Falconn++ can filter out potential far away points in any hash bucket before querying, which results in higher quality candidates compared to other hashing-based solutions. Theoretically, Falconn++ asymptotically achieves lower query time complexity than Falconn, an optimal locality-sensitive hashing scheme on angular distance. Empirically, Falconn++ achieves higher recall-speed tradeoffs than Falconn on many real-world data sets. Falconn++ is also competitive with HNSW, an efficient representative of graphbased solutions on high search recall regimes.

Last-layer retraining methods have emerged as an efficient framework for correcting existing base models. Within this framework, several methods have been proposed to deal with correcting models for subgroup fairness with and without group membership information. Importantly, prior work has demonstrated that many methods are susceptible to noisy labels. To this end, we propose a drop-in correction for label noise in last-layer retraining, and demonstrate that it achieves state-ofthe-art worst-group accuracy for a broad range of symmetric label noise and across a wide variety of datasets exhibiting spurious correlations. Our proposed approach uses label spreading on a latent nearest neighbors graph and has minimal computational overhead compared to existing methods.

We rigorously establish the correctness of the methodology and show by experimentation using LSH that it is competitive in practice with available alternatives.

We thank all reviewers for their constructive comments. We fixed the architecture g in our previous experiments to a two layer neural network. We discussed how to select the layer choice and its impact above. The computational cost is low since the pretrained model is fixed, and we only optimize for g and c. We didn't test on Imagenet since we can't visualize results for all 1000 classes.

This is indeed an omission, but it is not terribly complicated and we will add it to the paper.

Approximate nearest neighbor (ANN) search is a key component in many modern machine learning pipelines; recent use cases include retrieval-augmented generation (RAG) and vector databases. Clustering-based ANN algorithms, that use score computation methods based on product quantization (PQ), are often used in industrial-scale applications due to their scalability and suitability for distributed and disk-based implementations. However, they have slower query times than the leading graph-based ANN algorithms. In this work, we propose a new supervised score computation method based on the observation that inner product approximation is a multivariate (multi-output) regression problem that can be solved efficiently by reduced-rank regression. Our experiments show that on modern high-dimensional data sets, the proposed reduced-rank regression (RRR) method is superior to PQ in both query latency and memory usage.

We consider the problem of learning the nearest neighbor graph of a dataset of n items. The metric is unknown, but we can query an oracle to obtain a noisy estimate of the distance between any pair of items. This framework applies to problem domains where one wants to learn people's preferences from responses commonly modeled as noisy distance judgments. In this paper, we propose an active algorithm to find the graph with high probability and analyze its query complexity. In contrast to existing work that forces Euclidean structure, our method is valid for general metrics, assuming only symmetry and the triangle inequality.

Current state-of-the-art approximate nearest neighbor search (ANNS) algorithms generate indices that must be stored in main memory for fast high-recall search. This makes them expensive and limits the size of the dataset. We present a new graph-based indexing and search system called DiskANN that can index, store, and search a billion point database on a single workstation with just 64GB RAM and an inexpensive solid-state drive (SSD). Contrary to current wisdom, we demonstrate that the SSD-based indices built by DiskANN can meet all three desiderata for large-scale ANNS: high-recall, low query latency and high density (points indexed per node). On the billion point SIFT1B bigann dataset, DiskANN serves > 5000 queries a second with < 3ms mean latency and 95%+ 1-recall@1 on a 16 core machine, where state-of-the-art billion-point ANNS algorithms with similar memory footprint like FAISS [18] and IVFOADC+G+P [8] plateau at around 50% 1-recall@1. Alternately, in the high recall regime, DiskANN can index and serve 5 10x more points per node compared to state-of-the-art graphbased methods such as HNSW [21] and NSG [13]. Finally, as part of our overall DiskANN system, we introduce Vamana, a new graph-based ANNS index that is more versatile than the existing graph indices even for in-memory indices.