# Exploiting Structural Properties for Efficient Constraint-Aware HNSW Hyperparameter Tuning

arXiv: https://arxiv.org/abs/2607.04630 · HTML: https://mlsanity.com/paper/2607.04630/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Vector search and ANN indexes, one of 15 directions in Retrieval-augmented generation.
- Builds on 18 of its 48 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Placed in

- Retrieval-augmented generation / [Vector search and ANN indexes](https://mlsanity.com/rag/vector-search-and-ann-indexes/)

## Builds on (most cited first, 18 of 18)

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- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Generalization through Memorization: Nearest Neighbor Language Models](https://mlsanity.com/paper/1911.00172/) (2019)
- [REPLUG: Retrieval-Augmented Black-Box Language Models](https://mlsanity.com/paper/2301.12652/) (2023)
- [Hallucination is Inevitable: An Innate Limitation of Large Language Models](https://mlsanity.com/paper/2401.11817/) (2024)
- [Distilling Knowledge from Reader to Retriever for Question Answering](https://mlsanity.com/paper/2012.04584/) (2020)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [ANN-Benchmarks: A Benchmarking Tool for Approximate Nearest Neighbor Algorithms](https://mlsanity.com/paper/1807.05614/) (2018)
- [Hyper-Parameter Optimization: A Review of Algorithms and Applications](https://mlsanity.com/paper/2003.05689/) (2020)
- [Fast Approximate Nearest Neighbor Search With The Navigating Spreading-out Graph](https://mlsanity.com/paper/1707.00143/) (2017)
- [Grid Search, Random Search, Genetic Algorithm: A Big Comparison for NAS](https://mlsanity.com/paper/1912.06059/) (2019)
- [A Comprehensive Survey and Experimental Comparison of Graph-Based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2101.12631/) (2021)
- [A Comprehensive Survey on Vector Database: Storage and Retrieval Technique, Challenge](https://mlsanity.com/paper/2310.11703/) (2023)
- [boldsymbolSteiner-Hardness: A Query Hardness Measure for Graph-Based ANN Indexes](https://mlsanity.com/paper/2408.13899/) (2024)

## Abstract (arXiv)

Vector databases (VectorDBs) are a core component of modern retrieval systems, including Retrieval-Augmented Generation (RAG), where efficient Approximate Nearest Neighbor Search (ANNS) is critical. Among ANNS algorithms, Hierarchical Navigable Small World (HNSW) graphs are widely adopted for their strong recalllatency trade-off. However, configuring HNSW remains challenging: its hyperparameters jointly affect search quality, latency, build time, and index size in nonlinear ways, while production deployments impose strict resource and tuning-time constraints.We study HNSW hyperparameter tuning from a systems perspective and show that its configuration space exhibits strong structural regularities. Specifically, we identify monotonic, dominant unimodal, and separable relationships among search-time and construction-time parameters, which induce feasibility boundaries under performance and resource constraints. Building on this insight, we propose CHAT, a constraint-aware tuning framework for HNSW. Unlike generic black-box optimizers, CHAT exploits HNSW-specific structure to perform deterministic, sample-efficient search and prune resource-infeasible configurations before full index construction. Across multiple datasets and HNSW-based vector search engines, CHAT identifies configurations that maximize recall or throughput while satisfying constraints on accuracy, latency, build time, index size, and tuning budget. Compared to strong baselines, CHAT achieves up to 45% higher throughput or 11% higher recall, and converges up to 44x faster. These results show that principled, structure-aware tuning enables efficient and robust HNSW deployment beyond generic black-box optimization.