectral decay of these embeddings. Using PCA to compact signal energy, PANORAMA evaluates candidate distances incrementally, computing at each step a strict lower bound on the full-vector distance and dynamically pruning candidates the moment this bound exceeds the running k-th nearest neighbor distance. While PCA's concentration of variance facilitates pruning, it breaks the uniform-variance assumption required by Product Quantization (PQ); we resolve this with a variance-shaping step that redistributes energy across subvectors, rendering accretive refinement compatible with quantized indexes. Optimized for modern memory hierarchies via vectorized bulk-pruning and cache-conscious data layouts, PANORAMA has been upstreamed into the FAISS library across major index families (IVFPQ/Flat, HNSW, and Refine). PANORAMA achieves higher QPS at any target recall with a cost that provably scales inversely with dataset spectral decay, delivering end-to-end speedups of up to 28.9x and outperforming probabilistic methods across all recall bands.

Approximate Nearest Neighbor Search (ANNS) plays a pivotal role in modern deep learning pipelines. Recently, many ANNS systems have been proposed to either provide broad functionality or reach high performance. However, it is yet difficult to achieve both with minimal programming efforts. We propose ANNLib to address the gap. ANNLib is a library that provides a programming framework for achieving high performance and flexible functionality in ANNS systems, based on popular graph-based ANNS algorithms. We carefully decouple and independently optimize both the algorithm and the data structure components of an ANNS system. In addition, we integrate state-of-the-art algorithms and data structures into ANNLib as modules, along with our new designs. Users can choose combinations of components to implement sophisticated settings with high performance, such as filter search, fully dynamic updates, and historical queries on snapshots. Our experiments show that our new solution provides a simple interface for various applications and achieves comparable or even better performance than previous work, specifically for each application.

By introducing RSLM (Rotated Scaled Lloyd-Max), a family of training-free vector quantization codecs compressing embeddings to 1--4 bits per dimension, we reduce memory cost and memory bandwidth of a typical large-scale Approximate Nearest Neighbor (ANN) search system, while reducing its complexity and keeping or improving recall across multiple benchmark datasets. State-of-the-art systems filter candidates using coarse partitions, approximately score them to narrow the set, and then rescore the best with higher precision representations (often >=8 bits per dimension). Our relativized codecs can bring this down to 2--4 bits per dimension. We use the properties of the ANN system to encode residual vectors instead of full vectors, both for the approximate scoring phase and the rescoring phase. Since Maximum Inner Product Search (MIPS) is very sensitive to vector norms, we correct the $L_2$ norms of quantized vectors. Our major innovation is that we correct the $L_2$ norm of the final reconstructed vector rather than just the residual. Our rescaling replaces more complicated schemes, such as Anisotropic loss. The residualization scheme gives us a more favorable quality vs size trade-off than generic quantization methods. Our high-performance implementation leverages a block-wise cascaded Fast Walsh-Hadamard Transform (FWHT) with linear-like complexity, AVX SIMD-optimized codebooks, and a steganographic encoding of scaling factors for perfect cache-line alignment.