Exact and Deterministic Patch Descriptor Retrieval via Hierarchical Normalization

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.

Geometric Analysis of Self-Supervised Vision Representations for Semantic Image Retrieval

Content-based image retrieval (CBIR) systems enable users to search images based on visual content instead of relying on metadata. The text domain has benefited from vector search of representations created with unsupervised methods such as BERT. However, modern self-supervised learning methods for vision are mostly not reported in CBIR-related literature, instead relying on supervised models or multi-modal methods that align text and vision. We evaluate how the representations learned by modern self-supervised learning methods for vision perform under typical retrieval stacks that leverage vector databases and nearest neighbor search. Our evaluation reveals that the latent space geometry impacts approximate nearest neighbor (ANN) indexing. Specifically, highly anisotropic representations with high skewness produced by several modern SSL methods degrade the performance of partition-based and hashing-based search, even if their own linear probe or K-NN accuracy is not affected. In contrast, representations with higher isotropy and local purity better satisfy the distance-based assumptions of ANN indexes, leading to improved semantic retrieval performance.