This works reports evidence for the topological signatures of ambiguity in
sentence embeddings that could be leveraged for ranking and/or explanation
purposes in the context of vector search and Retrieval Augmented Generation
(RAG) systems. We proposed a working definition of ambiguity and designed an
experiment where we have broken down a proprietary dataset into collections of
chunks of varying size - 3, 5, and 10 lines and used the different collections
successively as queries and answers sets. It allowed us to test the signatures
of ambiguity with removal of confounding factors. Our results show that proxy
ambiguous queries (size 10 queries against size 3 documents) display different
distributions of homologies 0 and 1 based features than proxy clear queries
(size 5 queries against size 10 documents). We then discuss those results in
terms increased manifold complexity and/or approximately discontinuous
embedding submanifolds. Finally we propose a strategy to leverage those
findings as a new scoring strategy of semantic similarities.

本研究通过分析句子嵌入中的拓扑特征，提出了一种新的语义相似性评分策略，并探讨了歧义性在向量搜索和生成增强检索系统中的应用。

Blowfish：用于量化语义搜索中的歧义的拓扑和统计特征

Blowfish: Topological and statistical signatures for quantifying  ambiguity in semantic search

In recent years, the dominant accuracy metric for vector search is the recall
of a result list of fixed size (top-k retrieval), considering as ground truth
the exact vector retrieval results. Although convenient to compute, this metric
is distantly related to the end-to-end accuracy of a full system that
integrates vector search. In this paper we focus on the common case where a
hard decision needs to be taken depending on the vector retrieval results, for
example, deciding whether a query image matches a database image or not. We
solve this as a range search task, where all vectors within a certain radius
from the query are returned.
We show that the value of a range search result can be modeled rigorously
based on the query-to-vector distance. This yields a metric for range search,
RSM, that is both principled and easy to compute without running an end-to-end
evaluation. We apply this metric to the case of image retrieval. We show that
indexing methods that are adapted for top-k retrieval do not necessarily
maximize the RSM. In particular, for inverted file based indexes, we show that
visiting a limited set of clusters and encoding vectors compactly yields near
optimal results.

研究了向量搜索中的召回率指标问题，提出基于范围搜索任务的 RSM 指标，以评估向量搜索的精确性，并证明了适应于 top-k 检索的索引方法不一定能最大化 RSM。

小半径向量搜索

Vector search with small radiuses

Vector search has emerged as the foundation for large-scale information
retrieval and machine learning systems, with search engines like Google and
Bing processing tens of thousands of queries per second on petabyte-scale
document datasets by evaluating vector similarities between encoded query texts
and web documents. As performance demands for vector search systems surge,
accelerated hardware offers a promising solution in the post-Moore's Law era.
We introduce \textit{FANNS}, an end-to-end and scalable vector search framework
on FPGAs. Given a user-provided recall requirement on a dataset and a hardware
resource budget, \textit{FANNS} automatically co-designs hardware and
algorithm, subsequently generating the corresponding accelerator. The framework
also supports scale-out by incorporating a hardware TCP/IP stack in the
accelerator. \textit{FANNS} attains up to 23.0$\times$ and 37.2$\times$ speedup
compared to FPGA and CPU baselines, respectively, and demonstrates superior
scalability to GPUs, achieving 5.5$\times$ and 7.6$\times$ speedup in median
and 95\textsuperscript{th} percentile (P95) latency within an eight-accelerator
configuration. The remarkable performance of \textit{FANNS} lays a robust
groundwork for future FPGA integration in data centers and AI supercomputers.

介绍了一种基于 FPGA 的可扩展矢量搜索框架 FANNS，通过自动协同设计硬件和算法来生成相应的加速器，以在数据中心和 AI 超算中实现未来的 FPGA 集成。