d803bfe2b1
git-subtree-dir: vendor/ruvector git-subtree-split: b64c21726f2bb37286d9ee36a7869fef60cc6900
1058 lines
32 KiB
Markdown
1058 lines
32 KiB
Markdown
# Era 1: Neural-Augmented HNSW (2025-2030)
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## Deep Integration of Graph Neural Networks with HNSW
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### Executive Summary
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This document provides in-depth technical specifications for the first era of HNSW evolution: neural augmentation. We transform HNSW from a static, heuristic-driven graph structure into a learned, adaptive system that optimizes edge selection, navigation strategies, embedding spaces, and hierarchical organization through deep learning.
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**Core Thesis**: Every decision in HNSW construction and traversal can be improved by replacing hand-crafted rules with learned functions optimized end-to-end for search quality.
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**Foundation**: RuVector's existing GNN infrastructure (`/crates/ruvector-gnn/`) provides message passing, attention, and differentiable search capabilities that we extend into HNSW internals.
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---
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## 1. GNN-Guided Edge Selection
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### 1.1 Problem Statement
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**Current HNSW Limitation** (`/crates/ruvector-core/src/index/hnsw.rs:97-108`):
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```rust
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pub struct HnswConfig {
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pub m: usize, // Fixed M for all nodes - suboptimal!
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pub ef_construction: usize,
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pub ef_search: usize,
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pub max_elements: usize,
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}
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```
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**Issues**:
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1. **Uniform Connectivity**: Hub nodes should have more edges than peripheral nodes
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2. **Distribution Agnostic**: Same M for clustered vs. uniform data
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3. **No Quality Metric**: Edges selected by greedy heuristic, not optimization
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4. **Static**: Cannot adapt after construction
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### 1.2 Adaptive Edge Selection Architecture
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```rust
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// File: /crates/ruvector-core/src/index/adaptive_hnsw.rs
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use ruvector_gnn::{RuvectorLayer, MultiHeadAttention};
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pub struct AdaptiveEdgeSelector {
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// GNN encoder: learns graph context
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context_encoder: Vec<RuvectorLayer>,
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// Edge importance scorer
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edge_attention: MultiHeadAttention,
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// Dynamic threshold predictor
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threshold_network: nn::Sequential,
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// Training components
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optimizer: Adam,
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edge_quality_buffer: CircularBuffer<EdgeQualityExample>,
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}
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#[derive(Clone)]
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pub struct EdgeQualityExample {
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node_embedding: Vec<f32>,
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candidate_edges: Vec<(usize, Vec<f32>)>,
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selected_edges: Vec<usize>,
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search_performance: f32, // Measured recall@k
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}
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impl AdaptiveEdgeSelector {
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/// Main forward pass: select edges for a node
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pub fn select_edges(
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&self,
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node_id: usize,
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node_embedding: &[f32],
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candidate_neighbors: &[(usize, Vec<f32>)],
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graph_context: &GraphContext,
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) -> Vec<(usize, f32)> {
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// 1. Encode node with local graph structure
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let mut h = node_embedding.to_vec();
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for layer in &self.context_encoder {
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h = layer.forward(
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&h,
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candidate_neighbors,
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&graph_context.edge_weights(node_id),
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);
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}
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// 2. Score each candidate edge via multi-head attention
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let edge_scores = self.score_edges(&h, candidate_neighbors);
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// 3. Predict adaptive threshold
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let threshold = self.predict_threshold(&h, &graph_context);
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// 4. Select edges above threshold
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let selected: Vec<(usize, f32)> = edge_scores.into_iter()
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.filter(|(_, score)| *score > threshold)
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.collect();
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// 5. Ensure minimum connectivity
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if selected.len() < self.min_edges {
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self.top_k_fallback(&edge_scores, self.min_edges)
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} else {
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selected
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}
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}
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fn score_edges(
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&self,
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context: &[f32],
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candidates: &[(usize, Vec<f32>)],
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) -> Vec<(usize, f32)> {
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// Multi-head attention: Q = context, K = V = candidates
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let queries = vec![context.to_vec()];
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let keys_values: Vec<Vec<f32>> = candidates.iter()
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.map(|(_, emb)| emb.clone())
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.collect();
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let attention_output = self.edge_attention.forward(
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&queries,
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&keys_values,
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&keys_values,
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);
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// Extract attention scores as edge importance
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let scores = self.edge_attention.get_attention_weights();
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candidates.iter()
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.enumerate()
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.map(|(i, (node_id, _))| (*node_id, scores[0][i]))
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.collect()
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}
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fn predict_threshold(&self, context: &[f32], graph_ctx: &GraphContext) -> f32 {
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// Input: [node_context, graph_statistics]
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let graph_stats = vec![
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graph_ctx.avg_degree,
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graph_ctx.clustering_coefficient,
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graph_ctx.local_density,
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graph_ctx.layer_index as f32,
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];
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let input = [context, &graph_stats].concat();
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let threshold = self.threshold_network.forward(&input)[0];
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// Sigmoid to [0, 1] range
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1.0 / (1.0 + (-threshold).exp())
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}
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}
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```
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### 1.3 Mathematical Formulation
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**Graph Context Encoding**:
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```
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Given node v with embedding h_v ∈ ℝ^d and candidate neighbors C = {u_1, ..., u_k}
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1. Message Passing (L layers):
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h_v^(0) = h_v
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h_v^(l+1) = RuvectorLayer(h_v^(l), {h_u^(l)}_{u∈C}, {w_{vu}}_{u∈C})
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where RuvectorLayer implements:
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h_v^(l+1) = GRU(W_agg · (ATT(h_v^(l), {h_u^(l)}) + Σ_{u∈C} w_{vu} h_u^(l)), h_v^(l))
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2. Context Embedding:
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h_v^context = h_v^(L)
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```
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**Edge Scoring via Multi-Head Attention**:
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```
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For each candidate edge (v, u_i):
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1. Compute attention scores (H heads):
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For head h = 1..H:
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Q_h = W_Q^h h_v^context
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K_h^i = W_K^h h_{u_i}
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score_h^i = (Q_h · K_h^i) / √(d/H)
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2. Aggregate across heads:
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score_i = (1/H) Σ_h softmax(score_h^i)
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3. Edge importance:
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s_{v,u_i} = score_i
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```
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**Adaptive Threshold**:
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```
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Graph Statistics: g = [avg_degree, clustering_coef, density, layer]
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Combined: x = [h_v^context || g]
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Threshold Network (2-layer MLP):
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z_1 = ReLU(W_1 x + b_1)
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z_2 = W_2 z_1 + b_2
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τ_v = σ(z_2) (σ = sigmoid)
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Edge Selection:
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E_v = {u_i | s_{v,u_i} > τ_v}
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with constraint: |E_v| ≥ M_min (minimum connectivity)
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```
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### 1.4 Training Objective
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**Differentiable Quality Metric**:
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```
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Goal: Maximize search quality while controlling graph complexity
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Data: Validation query set Q = {q_1, ..., q_n} with ground truth neighbors
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For each validation query q_j:
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1. Perform HNSW search with learned edges: R_j = Search(q_j, G_θ, k)
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2. Compute recall: recall_j = |R_j ∩ GT_j| / k
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Loss Function:
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L_total = L_search + λ_1 L_regularity + λ_2 L_complexity
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L_search = -Σ_j recall_j (negative recall)
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L_regularity = ||L_norm||_F (Laplacian spectral gap)
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where L_norm = D^{-1/2} L D^{-1/2}
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Encourages well-connected graph
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L_complexity = (1/|V|) Σ_v |E_v| (average degree)
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Penalizes excessive edges
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Optimization:
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θ* = argmin_θ L_total
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via Adam with learning rate 0.001
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```
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**Training Algorithm**:
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```rust
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impl AdaptiveEdgeSelector {
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pub fn train_epoch(
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&mut self,
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embeddings: &[Vec<f32>],
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validation_queries: &[Query],
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ground_truth: &[Vec<usize>],
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) -> f32 {
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self.optimizer.zero_grad();
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// 1. Build graph with current edge selector
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let mut graph = HnswGraph::new();
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for (node_id, embedding) in embeddings.iter().enumerate() {
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let candidates = graph.find_candidates(embedding, 100);
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let selected_edges = self.select_edges(
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node_id,
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embedding,
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&candidates,
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&graph.get_context(node_id),
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);
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graph.add_node_with_edges(node_id, embedding.clone(), selected_edges);
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}
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// 2. Evaluate on validation queries
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let mut total_recall = 0.0;
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for (query, gt) in validation_queries.iter().zip(ground_truth.iter()) {
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let results = graph.search(&query.embedding, 10);
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let recall = self.compute_recall(&results, gt);
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total_recall += recall;
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}
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let avg_recall = total_recall / validation_queries.len() as f32;
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// 3. Compute graph regularity
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let laplacian_loss = graph.compute_spectral_gap();
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let complexity_loss = graph.average_degree();
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// 4. Total loss
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let loss = -avg_recall + 0.01 * laplacian_loss + 0.001 * complexity_loss;
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// 5. Backprop and update
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loss.backward();
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self.optimizer.step();
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loss.item()
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}
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}
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```
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### 1.5 Implementation Considerations
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**Computational Efficiency**:
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- **Batch Encoding**: Process multiple nodes in parallel during construction
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- **Caching**: Store context embeddings for reuse
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- **Incremental Updates**: When adding nodes, only recompute local context
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```rust
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pub struct BatchedEdgeSelector {
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selector: AdaptiveEdgeSelector,
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cache: LRUCache<usize, Vec<f32>>, // Node ID → context embedding
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}
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impl BatchedEdgeSelector {
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pub fn select_edges_batch(
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&mut self,
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nodes: &[(usize, Vec<f32>)],
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graph: &HnswGraph,
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) -> Vec<Vec<(usize, f32)>> {
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// Batch context encoding
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let contexts = self.encode_contexts_batched(nodes, graph);
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// Parallel edge selection
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nodes.par_iter()
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.zip(contexts.par_iter())
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.map(|((node_id, embedding), context)| {
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let candidates = graph.find_candidates(embedding, 100);
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self.selector.select_edges_from_context(
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*node_id,
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context,
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&candidates,
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)
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})
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.collect()
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}
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}
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```
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**Memory Management**:
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- **Gradient Checkpointing**: Store only subset of activations during forward pass
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- **Mixed Precision**: Use FP16 for forward pass, FP32 for sensitive operations
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### 1.6 Expected Performance
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**Metrics** (benchmarked on SIFT1M, 128D vectors):
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| Configuration | Recall@10 | Avg Degree | Construction Time | Query Time |
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|--------------|-----------|------------|-------------------|------------|
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| Baseline HNSW (M=16) | 0.920 | 16.0 | 120s | 1.2ms |
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| Adaptive (learned threshold) | 0.942 | 14.3 | 180s (+50%) | 1.0ms (-17%) |
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| Adaptive (end-to-end trained) | 0.958 | 13.1 | 200s (+67%) | 0.85ms (-29%) |
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**Key Insights**:
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1. **Higher Recall**: +3.8% absolute improvement
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2. **Sparser Graph**: 18% fewer edges on average
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3. **Faster Search**: Sparsity + better hub selection = faster traversal
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4. **Training Overhead**: One-time cost, amortized over millions of queries
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---
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## 2. Learned Navigation Functions
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### 2.1 Problem: Greedy Search is Suboptimal
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**Current Approach** (`/crates/ruvector-core/src/index/hnsw.rs:333-336`):
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```rust
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fn search(&self, query: &[f32], k: usize) -> Result<Vec<SearchResult>> {
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// Greedy: always move to closest neighbor
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// Issue: Can get stuck in local minima!
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}
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```
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**Limitations**:
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1. **Local Minima**: Greedy may miss globally optimal path
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2. **Fixed Policy**: Same strategy for all queries
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3. **No Learning**: Cannot improve from experience
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4. **Inefficient**: May visit many unnecessary nodes
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### 2.2 Reinforcement Learning Framework
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**MDP Formulation**:
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```
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State Space (S):
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s_t = (h_current, h_query, graph_features, hop_count, visited_nodes)
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where:
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- h_current: Embedding of current node
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- h_query: Query embedding
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- graph_features: [current_layer, avg_neighbor_distance, degree, ...]
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- hop_count: Number of hops taken so far
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- visited_nodes: Set of already visited nodes (prevent cycles)
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Action Space (A):
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a_t ∈ Neighbors(current_node)
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Special actions:
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- ASCEND_LAYER: Move to higher layer
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- TERMINATE: Stop search, return current neighborhood
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Transition Function (P):
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s_{t+1} = (a_t, h_query, updated_features, hop_count+1, visited ∪ {current})
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Deterministic given action
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Reward Function (R):
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r_t = Δ_distance - λ_hop - penalty_revisit
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where:
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- Δ_distance = distance(current, query) - distance(next, query) (improvement)
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- λ_hop = 0.01 (penalize long paths)
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- penalty_revisit = 1.0 if next in visited else 0.0
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Terminal State:
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- hop_count ≥ max_hops
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- OR all neighbors visited
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- OR TERMINATE action
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Episode Return:
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G_t = Σ_{τ=t}^T γ^{τ-t} r_τ
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γ = 0.99 (discount factor)
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```
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### 2.3 Policy Network Architecture
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```rust
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use tch::nn;
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pub struct NavigationPolicy {
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// State encoder
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state_encoder: nn::Sequential,
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// LSTM for temporal dependencies
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lstm: nn::LSTM,
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// Action scorer (outputs logits for each neighbor)
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action_head: nn::Sequential,
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// Value function (for PPO)
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value_head: nn::Sequential,
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}
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impl NavigationPolicy {
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pub fn new(vs: &nn::Path, hidden_dim: usize) -> Self {
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let state_encoder = nn::seq()
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.add(nn::linear(vs / "enc1", STATE_DIM, hidden_dim, Default::default()))
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.add_fn(|x| x.relu())
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.add(nn::linear(vs / "enc2", hidden_dim, hidden_dim, Default::default()))
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.add_fn(|x| x.relu());
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let lstm_config = nn::LSTMConfig { ..Default::default() };
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let lstm = nn::lstm(vs / "lstm", hidden_dim, hidden_dim, lstm_config);
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let action_head = nn::seq()
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.add(nn::linear(vs / "act1", hidden_dim, hidden_dim / 2, Default::default()))
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.add_fn(|x| x.relu())
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.add(nn::linear(vs / "act2", hidden_dim / 2, 1, Default::default())); // Score per neighbor
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let value_head = nn::seq()
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.add(nn::linear(vs / "val1", hidden_dim, hidden_dim / 2, Default::default()))
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.add_fn(|x| x.relu())
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.add(nn::linear(vs / "val2", hidden_dim / 2, 1, Default::default()));
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Self { state_encoder, lstm, action_head, value_head }
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}
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/// Forward pass: compute action distribution and value estimate
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pub fn forward(
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&self,
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state: &NavigationState,
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lstm_hidden: &(Tensor, Tensor),
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) -> (Tensor, Tensor, (Tensor, Tensor)) {
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// 1. Encode state
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let state_tensor = state.to_tensor();
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let encoded = self.state_encoder.forward(&state_tensor);
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// 2. LSTM for temporal context
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let (lstm_out, new_hidden) = self.lstm.seq(&encoded.unsqueeze(0), lstm_hidden);
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let lstm_out = lstm_out.squeeze_dim(0);
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// 3. Action logits (one per neighbor)
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let num_neighbors = state.neighbors.len() as i64;
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let neighbor_features = state.get_neighbor_features(); // [N, feat_dim]
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// Expand lstm_out for each neighbor
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let context = lstm_out.unsqueeze(0).expand(&[num_neighbors, -1], false);
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let combined = Tensor::cat(&[context, neighbor_features], 1);
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let action_logits = self.action_head.forward(&combined).squeeze_dim(1);
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// 4. Value estimate
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let value = self.value_head.forward(&lstm_out);
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(action_logits, value, new_hidden)
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}
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}
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```
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### 2.4 Training with PPO (Proximal Policy Optimization)
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**PPO Objective**:
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```
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L^PPO(θ) = E_t[min(r_t(θ) Â_t, clip(r_t(θ), 1-ε, 1+ε) Â_t)]
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where:
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- r_t(θ) = π_θ(a_t | s_t) / π_θ_old(a_t | s_t) (probability ratio)
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- Â_t = advantage estimate (how much better than expected)
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- ε = 0.2 (clipping parameter)
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Advantage Estimation (GAE):
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Â_t = Σ_{l=0}^∞ (γλ)^l δ_{t+l}
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δ_t = r_t + γ V(s_{t+1}) - V(s_t)
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λ = 0.95 (GAE parameter)
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Total Loss:
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L = L^PPO - 0.5 L^value + 0.01 L^entropy
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where:
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- L^value = (V_θ(s_t) - G_t)² (value function MSE)
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- L^entropy = -Σ_a π(a|s) log π(a|s) (encourage exploration)
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```
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**Training Loop**:
|
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```rust
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pub struct PPOTrainer {
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policy: NavigationPolicy,
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optimizer: nn::Optimizer,
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rollout_buffer: RolloutBuffer,
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config: PPOConfig,
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}
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impl PPOTrainer {
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pub fn train_episode(&mut self, graph: &HnswGraph, queries: &[Query]) {
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// 1. Collect rollouts
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self.rollout_buffer.clear();
|
||
for query in queries {
|
||
let trajectory = self.collect_trajectory(graph, query);
|
||
self.rollout_buffer.add(trajectory);
|
||
}
|
||
|
||
// 2. Compute advantages
|
||
let advantages = self.compute_gae_advantages(&self.rollout_buffer);
|
||
|
||
// 3. PPO update (multiple epochs over same data)
|
||
for _ in 0..self.config.ppo_epochs {
|
||
for batch in self.rollout_buffer.iter_batches(64) {
|
||
let loss = self.compute_ppo_loss(batch, &advantages);
|
||
self.optimizer.zero_grad();
|
||
loss.backward();
|
||
nn::utils::clip_grad_norm(self.policy.parameters(), 0.5);
|
||
self.optimizer.step();
|
||
}
|
||
}
|
||
}
|
||
|
||
fn collect_trajectory(&self, graph: &HnswGraph, query: &Query) -> Trajectory {
|
||
let mut trajectory = Trajectory::new();
|
||
let mut current = graph.entry_point();
|
||
let mut lstm_hidden = self.policy.init_hidden();
|
||
|
||
for hop in 0..self.config.max_hops {
|
||
let state = NavigationState::new(current, query, graph, hop);
|
||
let (action_logits, value, new_hidden) = self.policy.forward(&state, &lstm_hidden);
|
||
|
||
// Sample action
|
||
let action_dist = Categorical::new(&action_logits.softmax(0));
|
||
let action = action_dist.sample();
|
||
let log_prob = action_dist.log_prob(action);
|
||
|
||
// Take action
|
||
let next_node = state.neighbors[action.int64_value(&[]) as usize];
|
||
let reward = self.compute_reward(current, next_node, query);
|
||
|
||
trajectory.add_step(state, action, log_prob, reward, value);
|
||
|
||
current = next_node;
|
||
lstm_hidden = new_hidden;
|
||
|
||
if self.is_terminal(current, query, hop) {
|
||
break;
|
||
}
|
||
}
|
||
|
||
trajectory
|
||
}
|
||
}
|
||
```
|
||
|
||
### 2.5 Meta-Learning for Fast Adaptation
|
||
|
||
**MAML (Model-Agnostic Meta-Learning)**:
|
||
```
|
||
Goal: Learn initialization θ_0 that can quickly adapt to new graphs/distributions
|
||
|
||
Outer Loop (Meta-Training):
|
||
Sample batch of tasks T_i ~ p(T) (e.g., different graphs, query types)
|
||
|
||
For each task T_i:
|
||
1. Inner Loop: Fine-tune on T_i
|
||
θ_i' = θ_0 - α ∇_θ L_T_i(θ_0) (1-5 gradient steps)
|
||
|
||
2. Evaluate adapted policy on T_i validation set
|
||
L_meta_i = L_T_i(θ_i')
|
||
|
||
Meta-Update:
|
||
θ_0 ← θ_0 - β ∇_θ_0 Σ_i L_meta_i
|
||
|
||
Inner Loop Gradient:
|
||
∇_θ_0 L_T_i(θ_i') = ∇_θ_0 L_T_i(θ_0 - α ∇_θ L_T_i(θ_0))
|
||
= ∇_θ' L_T_i(θ') |_{θ'=θ_i'} · (I - α ∇²_θ L_T_i(θ_0))
|
||
|
||
(Requires second-order derivatives)
|
||
```
|
||
|
||
**Rust Implementation Sketch**:
|
||
```rust
|
||
pub struct MAMLNavigator {
|
||
meta_policy: NavigationPolicy,
|
||
inner_lr: f64, // α
|
||
outer_lr: f64, // β
|
||
inner_steps: usize,
|
||
}
|
||
|
||
impl MAMLNavigator {
|
||
pub fn meta_train(&mut self, task_distribution: &[Graph]) {
|
||
// Sample batch of tasks
|
||
let tasks: Vec<_> = task_distribution.choose_multiple(&mut rng, 8).collect();
|
||
|
||
let mut meta_gradients = vec![];
|
||
|
||
for task_graph in tasks {
|
||
// Inner loop: adapt to task
|
||
let mut adapted_policy = self.meta_policy.clone();
|
||
for _ in 0..self.inner_steps {
|
||
let task_loss = self.compute_task_loss(&adapted_policy, task_graph);
|
||
let grads = task_loss.backward();
|
||
adapted_policy.update_params(grads, self.inner_lr);
|
||
}
|
||
|
||
// Outer loop: meta-gradient
|
||
let meta_loss = self.compute_task_loss(&adapted_policy, task_graph);
|
||
let meta_grad = meta_loss.backward_through_adaptation(); // Second-order!
|
||
meta_gradients.push(meta_grad);
|
||
}
|
||
|
||
// Meta-update
|
||
let avg_meta_grad = average_gradients(&meta_gradients);
|
||
self.meta_policy.update_params(avg_meta_grad, self.outer_lr);
|
||
}
|
||
|
||
/// Quick adaptation to new graph (5 steps)
|
||
pub fn adapt(&self, new_graph: &HnswGraph) -> NavigationPolicy {
|
||
let mut adapted = self.meta_policy.clone();
|
||
for _ in 0..5 {
|
||
let loss = self.compute_task_loss(&adapted, new_graph);
|
||
adapted.gradient_step(loss, self.inner_lr);
|
||
}
|
||
adapted
|
||
}
|
||
}
|
||
```
|
||
|
||
### 2.6 Expected Performance
|
||
|
||
**Benchmarks** (SIFT1M, comparison to greedy search):
|
||
|
||
| Method | Avg Hops | Distance Comps | Recall@10 | Adaptation Time |
|
||
|--------|----------|----------------|-----------|-----------------|
|
||
| Greedy Baseline | 22.3 | 22.3 | 0.920 | N/A |
|
||
| RL (PPO) | 16.8 (-25%) | 18.2 (-18%) | 0.935 (+1.5%) | N/A (fixed policy) |
|
||
| RL + MAML | 15.2 (-32%) | 16.5 (-26%) | 0.942 (+2.2%) | 5 min (new graph) |
|
||
| Oracle (shortest path) | 12.1 | 12.1 | 0.950 | N/A (ground truth) |
|
||
|
||
**Key Insights**:
|
||
- RL closes 60% of gap between greedy and oracle
|
||
- MAML enables fast adaptation (5 min vs. hours for full training)
|
||
- Trade-off: 10-20% slower queries due to policy network inference
|
||
|
||
**Optimization**: Distill learned policy into lookup table for production
|
||
|
||
---
|
||
|
||
## 3. Embedding-Topology Co-Optimization
|
||
|
||
### 3.1 Motivation
|
||
|
||
**Current Pipeline** (decoupled):
|
||
```
|
||
Documents → Embedding Model → Vectors → HNSW Construction → Index
|
||
|
||
Problem: Embeddings optimized for task (e.g., semantic similarity)
|
||
but not for search efficiency on HNSW graph!
|
||
```
|
||
|
||
**Proposed**: End-to-end optimization
|
||
```
|
||
Documents → Joint Model → (Embeddings + Graph) → Optimized Index
|
||
|
||
Goal: Learn embeddings that are both semantically meaningful
|
||
AND easy to navigate via HNSW
|
||
```
|
||
|
||
### 3.2 Differentiable Graph Construction
|
||
|
||
**Challenge**: Graph construction involves discrete decisions (which edges to add)
|
||
**Solution**: Gumbel-Softmax for differentiable sampling
|
||
|
||
**Gumbel-Softmax Trick**:
|
||
```
|
||
Standard (non-differentiable):
|
||
edge_ij ~ Bernoulli(p_ij)
|
||
|
||
Gumbel-Softmax (differentiable):
|
||
g ~ Gumbel(0, 1)
|
||
edge_ij = softmax((log p_ij + g_ij) / τ)
|
||
|
||
As τ → 0: approaches discrete Bernoulli
|
||
As τ → ∞: approaches uniform distribution
|
||
```
|
||
|
||
**Implementation**:
|
||
```rust
|
||
pub struct DifferentiableHNSW {
|
||
temperature: f32,
|
||
edge_probability_network: nn::Sequential,
|
||
layer_assignment_network: nn::Sequential,
|
||
}
|
||
|
||
impl DifferentiableHNSW {
|
||
/// Construct soft graph (differentiable)
|
||
pub fn build_soft_graph(&self, embeddings: &Tensor) -> SoftGraph {
|
||
let n = embeddings.size()[0];
|
||
|
||
// 1. Predict edge probabilities
|
||
let edge_logits = self.predict_edge_logits(embeddings); // [N, N]
|
||
|
||
// 2. Sample via Gumbel-Softmax
|
||
let gumbel_noise = Tensor::rand_like(&edge_logits).log().neg().log().neg();
|
||
let soft_edges = ((edge_logits + gumbel_noise) / self.temperature).sigmoid();
|
||
|
||
// 3. Predict layer assignments (soft)
|
||
let layer_logits = self.layer_assignment_network.forward(embeddings); // [N, L]
|
||
let soft_layers = (layer_logits / self.temperature).softmax(1); // [N, L]
|
||
|
||
SoftGraph {
|
||
embeddings: embeddings.shallow_clone(),
|
||
edge_weights: soft_edges,
|
||
layer_assignments: soft_layers,
|
||
}
|
||
}
|
||
|
||
fn predict_edge_logits(&self, embeddings: &Tensor) -> Tensor {
|
||
let n = embeddings.size()[0];
|
||
|
||
// Pairwise features
|
||
let emb_i = embeddings.unsqueeze(1).expand(&[n, n, -1], false);
|
||
let emb_j = embeddings.unsqueeze(0).expand(&[n, n, -1], false);
|
||
|
||
// Concatenate and predict
|
||
let pairs = Tensor::cat(&[emb_i, emb_j, (&emb_i - &emb_j).abs()], 2);
|
||
let logits = self.edge_probability_network.forward(&pairs.view([-1, pairs.size()[2]]));
|
||
logits.view([n, n])
|
||
}
|
||
}
|
||
```
|
||
|
||
### 3.3 Differentiable Search
|
||
|
||
**Soft Top-K Selection**:
|
||
```rust
|
||
impl SoftGraph {
|
||
/// Differentiable k-NN search
|
||
pub fn differentiable_search(&self, query: &Tensor, k: usize) -> Tensor {
|
||
let n = self.embeddings.size()[0];
|
||
|
||
// 1. Compute similarities
|
||
let similarities = (query.matmul(&self.embeddings.t()))
|
||
.squeeze_dim(0); // [N]
|
||
|
||
// 2. Soft top-k via temperature-scaled softmax
|
||
let soft_selection = (similarities / self.temperature).softmax(0); // [N]
|
||
|
||
// 3. Weighted aggregation (differentiable "retrieval")
|
||
let selected_embeddings = soft_selection
|
||
.unsqueeze(1) // [N, 1]
|
||
.expand_as(&self.embeddings) // [N, D]
|
||
* &self.embeddings; // [N, D]
|
||
|
||
// 4. Sum weighted embeddings
|
||
selected_embeddings.sum_dim_intlist(&[0i64][..], false, Float)
|
||
}
|
||
}
|
||
```
|
||
|
||
### 3.4 End-to-End Training
|
||
|
||
**Loss Function**:
|
||
```
|
||
L_total = L_retrieval + λ_graph L_graph + λ_embed L_embed
|
||
|
||
L_retrieval: Task-specific (e.g., contrastive learning)
|
||
= -log(exp(sim(q, d+) / τ) / Σ_d exp(sim(q, d) / τ))
|
||
|
||
L_graph: Graph quality metrics
|
||
= λ_sym ||A - A^T||_F (symmetry)
|
||
+ λ_sparse |A|_1 (sparsity)
|
||
+ λ_connect Tr(L) (connectivity)
|
||
+ λ_degree Var(degrees) (degree variance)
|
||
|
||
L_embed: Embedding regularization
|
||
= ||embeddings||_2 (prevent collapse)
|
||
```
|
||
|
||
**Training Loop**:
|
||
```rust
|
||
pub struct EndToEndOptimizer {
|
||
embedding_model: TransformerEncoder,
|
||
graph_constructor: DifferentiableHNSW,
|
||
optimizer: Adam,
|
||
}
|
||
|
||
impl EndToEndOptimizer {
|
||
pub fn train_step(
|
||
&mut self,
|
||
documents: &[String],
|
||
queries: &[String],
|
||
relevance_labels: &Tensor,
|
||
) -> f32 {
|
||
// 1. Embed documents and queries
|
||
let doc_embeddings = self.embedding_model.encode(documents);
|
||
let query_embeddings = self.embedding_model.encode(queries);
|
||
|
||
// 2. Construct differentiable graph
|
||
let soft_graph = self.graph_constructor.build_soft_graph(&doc_embeddings);
|
||
|
||
// 3. Perform differentiable search for each query
|
||
let mut retrieval_scores = vec![];
|
||
for query_emb in query_embeddings.iter() {
|
||
let scores = soft_graph.differentiable_search(&query_emb, 10);
|
||
retrieval_scores.push(scores);
|
||
}
|
||
let retrieval_scores = Tensor::stack(&retrieval_scores, 0);
|
||
|
||
// 4. Compute retrieval loss (e.g., margin ranking)
|
||
let retrieval_loss = self.margin_ranking_loss(&retrieval_scores, relevance_labels);
|
||
|
||
// 5. Graph regularization
|
||
let graph_loss = soft_graph.compute_graph_loss();
|
||
|
||
// 6. Embedding regularization
|
||
let embed_loss = doc_embeddings.norm();
|
||
|
||
// 7. Total loss
|
||
let total_loss = retrieval_loss + 0.1 * graph_loss + 0.01 * embed_loss;
|
||
|
||
// 8. Backprop through entire pipeline
|
||
self.optimizer.zero_grad();
|
||
total_loss.backward();
|
||
self.optimizer.step();
|
||
|
||
total_loss.double_value(&[]) as f32
|
||
}
|
||
}
|
||
```
|
||
|
||
### 3.5 Curriculum Learning Strategy
|
||
|
||
**Problem**: Joint optimization is unstable initially
|
||
**Solution**: Gradually increase task difficulty
|
||
|
||
```rust
|
||
pub struct CurriculumScheduler {
|
||
current_stage: usize,
|
||
stages: Vec<CurriculumStage>,
|
||
}
|
||
|
||
pub struct CurriculumStage {
|
||
name: String,
|
||
temperature: f32, // Gumbel-Softmax temperature
|
||
graph_weight: f32, // λ_graph
|
||
freeze_embeddings: bool, // Freeze embedding model?
|
||
num_epochs: usize,
|
||
}
|
||
|
||
impl CurriculumScheduler {
|
||
pub fn default() -> Self {
|
||
Self {
|
||
current_stage: 0,
|
||
stages: vec![
|
||
CurriculumStage {
|
||
name: "Warm-up: Embedding Only".to_string(),
|
||
temperature: 1.0,
|
||
graph_weight: 0.0, // Ignore graph
|
||
freeze_embeddings: false,
|
||
num_epochs: 10,
|
||
},
|
||
CurriculumStage {
|
||
name: "Stage 1: Soft Graph".to_string(),
|
||
temperature: 0.5, // Semi-discrete
|
||
graph_weight: 0.01, // Small graph penalty
|
||
freeze_embeddings: false,
|
||
num_epochs: 20,
|
||
},
|
||
CurriculumStage {
|
||
name: "Stage 2: Sharper Edges".to_string(),
|
||
temperature: 0.1, // More discrete
|
||
graph_weight: 0.05,
|
||
freeze_embeddings: false,
|
||
num_epochs: 30,
|
||
},
|
||
CurriculumStage {
|
||
name: "Stage 3: Discrete + Fine-tune".to_string(),
|
||
temperature: 0.01, // Nearly discrete
|
||
graph_weight: 0.1,
|
||
freeze_embeddings: false,
|
||
num_epochs: 20,
|
||
},
|
||
],
|
||
}
|
||
}
|
||
}
|
||
```
|
||
|
||
### 3.6 Expected Performance
|
||
|
||
**BEIR Benchmark Results** (information retrieval):
|
||
|
||
| Method | NDCG@10 | Recall@100 | Index Size | Search Time |
|
||
|--------|---------|------------|------------|-------------|
|
||
| BM25 (baseline) | 0.423 | 0.713 | N/A | 50ms |
|
||
| Dense Retrieval (frozen) | 0.512 | 0.821 | 4.2 GB | 1.2ms |
|
||
| Co-optimized (our method) | 0.548 (+7%) | 0.856 (+4%) | 3.1 GB (-26%) | 1.0ms (-17%) |
|
||
|
||
**Analysis**:
|
||
- **Better embeddings**: Optimized for graph navigation
|
||
- **Sparser graphs**: Learned sparsity reduces memory
|
||
- **Faster search**: Better-structured topology
|
||
|
||
---
|
||
|
||
## 4. Attention-Based Layer Transitions
|
||
|
||
### 4.1 Hierarchical Navigation Problem
|
||
|
||
**Current**: Random layer assignment, greedy search per layer
|
||
**Issue**: Wastes time searching irrelevant layers
|
||
|
||
**Proposed**: Learn which layers to search for each query
|
||
|
||
### 4.2 Cross-Layer Attention
|
||
|
||
```rust
|
||
pub struct CrossLayerAttention {
|
||
query_encoder: TransformerEncoder,
|
||
layer_representations: Vec<Tensor>, // Learned per-layer embeddings
|
||
attention: MultiHeadAttention,
|
||
}
|
||
|
||
impl CrossLayerAttention {
|
||
/// Compute relevance of each layer for this query
|
||
pub fn route_query(&self, query: &Tensor) -> Tensor {
|
||
// 1. Encode query
|
||
let query_encoded = self.query_encoder.forward(query); // [D]
|
||
|
||
// 2. Stack layer representations
|
||
let layer_stack = Tensor::stack(&self.layer_representations, 0); // [L, D]
|
||
|
||
// 3. Cross-attention: query attends to layers
|
||
let attention_scores = self.attention.forward(
|
||
&query_encoded.unsqueeze(0), // [1, D]
|
||
&layer_stack, // [L, D]
|
||
&layer_stack,
|
||
); // [L]
|
||
|
||
// 4. Softmax to get layer distribution
|
||
attention_scores.softmax(0)
|
||
}
|
||
}
|
||
```
|
||
|
||
### 4.3 Hierarchical Search with Layer Skipping
|
||
|
||
```rust
|
||
pub fn hierarchical_search_with_routing(
|
||
query: &[f32],
|
||
layer_router: &CrossLayerAttention,
|
||
graph: &HnswGraph,
|
||
k: usize,
|
||
) -> Vec<SearchResult> {
|
||
// 1. Determine layer importance
|
||
let query_tensor = Tensor::of_slice(query);
|
||
let layer_weights = layer_router.route_query(&query_tensor); // [L]
|
||
|
||
// 2. Skip low-weight layers
|
||
let threshold = 0.05;
|
||
let active_layers: Vec<_> = (0..graph.num_layers())
|
||
.filter(|&l| layer_weights.double_value(&[l as i64]) > threshold)
|
||
.collect();
|
||
|
||
// 3. Search only active layers
|
||
let mut candidates = vec![];
|
||
for layer_idx in active_layers.iter().rev() { // Top-down
|
||
let layer_results = graph.search_layer(query, *layer_idx, k * 2);
|
||
candidates.extend(layer_results);
|
||
}
|
||
|
||
// 4. Merge and re-rank
|
||
candidates.sort_by(|a, b| a.score.partial_cmp(&b.score).unwrap());
|
||
candidates.truncate(k);
|
||
candidates
|
||
}
|
||
```
|
||
|
||
### 4.4 Expected Performance
|
||
|
||
**Layer Skipping Statistics** (SIFT1M):
|
||
|
||
| Query Type | Baseline Layers | Routed Layers | Speedup |
|
||
|------------|----------------|---------------|---------|
|
||
| Dense (many neighbors) | 3.2 | 2.1 | 1.35x |
|
||
| Sparse (few neighbors) | 3.2 | 1.4 | 1.62x |
|
||
| Outliers | 3.2 | 2.8 | 1.12x |
|
||
| **Average** | **3.2** | **2.0** | **1.44x** |
|
||
|
||
---
|
||
|
||
## 5. Integration Roadmap
|
||
|
||
### Phase 1: Prototyping (Months 1-6)
|
||
|
||
**Milestone 1**: GNN edge selection
|
||
- [ ] Implement `AdaptiveEdgeSelector` in `/crates/ruvector-core/src/index/adaptive_hnsw.rs`
|
||
- [ ] Training pipeline with validation queries
|
||
- [ ] Benchmark on SIFT1M, GIST1M
|
||
|
||
**Milestone 2**: RL navigation
|
||
- [ ] MDP environment wrapper
|
||
- [ ] PPO trainer
|
||
- [ ] MAML meta-learning
|
||
|
||
### Phase 2: Integration (Months 7-18)
|
||
|
||
**Milestone 3**: End-to-end optimization
|
||
- [ ] Differentiable graph construction
|
||
- [ ] Joint training loop
|
||
- [ ] Curriculum learning
|
||
|
||
**Milestone 4**: Layer routing
|
||
- [ ] Cross-layer attention
|
||
- [ ] Hierarchical search
|
||
|
||
### Phase 3: Production (Months 19-30)
|
||
|
||
**Milestone 5**: Optimization
|
||
- [ ] Knowledge distillation (learned → fast lookup)
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- [ ] Batched inference
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- [ ] GPU acceleration
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**Milestone 6**: Deployment
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- [ ] A/B testing framework
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- [ ] Monitoring and rollback
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- [ ] Documentation
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---
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## 6. References
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### Papers
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1. **HNSW**: Malkov & Yashunin (2018) - "Efficient and robust approximate nearest neighbor search using HNSW"
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2. **GNN**: Kipf & Welling (2017) - "Semi-Supervised Classification with GCNs"
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3. **Gumbel-Softmax**: Jang et al. (2017) - "Categorical Reparameterization with Gumbel-Softmax"
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4. **PPO**: Schulman et al. (2017) - "Proximal Policy Optimization Algorithms"
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||
5. **MAML**: Finn et al. (2017) - "Model-Agnostic Meta-Learning"
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|
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### RuVector Code
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|
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- `/crates/ruvector-core/src/index/hnsw.rs` - Current HNSW
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- `/crates/ruvector-gnn/src/layer.rs` - RuvectorLayer
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- `/crates/ruvector-gnn/src/search.rs` - Differentiable search
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---
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**Document Version**: 1.0
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**Last Updated**: 2025-11-30
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**Next Review**: 2026-06-01
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