wifi-densepose/docs/project-phases/PHASE6_ADVANCED.md

Phase 6: Advanced Techniques - Implementation Guide

Overview

Phase 6 implements cutting-edge features for next-generation vector search:

• Hypergraphs: N-ary relationships beyond pairwise similarity
• Learned Indexes: Neural network-based index structures (RMI)
• Neural Hash Functions: Similarity-preserving binary projections
• Topological Data Analysis: Embedding quality assessment

Features Implemented

1. Hypergraph Support

Location: /crates/ruvector-core/src/advanced/hypergraph.rs

Core Components:

// Hyperedge connecting multiple vectors
pub struct Hyperedge {
    pub id: String,
    pub nodes: Vec<VectorId>,
    pub description: String,
    pub embedding: Vec<f32>,
    pub confidence: f32,
}

// Temporal hyperedge with time attributes
pub struct TemporalHyperedge {
    pub hyperedge: Hyperedge,
    pub timestamp: u64,
    pub granularity: TemporalGranularity,
}

// Hypergraph index with bipartite storage
pub struct HypergraphIndex {
    entities: HashMap<VectorId, Vec<f32>>,
    hyperedges: HashMap<String, Hyperedge>,
    temporal_index: HashMap<u64, Vec<String>>,
}

Key Features:

• ✅ N-ary relationships (3+ entities)
• ✅ Bipartite graph transformation for efficient storage
• ✅ Temporal indexing with multiple granularities
• ✅ K-hop neighbor traversal
• ✅ Semantic search over hyperedges

Use Cases:

• Multi-document relationships: Papers co-cited in reviews
• Temporal patterns: User interaction sequences
• Complex knowledge graphs: Multi-entity relationships

2. Causal Hypergraph Memory

Location: /crates/ruvector-core/src/advanced/hypergraph.rs

Core Component:

pub struct CausalMemory {
    index: HypergraphIndex,
    causal_counts: HashMap<(VectorId, VectorId), u32>,
    latencies: HashMap<VectorId, f32>,
    // Utility weights: α=0.7, β=0.2, γ=0.1
}

Utility Function:

U = α·semantic_similarity + β·causal_uplift - γ·latency

Where:

• α = 0.7: Weight for semantic similarity
• β = 0.2: Weight for causal strength (success count)
• γ = 0.1: Penalty for action latency

Key Features:

• ✅ Cause-effect relationship tracking
• ✅ Multi-entity causal inference
• ✅ Confidence weights
• ✅ Latency-aware queries

Use Cases:

• Agent reasoning: Learn which actions lead to success
• Skill consolidation: Identify successful patterns
• Reflexion memory: Store self-critique with causal links

3. Learned Index Structures

Location: /crates/ruvector-core/src/advanced/learned_index.rs

Recursive Model Index (RMI):

pub struct RecursiveModelIndex {
    root_model: LinearModel,      // Coarse prediction
    leaf_models: Vec<LinearModel>, // Fine prediction
    data: Vec<(Vec<f32>, VectorId)>,
    max_error: usize,              // Bounded error for binary search
}

Implementation:

• Root model predicts leaf model
• Leaf models predict positions
• Bounded error correction with binary search
• Linear models for simplicity (production would use neural networks)

Performance Targets:

• 1.5-3x lookup speedup on sorted data
• 10-100x space reduction vs traditional B-trees
• Best for read-heavy workloads

Hybrid Index:

pub struct HybridIndex {
    learned: RecursiveModelIndex,    // Static segment
    dynamic_buffer: HashMap<...>,     // Dynamic updates
    rebuild_threshold: usize,
}

• Learned index for static data
• Dynamic buffer for updates
• Periodic rebuilds

4. Neural Hash Functions

Location: /crates/ruvector-core/src/advanced/neural_hash.rs

Deep Hash Embedding:

pub struct DeepHashEmbedding {
    projections: Vec<Array2<f32>>, // Multi-layer projections
    biases: Vec<Array1<f32>>,
    output_bits: usize,
}

Training:

• Contrastive loss on positive/negative pairs
• Similar vectors → small Hamming distance
• Dissimilar vectors → large Hamming distance

Compression Ratios:

• 128D → 32 bits: 128x compression
• 384D → 64 bits: 192x compression
• 90-95% recall with proper training

Simple LSH Baseline:

pub struct SimpleLSH {
    projections: Array2<f32>, // Random Gaussian projections
    num_bits: usize,
}

• Random projection baseline
• No training required
• 80-85% recall

Hash Index:

pub struct HashIndex<H: NeuralHash> {
    hasher: H,
    tables: HashMap<Vec<u8>, Vec<VectorId>>,
    vectors: HashMap<VectorId, Vec<f32>>,
}

• Fast approximate nearest neighbor search
• Hamming distance filtering
• Re-ranking with full precision

5. Topological Data Analysis

Location: /crates/ruvector-core/src/advanced/tda.rs

Topological Analyzer:

pub struct TopologicalAnalyzer {
    k_neighbors: usize,
    epsilon: f32,
}

Metrics Computed:

pub struct EmbeddingQuality {
    pub dimensions: usize,
    pub num_vectors: usize,
    pub connected_components: usize,
    pub clustering_coefficient: f32,
    pub mode_collapse_score: f32,    // 0=collapsed, 1=good
    pub degeneracy_score: f32,       // 0=full rank, 1=degenerate
    pub quality_score: f32,          // Overall: 0-1
}

Detection Capabilities:

• Mode collapse: Vectors clustering too closely
• Degeneracy: Embeddings in lower-dimensional manifold
• Connectivity: Graph structure analysis
• Persistence: Topological features across scales

Use Cases:

• Embedding quality assessment: Detect training issues
• Model validation: Ensure diverse representations
• Topological regularization: Guide training

Usage Examples

Basic Hypergraph:

use ruvector_core::advanced::{HypergraphIndex, Hyperedge};
use ruvector_core::types::DistanceMetric;

let mut index = HypergraphIndex::new(DistanceMetric::Cosine);

// Add entities
index.add_entity(1, vec![1.0, 0.0, 0.0]);
index.add_entity(2, vec![0.0, 1.0, 0.0]);
index.add_entity(3, vec![0.0, 0.0, 1.0]);

// Add hyperedge connecting 3 entities
let edge = Hyperedge::new(
    vec![1, 2, 3],
    "Triple relationship".to_string(),
    vec![0.5, 0.5, 0.5],
    0.9
);
index.add_hyperedge(edge)?;

// Search for similar relationships
let results = index.search_hyperedges(&[0.6, 0.3, 0.1], 5);

Causal Memory:

use ruvector_core::advanced::CausalMemory;

let mut memory = CausalMemory::new(DistanceMetric::Cosine)
    .with_weights(0.7, 0.2, 0.1);

// Record causal relationship
memory.add_causal_edge(
    1,     // cause action
    2,     // effect
    vec![3], // context
    "Action leads to success".to_string(),
    vec![0.5, 0.5, 0.0],
    100.0  // latency in ms
)?;

// Query with utility function
let results = memory.query_with_utility(&[0.6, 0.4, 0.0], 1, 5);

Learned Index:

use ruvector_core::advanced::{RecursiveModelIndex, LearnedIndex};

let mut rmi = RecursiveModelIndex::new(2, 4);

// Build from sorted data
let data: Vec<(Vec<f32>, u64)> = /* ... */;
rmi.build(data)?;

// Fast lookup
let pos = rmi.predict(&[0.5, 0.25])?;
let result = rmi.search(&[0.5, 0.25])?;

Neural Hashing:

use ruvector_core::advanced::{SimpleLSH, HashIndex};

let lsh = SimpleLSH::new(128, 32); // 128D -> 32 bits
let mut index = HashIndex::new(lsh, 32);

// Insert vectors
for (id, vec) in vectors {
    index.insert(id, vec);
}

// Fast search
let results = index.search(&query, 10, 8); // k=10, max_hamming=8

Topological Analysis:

use ruvector_core::advanced::TopologicalAnalyzer;

let analyzer = TopologicalAnalyzer::new(5, 10.0);
let quality = analyzer.analyze(&embeddings)?;

println!("Quality: {}", quality.quality_score);
println!("Assessment: {}", quality.assessment());

if quality.has_mode_collapse() {
    eprintln!("Warning: Mode collapse detected!");
}

Testing

All features include comprehensive tests:

Location: /tests/advanced_tests.rs

Run tests:

cargo test --test advanced_tests

Run examples:

cargo run --example advanced_features

Performance Characteristics

Hypergraphs:

• Insert: O(|E|) where E is hyperedge size
• Search: O(k log n) for k results
• K-hop: O(exp(k)·N) - use sampling for large k

Learned Indexes:

• Build: O(n log n) sorting + O(n) training
• Lookup: O(1) prediction + O(log error) correction
• Speedup: 1.5-3x on read-heavy workloads

Neural Hashing:

• Encoding: O(d) forward pass
• Search: O(|B|·k) where B is bucket size
• Compression: 32-128x with 90-95% recall

TDA:

• Analysis: O(n²) for distance matrix
• Graph building: O(n·k) for k-NN
• Best use: Offline quality assessment

Integration with Existing Features

With HNSW:

• Use neural hashing for filtering
• Hypergraphs for relationship queries
• TDA for index quality monitoring

With AgenticDB:

• Causal memory for agent reasoning
• Skill consolidation via hypergraphs
• Reflexion episodes with causal links

With Quantization:

• Combined with learned hash functions
• Three-tier: binary → scalar → full precision

Future Enhancements

Short Term (Weeks):

• Proper neural network training (PyTorch/tch-rs)
• GPU-accelerated hash functions
• Persistent homology (full TDA)

Medium Term (Months):

• Dynamic RMI updates
• Multi-level hypergraph indexing
• Causal inference algorithms

Long Term (Year+):

• Neuromorphic hardware integration
• Quantum-inspired algorithms
• Advanced topology optimization

References

1. HyperGraphRAG (NeurIPS 2025): Multi-entity relationships
2. Learned Indexes (SIGMOD 2018): RMI architecture
3. Deep Hashing (CVPR): Similarity-preserving codes
4. Topological Data Analysis: Persistent homology

Notes

• All features are opt-in - no overhead if unused
• Experimental status: API may change
• Production readiness: Hypergraphs and TDA ready, learned indexes experimental
• Performance tuning: Profile before production deployment

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Status: ✅ Phase 6 Complete Next: Integration testing and production deployment