In our experiments, we adopt the standard exact Hamming search by linear scan. On a single core 2.0GHz CPU compiled with C++, searching over 1M samples onSIFT takes 17 approximately 0.15s per query withb = 512. Note that linear scan is a naive strategy. Firstly,we see that the differences among the curvesare very small. B.2 RankingEfficiency:MorecandρValues we provide more theoretical comparisons on the ranking efficiency at moreρ and c values. Figure 14: CIFAR-VGGTop-10 retrieved images (right) for two example query images (left, automobile and cat) withb = 512.

The industry practice has been moving to embedding based retrieval (EBR). For example, in many applications, the embedding vectors are trained by some form of two-tower models. During serving phase, candidates (embedding vectors) are retrieved according to the rankings of cosine similarities either exhaustively or by approximate near neighbor (ANN) search algorithms. For those applications, it is natural to apply ``sign random projections'' (SignRP) or variants, on the trained embedding vectors to facilitate efficient data storage and cosine distance computations. SignRP is also one of the standard indexing schemes for conducting approximate near neighbor search.

The industry practice has been moving to embedding based retrieval (EBR).

The industry practice has been moving to embedding based retrieval (EBR). For example, in many applications, the embedding vectors are trained by some form of two-tower models. During serving phase, candidates (embedding vectors) are retrieved according to the rankings of cosine similarities either exhaustively or by approximate near neighbor (ANN) search algorithms. For those applications, it is natural to apply sign random projections'' (SignRP) or variants, on the trained embedding vectors to facilitate efficient data storage and cosine distance computations. SignRP is also one of the standard indexing schemes for conducting approximate near neighbor search.