cs.CVJun 25, 2026

Exact and Deterministic Patch Descriptor Retrieval via Hierarchical Normalization

Authors: Koichi Sato

Abstract

We present a patch descriptor retrieval method that returns the exact nearest neighbour -- provably identical to exhaustive full-vector search -- while evaluating only a small fraction of the database, and does so deterministically: the same (database, query) pair always produces the same result, independent of run order, thread count, or hardware. This contrasts with approximate nearest-neighbour (ANN) approaches such as HNSW and IVF-PQ, which trade exactness for speed and may return different results across runs. The enabling mechanism is Hierarchical Normalization (HN): a normalisation scheme that splits the pre-normalisation feature vector into a K-dim major component (norm sqrt(1-alpha)) and a (128-K)-dim minor component (norm sqrt(alpha)). Since the minor inner product is bounded by alpha (Cauchy-Schwarz on the prescribed norms), the major similarity plus alpha is an admissible upper bound on the full similarity: the search scans the K-dim major component for all entries, then applies full 128-dim evaluation only to entries that cannot be pruned -- a provably exact branch-and-bound scan. We train HN-modified HardNet on the notredame split of the UBC patch dataset and evaluate on trevi and halfdome. With a cache-optimised Structure-of-Arrays layout and K=8, alpha=1/32, the search achieves 13.7x (trevi) / 12.7x (halfdome) speed-up over brute-force 128-dim search, with only 0.4% of entries requiring full evaluation. At K=16, alpha=1/8, FPR@95 rises from 0.0062 to 0.0064 on trevi at 7.2x speed-up, with 98.8% of entries bypassing full evaluation.

Explore similar work

CardsList
Oct 1, 2025cs.LG

Panorama: Fast-Track Nearest Neighbors

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.
Vansh Ramani, Alexis Schlomer, Akash Nayar +3
Approximate Nearest-Neighbor SearchK-Nearest-NeighborNeural Architecture SearchCalibration-Free Low-Bit Vector QuantizationHyperspherical Embedding GeometryPrincipal Component Analysis+3
AskPDF
Jun 7, 2026cs.DC

Aperon Technical Report: Hierarchical No-Pointer Tangent-Local Search for High-Dimensional Approximate Nearest Neighbors

We present HNTL (Hierarchical No-pointer Tangent-Local), the core vector indexing and candidate generation framework of the Aperon vector memory system. Proximity graphs (e.g., HNSW) incur a heavy pointer tax in memory overhead and induce irregular memory accesses that stall CPU pipelines. HNTL resolves this by partitioning the high-dimensional space into local, coherent grains, representing vectors as low-dimensional coordinates on local tangent spaces, and scanning them sequentially using a pointerless Block-SoA (Structure-of-Arrays) layout. On anisotropic manifold data (d=768, N=10,000), local PCA captures 96.3% of the variance, allowing HNTL to achieve a final Rerank Recall@10 of 1.0000 with a candidate pool size of only C=20 vectors. Hardware profiling via Apple kperf CPU Performance Monitoring Unit (PMU) counters demonstrates a 3.61x speedup (4.137 ns/vector vs. 14.951 ns/vector) for our NEON auto-vectorized C++ Block-SoA scan engine over standard pointer-chasing graph traversals, driven by a 3.59x IPC (Instructions Per Cycle) and near-zero L1/L2 data cache misses.
Yong Fu
Approximate Nearest-Neighbor SearchVector DatabaseVectorizationIndexParallel Continuous Local SearchBreadth-First Search+2
AskPDF
Apr 22, 2026cs.IR

Semantic Recall for Vector Search

We introduce Semantic Recall, a novel metric to assess the quality of approximate nearest neighbor search algorithms by considering only semantically relevant objects that are theoretically retrievable via exact nearest neighbor search. Unlike traditional recall, semantic recall does not penalize algorithms for failing to retrieve objects that are semantically irrelevant to the query, even if those objects are among their nearest neighbors. We demonstrate that semantic recall is particularly useful for assessing retrieval quality on queries that have few relevant results among their nearest neighbors-a scenario we uncover to be common within embedding datasets. Additionally, we introduce Tolerant Recall, a proxy metric that approximates semantic recall when semantically relevant objects cannot be identified. We empirically show that our metrics are more effective indicators of retrieval quality, and that optimizing search algorithms for these metrics can lead to improved cost-quality tradeoffs.
Leonardo Kuffo, Ioanna Tsakalidou, Roberta De Viti +3
Approximate Nearest-Neighbor SearchConflict-Based SearchSemantic RecallFactual Recall
AskPDF