Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Approximate Nearest Neighbor Search for Modern AI: A Projection-Augmented Graph Approach

Kejing Lu, Zhenpeng Pan, Jianbin Qin, Yoshiharu Ishikawa, Chuan Xiao

TL;DR

Projection-Augmented Graph (PAG), a new ANNS framework that integrates projection techniques into a graph index to satisfy six critical demands of modern AI applications: high query efficiency, fast indexing, low memory footprint, scalability to high dimensionality, robustness across varying retrieval sizes, and support for online insertions.

Abstract

Approximate Nearest Neighbor Search (ANNS) is fundamental to modern AI applications. Most existing solutions optimize query efficiency but fail to align with the practical requirements of modern workloads. In this paper, we outline six critical demands of modern AI applications: high query efficiency, fast indexing, low memory footprint, scalability to high dimensionality, robustness across varying retrieval sizes, and support for online insertions. To satisfy all these demands, we introduce Projection-Augmented Graph (PAG), a new ANNS framework that integrates projection techniques into a graph index. PAG reduces unnecessary exact distance computations through asymmetric comparisons between exact and approximate distances as guided by projection-based statistical tests. Three key components are designed and unified to the graph index to optimize indexing and searching. Experiments on six modern datasets demonstrate that PAG consistently achieves superior query per second (QPS)-recall performance -- up to 5x faster than HNSW -- while offering fast indexing speed and moderate memory footprint. PAG remains robust as dimensionality and retrieval size increase and naturally supports online insertions.

Approximate Nearest Neighbor Search for Modern AI: A Projection-Augmented Graph Approach

TL;DR

Projection-Augmented Graph (PAG), a new ANNS framework that integrates projection techniques into a graph index to satisfy six critical demands of modern AI applications: high query efficiency, fast indexing, low memory footprint, scalability to high dimensionality, robustness across varying retrieval sizes, and support for online insertions.

Abstract

Approximate Nearest Neighbor Search (ANNS) is fundamental to modern AI applications. Most existing solutions optimize query efficiency but fail to align with the practical requirements of modern workloads. In this paper, we outline six critical demands of modern AI applications: high query efficiency, fast indexing, low memory footprint, scalability to high dimensionality, robustness across varying retrieval sizes, and support for online insertions. To satisfy all these demands, we introduce Projection-Augmented Graph (PAG), a new ANNS framework that integrates projection techniques into a graph index. PAG reduces unnecessary exact distance computations through asymmetric comparisons between exact and approximate distances as guided by projection-based statistical tests. Three key components are designed and unified to the graph index to optimize indexing and searching. Experiments on six modern datasets demonstrate that PAG consistently achieves superior query per second (QPS)-recall performance -- up to 5x faster than HNSW -- while offering fast indexing speed and moderate memory footprint. PAG remains robust as dimensionality and retrieval size increase and naturally supports online insertions.
Paper Structure (40 sections, 1 theorem, 40 equations, 19 figures, 4 tables, 2 algorithms)

This paper contains 40 sections, 1 theorem, 40 equations, 19 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Prior Works
  3. Our Solution
  4. Problem Setting
  5. Background of RobustPrune
  6. Towards Fast Graph Construction
  7. Towards High Graph Connectivity
  8. Projection-Augmented Graph
  9. Neighborhood Relations via Random Projection
  10. Probabilistic Routing Test
  11. Test Feedback Buffer
  12. Probabilistic Edge Selection
  13. Implementation and Analysis
  14. Implementation
  15. Algorithm Pseudo-Codes of PAG
  16. ...and 25 more sections

Key Result

Theorem 3.1

Under A1--A3, as $L \rightarrow \infty$, $d/L \rightarrow \infty$, and $m$ grows sufficiently fast with respect to $d/L$, $\bm{X}=[\cos \theta_1,\ldots,\cos \theta_t]^{\top}$, conditioned on $\{\alpha_i, \beta_i\}_{i=1}^t$, is asymptotically Gaussian: where the mean is $\bar{\mu} = [\cos \alpha_1 \cos \beta_1,\ldots,\cos \alpha_t \cos \beta_t]^{\top}$, and $\bar{\Sigma}_{m,L} = O(\epsilon_m/L)$ w

Figures (19)

  • Figure 1: An overview of PAG. In this example, $\bm{u}$ has 7 out-neighbors $\{\bm{w_i}\}^7_{i=1}$. Let $\{\bm{e_i}\}^7_{i=1}$ denote the edges between $\bm{u}$ and $\{\bm{w_i}\}^7_{i=1}$, which are sent to PRT, where the threshold is determined by $\bm{z_{\max}}$. As a result, only $\bm{w_3}$ and $\bm{w_5}$ pass PRT, and their exact distances to $\bm{v}$ are computed. By distance comparison, node $\bm{w_5}$ is identified as a false positive, not added to $W$, and thus sent to $R_F$. Node $\bm{w_3}$ is inserted into $W$, causing $\bm{z_{\max}}$ to be ejected from $W$ and sent to $R_T$. The two rings $R_F$ and $R_T$ are merged and refilled into $W$. On the other route, by a left shift, the signs of both $\bm{w_3}$ and $\bm{w_5}$ are reversed, and all signs become negative, indicating that $\bm{u}$ is rejected by the PES test. Consequently, $\vec{\bm{uv}}$ is treated as a candidate edge and added to the PES set.
  • Figure 2: Illustration of PES (left: the role of PES; right: geometric illustration). Let $\bm{v}$ be the node to be inserted. The four green nodes are out-neighbors of $\bm{v}$. Without PES, we can obtain only a single in-neighbor via RobustPrune. By taking all other visited nodes (the blue ones) into account, we apply PES, followed by RobustPrune. As such, we can identify three additional promising in-neighbors, thereby strengthening the connectivity of the neighborhood of $\bm{v}$.
  • Figure 3: QPS-recall, $K = 100$. SymQG runs out of memory on MajorTOM. Recall is plotted in logarithmic scale to highlight large values.
  • Figure 4: Indexing time and peak memory usage. SymQG runs out of memory on MajorTOM.
  • Figure 5: QPS-recall, $K = 10$.
  • ...and 14 more figures

Theorems & Definitions (1)

  • Theorem 3.1