# Probabilistic Kernel Function for Fast Angle Testing

arXiv: https://arxiv.org/abs/2505.20274 · HTML: https://mlsanity.com/paper/2505.20274/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 14 of 14)

- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Practical and Optimal LSH for Angular Distance](https://mlsanity.com/paper/1509.02897/) (2015)
- [Fast Approximate Nearest Neighbor Search With The Navigating Spreading-out Graph](https://mlsanity.com/paper/1707.00143/) (2017)
- [RaBitQ: Quantizing High-Dimensional Vectors with a Theoretical Error Bound for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2405.12497/) (2024)
- [High-Dimensional Approximate Nearest Neighbor Search: with Reliable and Efficient Distance Comparison Operations](https://mlsanity.com/paper/2303.09855/) (2023)
- [Norm-Explicit Quantization: Improving Vector Quantization for Maximum Inner Product Search](https://mlsanity.com/paper/1911.04654/) (2019)
- [Learning to Route in Similarity Graphs](https://mlsanity.com/paper/1905.10987/) (2019)
- [Norm-Ranging LSH for Maximum Inner Product Search](https://mlsanity.com/paper/1809.08782/) (2018)
- [Effective and General Distance Computation for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2404.16322/) (2024)
- [Learning to Hash Robustly, Guaranteed](https://mlsanity.com/paper/2108.05433/) (2021)
- [Falconn++: A Locality-sensitive Filtering Approach for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2206.01382/) (2022)
- [SymphonyQG: Towards Symphonious Integration of Quantization and Graph for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2411.12229/) (2024)
- [FINGER: Fast Inference for Graph-based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2206.11408/) (2022)
- [Probabilistic Routing for Graph-Based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2402.11354/) (2024)

## Built on by (most cited first, 2 of 2)

- [Panorama: Fast-Track Nearest Neighbors](https://mlsanity.com/paper/2510.00566/) (2025)
- [Approximate Nearest Neighbor Search for Modern AI: A Projection-Augmented Graph Approach](https://mlsanity.com/paper/2603.06660/) (2026)

## Abstract (arXiv)

In this paper, we study the angle testing problem in the context of similarity search in high-dimensional Euclidean spaces and propose two projection-based probabilistic kernel functions, one designed for angle comparison and the other for angle thresholding. Unlike existing approaches that rely on random projection vectors drawn from Gaussian distributions, our approach leverages reference angles and adopts a deterministic structure for the projection vectors. Notably, our kernel functions do not require asymptotic assumptions, such as the number of projection vectors tending to infinity, and can be theoretically and experimentally shown to outperform Gaussian-distribution-based kernel functions. We apply the proposed kernel function to Approximate Nearest Neighbor Search (ANNS) and demonstrate that our approach achieves a 2.5x--3x higher query-per-second (QPS) throughput compared to the widely-used graph-based search algorithm HNSW.