Self-attention in transformer models is an incremental associative memory that maps key vectors to value vectors. One way to speed up self-attention is to employ GPU-compliant vector search algorithms, yet the standard partitioning methods yield poor results in this context, because (1) keys and queries follow different distributions and (2) the effect of RoPE positional encoding. In this paper, we introduce SAAP (Self-Attention with Asymmetric Partitions), which overcomes these problems. It is an asymmetrical indexing technique that employs distinct partitions for keys and queries, thereby approximating self-attention with a data-adaptive sparsity pattern. It works on pretrained language models without finetuning, as it only requires to train (offline) a small query classifier. On a long context Llama 3.1-8b model, with sequences ranging from 100k to 500k tokens, our method typically reduces by a factor 20 the fraction of memory that needs to be looked-up, which translates to a time saving of 60\% when compared to FlashAttention-v2.

Vector databases manage large collections of embedding vectors. As AI applications are growing rapidly, so are the number of embeddings that need to be stored and indexed. The Faiss library is dedicated to vector similarity search, a core functionality of vector databases. Faiss is a toolkit of indexing methods and related primitives used to search, cluster, compress and transform vectors. This paper first describes the tradeoff space of vector search, then the design principles of Faiss in terms of structure, approach to optimization and interfacing. We benchmark key features of the library and discuss a few selected applications to highlight its broad applicability.