PatANN - Pattern-Aware Vector Database and ANN Framework #
Below is an excerpt from our upcoming research paper. A full technical derivation, scalability analysis, and benchmark comparisons will be included in the complete publication.
Overview: Vector Search Reinvented — A Pattern-Aware Approach #
Traditional vector search solutions face critical limitations in today’s AI landscape, where massive high-dimensional datasets have outpaced the capabilities of existing frameworks like FAISS, ScaNN, and HNSW – hubness effects in high-dimensional spaces, rudimentary synchronous and memory bound execution, static data distribution patterns, to name a few.
In this paper, we describe PatANN, a pattern-aware, massively parallel, and distributed vector search framework for scalable nearest neighbor search. Unlike existing solutions, PatANN uniquely combines in-memory and on-disk execution with native async support, addressing the fundamental limitations of current approaches to deliver superior performance at scale.
Algorithm #
PatANN is a pattern-aware, massively parallel, and distributed vector search framework designed for scalable and efficient nearest neighbor search, operating both in-memory and on-disk. Unlike conventional algorithms, PatANN leverages macro and micro patterns within vectors to drastically reduce search space before performing costly distance computations.
The actual implementation is more involved. Vectors are encoded at multiple resolutions, capturing both macro and micro patterns within the data. This multi-scale approach ensures that both broad similarities and fine details are captured. The patterns are hashed to maintain locality of reference, minimizing cross-shard communication during distributed searches. PatANN also uses recursive patterns to mitigate the curse of dimensionality and hubness in high-dimensional data. The system dynamically selects which patterns to prioritize based on the distribution characteristics of the vector space, optimizing for the specific dataset. Additionally, PatANN employs probabilistic matching rather than exact pattern matching to achieve massive speed advantages while maintaining high recall (> 98%). A detailed research paper is forthcoming.
Mathematical Foundation #
PatANN’s pattern probing methodology is grounded in three key mathematical principles:
- manifold learning
- information-theoretic compression, and
- adaptive multi-resolution analysis.
Unlike traditional approximation methods that rely on random projections (e.g., LSH) or graph traversals (e.g., HNSW), PatANN approach formalizes vector similarity search as a sequential hypothesis testing problem.
Pattern Discovery #
Given a dataset $V \subset \mathbb{R}^d$, we construct a pattern dictionary
$P = {P_1, \dots, P_k}$,
where each $P_i$ represents a statistically significant subspace projection satisfying:
$$ \mathbb{E}_{v \sim V}\left[|P_i(v)|_2^2\right] \geq \eta \cdot \mathbb{E}\left[|v|_2^2\right] $$
for a significance threshold $\eta$
These projections are identified using adaptive k-means clustering in progressively refined subspaces.
Hierarchical Filtering #
For a query ( q ), we compute the pattern correlation score:
$$ s(q, v) = \sum_{i=1}^k w_i \cdot \langle P_i(q), P_i(v) \rangle $$
Weights $w_i$ are dynamically adjusted as:
$$ w_i = \frac{I(P_i; V)}{\sum_j I(P_j; V)} $$
where $I(\cdot; \cdot)$ denotes mutual information.
This prioritizes patterns that maximally reduce uncertainty about neighbor relationships.
Density-Aware Adaptation #
PatANN automatically tunes pattern granularity using local intrinsic dimension estimation:
$$ \hat{d}(v) = \frac{1}{\epsilon^2} \log \left( \frac{|B_\epsilon(v)|}{|V|} \right) $$
where $B_\epsilon(v)$ is the $\epsilon$-neighborhood of $v$.
Coarser patterns are used in regions with higher $\hat{d}$ to combat the curse of dimensionality.
Theoretical Advantages #
Provable recall bounds:
For any $\epsilon > 0$, there exists $\delta$ such that
$$ \mathbb{P}(\text{recall} \geq 1 - \epsilon) \geq 1 - \delta $$
Sublinear complexity:
Expected query time:
$$ O(|V|^{1 - \alpha}) \quad \text{for } \alpha > 0 $$
when data lies on a low intrinsic dimension manifold.
Optimal resource utilization:
PatANN minimizes the I/O–distance computation product:
$$ \min_P \mathbb{E}[\text{disk reads} \times \text{distance computations}] $$
A complete derivation appears in our forthcoming paper, including extensions to non-Euclidean metrics and streaming data scenarios.