Provable Guarantees for Graph-Based Neural Retrieval

Graph Foundry bridges the gap between empirical success and theoretical rigor in approximate nearest neighbor search. We establish formal accuracy guarantees for existing graph-based algorithms while enhancing their integration with relational infrastructure.

Explore Our Research

Research Focus

We enhance existing graph-based ANN algorithms (focusing on HNSW) with measurable accuracy guarantees, robust relational integration, and joint optimization with full-text indexing beyond simple reranking approaches.

From Empirical to Provable

Formal guarantees for graph-based ANN algorithms

The Fundamental Challenge

Graph-based approximate nearest neighbor algorithms achieve state-of-the-art empirical performance but lack formal accuracy guarantees, limiting their adoption in critical applications.

Bridging Theory and Practice

Popular graph-based ANN algorithms like HNSW demonstrate remarkable empirical performance but operate without formal accuracy bounds. This creates uncertainty in deployment and limits applications in domains requiring reliability guarantees.

  • No Formal Guarantees: Performance is measured empirically but lacks theoretical bounds.
  • Integration Challenges: Difficult to incorporate graph-based ANN into existing relational infrastructure.
  • Isolated Indexing: Graph indices operate separately from other database indices like full-text search.
  • Suboptimal Hybrid Queries: Combined similarity and attribute filtering uses inefficient reranking approaches.
Figure 1: Relational Integration Challenge

Example: Product database with vector embeddings and relational attributes

Product ID Product Name Price Image Embedding
101 Wireless Headphones $79.99 [0.24, -0.12, 0.87, ...]
102 Smart Watch $149.99 [-0.45, 0.33, 0.21, ...]
103 Bluetooth Speaker $59.99 [0.67, 0.05, -0.32, ...]
104 Gaming Mouse $89.99 [-0.12, 0.78, 0.09, ...]
SELECT * FROM products
WHERE price < 100
ORDER BY image_embedding <-> '[0.34, -0.21, 0.65, ...]'
LIMIT 10;

Challenge: Efficiently executing hybrid queries combining vector similarity with relational filters while maintaining accuracy guarantees.

Our Research Contributions

Graph Foundry develops theoretically grounded enhancements to existing graph-based ANN algorithms with practical integration frameworks.

Provable Accuracy Guarantees

We establish formal accuracy bounds for existing graph-based ANN algorithms, starting with HNSW. Our approach maintains empirical performance while adding measurable guarantee certificates for query results.

Key Insight: By analyzing graph connectivity properties and search path distributions, we derive probabilistic bounds on recall and error rates.

Relational Infrastructure Integration

We design optimization frameworks that embed graph-based ANN algorithms directly within relational query processors, enabling efficient hybrid queries over vector and attribute data.

Innovation: Our approach moves beyond post-processing reranking to integrated query planning with cost-based optimization for joint vector/relational operations.

Joint Indexing with Full-Text Search

We develop novel data structures and algorithms for unified graph and full-text indexing, enabling optimized multi-modal retrieval beyond simple reranking approaches.

Breakthrough: Our fused index architecture enables simultaneous traversal of semantic and lexical similarity spaces with formal convergence guarantees.

Beyond Reranking: Joint Index Optimization

Current approaches to multi-modal retrieval use separate indices with reranking. We develop fused indexing structures that enable simultaneous traversal.

Figure 2: Joint Graph and Full-Text Index Fusion

Full-Text Index

Inverted indexes with BM25 scoring, term positions, and linguistic analysis

Graph ANN Index

Hierarchical Navigable Small World graphs with vector embeddings

Fused Retrieval System

Unified traversal with joint optimization, avoiding suboptimal reranking

Simultaneous semantic + lexical search
Formal convergence guarantees

Research Advancements

  • Unified cost model for hybrid queries
  • Adaptive traversal strategies
  • Dynamic pruning based on joint scores
  • Theoretical bounds on fusion accuracy
  • Optimization for skewed distributions
  • Minimal overhead over single-index retrieval

Research Collaborations

Graph Foundry is an academic research initiative. We welcome collaborations with researchers and industry partners.

For research collaborations, access to datasets, or implementation details:

Publications

Preprints and conference papers

Code

Reference implementations

Datasets

Benchmarks and evaluation tools

Contact Research Team