Research on Efficient Approximate Aggregated Nearest Neighbor Query Methods Based on Learned Representations

This paper focuses on the aggregated nearest neighbor query problem in learned representation spaces, proposing an efficient algorithmic framework that includes hierarchical navigation graph indexing, adaptive query routing, and learning-enhanced approximate boundaries. While maintaining a recall rate of over 95%, this framework improves query efficiency by 100-1000 times compared to linear scanning, providing key technical support for applications such as recommendation systems and image retrieval.

Core Challenges of Nearest Neighbor Queries

Nearest neighbor queries support multiple fields such as recommendation systems and image retrieval, but the 'curse of dimensionality' in high-dimensional data makes exact methods difficult to handle massive datasets, so approximate queries have become the mainstream.

Demand for Aggregated Nearest Neighbor Queries

In practical scenarios, aggregated queries such as group recommendation and multi-objective optimization need to be handled. The goal is to find data points that optimize the aggregation function (SUM/MAX/MIN), and their patterns are more complex.

Advantages of Learned Representations

• Semantic capture: Deep semantic relationships (e.g., analogical relationships in word embeddings)
• Dimensionality reduction and denoising: Compress high-dimensional data while retaining key information
• Cross-modal alignment: Map multi-modal data to the same space

Challenges in Query Efficiency

• High dimensionality: Hundreds to thousands of dimensions exacerbate the curse of dimensionality
• Unstructured nature: Traditional spatial indexes have poor performance
• Dynamic nature: Representation changes due to model updates need to be adapted to

Hierarchical Navigation Graph Indexing

Drawing on the idea of HNSW, a multi-layer graph structure is built, where the bottom layer contains all data and the upper layers are sparsely sampled; aggregation-aware edge selection optimizes the navigation mode.

Adaptive Query Routing

• Early pruning: Use the properties of aggregation functions to abandon invalid branches early
• Batch processing: Share computation cache to optimize multiple queries
• Dynamic trade-off: Adjust accuracy and efficiency according to requirements

Learning-Enhanced Approximate Boundaries

• Distance distribution prediction: Lightweight models predict distance distributions to set thresholds
• Query difficulty estimation: Allocate computing resources on demand

Experimental Setup

Datasets: SIFT1M, GloVe, Deep1B; Comparison methods: Linear scanning, IVF/HNSW, etc.; Metrics: Latency, recall rate, throughput.

Key Results

• Efficiency: At 95% recall rate, it is 100-1000 times faster than linear scanning and 2-5 times faster than general ANN methods
• Scalability: Supports billion-scale data with sublinear latency growth
• Adaptability: Effective for SUM/MAX/MIN aggregation functions, with the most significant optimization for SUM

Real-Time Recommendation Systems

Group recommendation on e-commerce platforms, completing aggregated queries in milliseconds to support real-time personalization.

Multimedia Content Retrieval

Multi-modal search (screenshot + description) on video platforms, efficiently matching semantically relevant content.

Intelligent Customer Service Q&A

Quickly locate relevant document collections in enterprise knowledge bases to assist in solving complex problems.

Current Limitations

• Static data assumption: High maintenance cost for dynamic data
• Single representation space: Need to expand for cross-space data
• Theoretical guarantees: Lack of strict approximation ratio and complexity analysis

Future Directions

• Dynamic index maintenance: Adapt to incremental/online learning
• Distributed expansion: Support ultra-large scale and concurrent queries
• Hardware acceleration: GPU/TPU optimization and model quantization
• Theoretical analysis: Establish approximation guarantees and complexity boundaries