d803bfe2b1
git-subtree-dir: vendor/ruvector git-subtree-split: b64c21726f2bb37286d9ee36a7869fef60cc6900
651 lines
29 KiB
Markdown
651 lines
29 KiB
Markdown
# ADR-002 Addendum: SOTA Optimizations for Dynamic Hierarchical j-Tree
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**Status**: Proposed
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**Date**: 2026-01-25
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**Extends**: ADR-002 (Dynamic Hierarchical j-Tree Decomposition)
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---
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## Executive Summary
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This addendum pushes ADR-002 to true state-of-the-art by integrating:
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1. **Predictive Dynamics** - SNN predicts updates before they happen
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2. **Neural Sparsification** - Learned edge selection via SpecNet
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3. **Lazy Hierarchical Evaluation** - Demand-paged j-tree levels
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4. **Warm-Start Cut-Matching** - Reuse computation across updates
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5. **256-Core Parallel Hierarchy** - Each core owns j-tree levels
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6. **Streaming Sketch Fallback** - O(n log n) space for massive graphs
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**Target**: Sub-microsecond approximate queries, <100μs exact verification
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---
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## Architecture: Predictive Dynamic j-Tree
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```
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┌─────────────────────────────────────────────────────────────────────────────────┐
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│ PREDICTIVE DYNAMIC J-TREE ARCHITECTURE │
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├─────────────────────────────────────────────────────────────────────────────────┤
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│ │
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│ ┌─────────────────────────────────────────────────────────────────────────────┐│
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│ │ LAYER 0: PREDICTION ENGINE ││
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│ │ ││
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│ │ ┌──────────────┐ ┌──────────────┐ ┌──────────────┐ ││
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│ │ │ SNN Policy │───►│ TD Learner │───►│ Prefetcher │ ││
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│ │ │ (R-STDP) │ │ (Value Net) │ │ (Speculate) │ ││
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│ │ └──────────────┘ └──────────────┘ └──────────────┘ ││
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│ │ │ │ │ ││
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│ │ ▼ ▼ ▼ ││
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│ │ Predict which Estimate cut Pre-compute ││
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│ │ levels change value change likely queries ││
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│ │ ││
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│ └─────────────────────────────────────────────────────────────────────────────┘│
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│ │ │
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│ ▼ │
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│ ┌─────────────────────────────────────────────────────────────────────────────┐│
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│ │ LAYER 1: NEURAL SPARSIFIER ││
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│ │ ││
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│ │ ┌────────────────────────────────────────────────────────────────────┐ ││
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│ │ │ SpecNet Integration (arXiv:2510.27474) │ ││
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│ │ │ │ ││
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│ │ │ Loss = λ₁·Laplacian_Alignment + λ₂·Feature_Preserve + λ₃·Sparsity │ ││
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│ │ │ │ ││
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│ │ │ • Joint Graph Evolution layer │ ││
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│ │ │ • Spectral Concordance preservation │ ││
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│ │ │ • Degree-based fast presparse (DSpar: 5.9x speedup) │ ││
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│ │ └────────────────────────────────────────────────────────────────────┘ ││
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│ │ ││
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│ └─────────────────────────────────────────────────────────────────────────────┘│
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│ │ │
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│ ▼ │
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│ ┌─────────────────────────────────────────────────────────────────────────────┐│
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│ │ LAYER 2: LAZY HIERARCHICAL J-TREE ││
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│ │ ││
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│ │ Level L ──┐ ││
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│ │ Level L-1 ├── Demand-paged: Only materialize when queried ││
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│ │ Level L-2 ├── Dirty marking: Track which levels need recomputation ││
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│ │ ... │ Warm-start: Reuse cut-matching state across updates ││
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│ │ Level 0 ──┘ ││
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│ │ ││
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│ │ Memory: O(active_levels × n_level) instead of O(L × n) ││
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│ │ ││
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│ └─────────────────────────────────────────────────────────────────────────────┘│
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│ │ │
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│ ▼ │
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│ ┌─────────────────────────────────────────────────────────────────────────────┐│
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│ │ LAYER 3: 256-CORE PARALLEL DISTRIBUTION ││
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│ │ ││
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│ │ ┌─────────┬─────────┬─────────┬─────────┬─────────┬─────────┐ ││
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│ │ │Core 0-31│Core32-63│Core64-95│Core96-127│Core128+ │Core 255│ ││
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│ │ │ Level 0 │ Level 1 │ Level 2 │ Level 3 │ ... │ Level L│ ││
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│ │ └─────────┴─────────┴─────────┴─────────┴─────────┴─────────┘ ││
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│ │ ││
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│ │ Work Stealing: Imbalanced levels redistribute to idle cores ││
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│ │ Atomic CAS: SharedCoordinator for global min-cut updates ││
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│ │ 8KB/core: CompactCoreState fits entire j-tree level ││
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│ │ ││
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│ └─────────────────────────────────────────────────────────────────────────────┘│
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│ │ │
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│ ▼ │
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│ ┌─────────────────────────────────────────────────────────────────────────────┐│
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│ │ LAYER 4: STREAMING SKETCH FALLBACK ││
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│ │ ││
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│ │ When n > 100K vertices: ││
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│ │ ┌────────────────────────────────────────────────────────────────────┐ ││
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│ │ │ Semi-Streaming Cut Sketch │ ││
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│ │ │ • O(n log n) space (two edges per vertex) │ ││
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│ │ │ • Reservoir sampling for edge selection │ ││
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│ │ │ • (1+ε) approximation maintained incrementally │ ││
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│ │ └────────────────────────────────────────────────────────────────────┘ ││
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│ │ ││
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│ └─────────────────────────────────────────────────────────────────────────────┘│
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│ │ │
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│ ▼ │
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│ ┌─────────────────────────────────────────────────────────────────────────────┐│
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│ │ LAYER 5: EXACT VERIFICATION ││
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│ │ ││
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│ │ El-Hayek/Henzinger/Li (arXiv:2512.13105) ││
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│ │ • Triggered only when approximate cut < threshold ││
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│ │ • O(n^{o(1)}) exact verification ││
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│ │ • Deterministic, no randomization ││
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│ │ ││
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│ └─────────────────────────────────────────────────────────────────────────────┘│
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│ │
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└─────────────────────────────────────────────────────────────────────────────────┘
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```
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---
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## Component 1: SNN Prediction Engine
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Exploits the triple isomorphism already in the codebase:
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| Graph Theory | Dynamical Systems | Neuromorphic |
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|--------------|-------------------|--------------|
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| MinCut value | Lyapunov exponent | Spike synchrony |
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| Edge contraction | Phase space flow | Synaptic plasticity |
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| Hierarchy level | Attractor basin | Memory consolidation |
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```rust
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/// Predictive j-tree using SNN dynamics
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pub struct PredictiveJTree {
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/// Core j-tree hierarchy
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hierarchy: JTreeHierarchy,
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/// SNN policy network for update prediction
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policy: PolicySNN,
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/// Value network for cut estimation
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value_net: ValueNetwork,
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/// Prefetch cache for speculative computation
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prefetch: PrefetchCache,
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/// SONA hooks for continuous adaptation
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sona_hooks: [usize; 4], // Layers 8, 16, 24, 28
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}
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impl PredictiveJTree {
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/// Predict which levels will need updates after edge change
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pub fn predict_affected_levels(&self, edge: (VertexId, VertexId)) -> Vec<usize> {
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// SNN encodes edge as spike pattern
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let spike_input = self.edge_to_spikes(edge);
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// Policy network predicts affected regions
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let activity = self.policy.forward(&spike_input);
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// Low activity regions are stable, high activity needs update
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activity.iter()
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.enumerate()
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.filter(|(_, &a)| a > ACTIVITY_THRESHOLD)
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.map(|(level, _)| level)
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.collect()
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}
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/// Speculative update: pre-compute before edge actually changes
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pub fn speculative_update(&mut self, likely_edge: (VertexId, VertexId), prob: f64) {
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if prob > SPECULATION_THRESHOLD {
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let affected = self.predict_affected_levels(likely_edge);
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// Pre-compute in background cores
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for level in affected {
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self.prefetch.schedule(level, likely_edge);
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}
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}
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}
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/// TD-learning update after observing actual cut change
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pub fn learn_from_observation(&mut self, predicted_cut: f64, actual_cut: f64) {
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let td_error = actual_cut - predicted_cut;
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// R-STDP: Reward-modulated spike-timing-dependent plasticity
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self.policy.apply_rstdp(td_error);
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// Update value network
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self.value_net.td_update(td_error);
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}
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}
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```
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**Performance Target**: Predict 80%+ of affected levels correctly → skip 80% of unnecessary recomputation
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---
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## Component 2: Neural Sparsifier (SpecNet Integration)
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Based on arXiv:2510.27474, learn which edges to keep:
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```rust
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/// Neural graph sparsifier with spectral concordance
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pub struct NeuralSparsifier {
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/// Graph evolution layer (learned edge selection)
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evolution_layer: GraphEvolutionLayer,
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/// Spectral concordance loss weights
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lambda_laplacian: f64, // λ₁ = 1.0
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lambda_feature: f64, // λ₂ = 0.5
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lambda_sparsity: f64, // λ₃ = 0.1
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/// Degree-based presparse threshold (DSpar optimization)
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degree_threshold: f64,
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}
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impl NeuralSparsifier {
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/// Fast presparse using degree heuristic (DSpar: 5.9x speedup)
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pub fn degree_presparse(&self, graph: &DynamicGraph) -> DynamicGraph {
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let mut sparse = graph.clone();
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// Effective resistance ≈ 1/(deg_u × deg_v)
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// Keep edges with high effective resistance
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for edge in graph.edges() {
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let deg_u = graph.degree(edge.source) as f64;
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let deg_v = graph.degree(edge.target) as f64;
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let eff_resistance = 1.0 / (deg_u * deg_v);
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// Sample with probability proportional to effective resistance
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if eff_resistance < self.degree_threshold {
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sparse.remove_edge(edge.source, edge.target);
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}
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}
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sparse
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}
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/// Spectral concordance loss for training
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pub fn spectral_concordance_loss(
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&self,
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original: &DynamicGraph,
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sparsified: &DynamicGraph,
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) -> f64 {
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// L₁: Laplacian eigenvalue alignment
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let laplacian_loss = self.laplacian_alignment(original, sparsified);
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// L₂: Feature geometry preservation (cut values)
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let feature_loss = self.cut_preservation_loss(original, sparsified);
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// L₃: Sparsity inducing trace penalty
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let sparsity_loss = sparsified.edge_count() as f64 / original.edge_count() as f64;
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self.lambda_laplacian * laplacian_loss
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+ self.lambda_feature * feature_loss
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+ self.lambda_sparsity * sparsity_loss
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}
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/// End-to-end learnable sparsification
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pub fn learn_sparsify(&mut self, graph: &DynamicGraph) -> SparseGraph {
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// 1. Fast presparse (DSpar)
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let presparse = self.degree_presparse(graph);
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// 2. Neural refinement (SpecNet)
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let edge_scores = self.evolution_layer.forward(&presparse);
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// 3. Top-k selection preserving spectral properties
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let k = (graph.vertex_count() as f64 * (graph.vertex_count() as f64).ln()) as usize;
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let selected = edge_scores.top_k(k);
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SparseGraph::from_edges(selected)
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}
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}
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```
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**Performance Target**: 90% edge reduction while maintaining 95%+ cut accuracy
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---
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## Component 3: Lazy Hierarchical Evaluation
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Don't compute levels until needed:
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```rust
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/// Lazy j-tree with demand-paged levels
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pub struct LazyJTreeHierarchy {
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/// Level states
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levels: Vec<LazyLevel>,
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/// Which levels are materialized
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materialized: BitSet,
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/// Dirty flags for incremental update
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dirty: BitSet,
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/// Cut-matching state for warm-start
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warm_state: Vec<CutMatchingState>,
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}
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#[derive(Clone)]
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enum LazyLevel {
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/// Not yet computed
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Unmaterialized,
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/// Computed and valid
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Materialized(JTree),
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/// Needs recomputation
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Dirty(JTree),
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}
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impl LazyJTreeHierarchy {
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/// Query with lazy materialization
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pub fn approximate_min_cut(&mut self) -> ApproximateCut {
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// Only materialize levels needed for query
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let mut current_level = self.levels.len() - 1;
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while current_level > 0 {
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self.ensure_materialized(current_level);
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let cut = self.levels[current_level].as_materialized().min_cut();
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// Early termination if cut is good enough
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if cut.approximation_factor < ACCEPTABLE_APPROX {
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return cut;
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}
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current_level -= 1;
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}
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self.levels[0].as_materialized().min_cut()
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}
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/// Ensure level is materialized (demand-paging)
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fn ensure_materialized(&mut self, level: usize) {
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match &self.levels[level] {
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LazyLevel::Unmaterialized => {
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// First-time computation
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let jtree = self.compute_level(level);
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self.levels[level] = LazyLevel::Materialized(jtree);
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self.materialized.insert(level);
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}
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LazyLevel::Dirty(old_jtree) => {
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// Warm-start from previous state (arXiv:2511.02943)
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let jtree = self.warm_start_recompute(level, old_jtree);
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self.levels[level] = LazyLevel::Materialized(jtree);
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self.dirty.remove(level);
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}
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LazyLevel::Materialized(_) => {
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// Already valid, no-op
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}
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}
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}
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/// Warm-start recomputation avoiding full recursion cost
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fn warm_start_recompute(&self, level: usize, old: &JTree) -> JTree {
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// Reuse cut-matching game state from warm_state
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let state = &self.warm_state[level];
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// Only recompute affected regions
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let mut new_jtree = old.clone();
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for node in state.affected_nodes() {
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new_jtree.recompute_node(node, state);
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}
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new_jtree
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}
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/// Mark levels dirty after edge update
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pub fn mark_dirty(&mut self, affected_levels: &[usize]) {
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for &level in affected_levels {
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if self.materialized.contains(level) {
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if let LazyLevel::Materialized(jtree) = &self.levels[level] {
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self.levels[level] = LazyLevel::Dirty(jtree.clone());
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self.dirty.insert(level);
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}
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}
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}
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}
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}
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```
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**Performance Target**: 70% reduction in level computations for typical query patterns
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---
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## Component 4: 256-Core Parallel Distribution
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Leverage the existing agentic chip architecture:
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```rust
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/// Parallel j-tree across 256 cores
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pub struct ParallelJTree {
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/// Core assignments: which cores handle which levels
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level_assignments: Vec<CoreRange>,
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/// Shared coordinator for atomic updates
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coordinator: SharedCoordinator,
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/// Per-core executors
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executors: [CoreExecutor; 256],
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}
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struct CoreRange {
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start_core: u8,
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end_core: u8,
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level: usize,
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}
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impl ParallelJTree {
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/// Distribute L levels across 256 cores
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pub fn distribute_levels(num_levels: usize) -> Vec<CoreRange> {
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let cores_per_level = 256 / num_levels;
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(0..num_levels)
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.map(|level| {
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let start = (level * cores_per_level) as u8;
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let end = ((level + 1) * cores_per_level - 1) as u8;
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CoreRange { start_core: start, end_core: end, level }
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})
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.collect()
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}
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/// Parallel update across all affected levels
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pub fn parallel_update(&mut self, edge: (VertexId, VertexId)) {
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// Phase 1: Distribute update to affected cores
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self.coordinator.phase.store(SharedCoordinator::PHASE_DISTRIBUTE, Ordering::Release);
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for assignment in &self.level_assignments {
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for core_id in assignment.start_core..=assignment.end_core {
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self.executors[core_id as usize].queue_update(edge);
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}
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}
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// Phase 2: Parallel compute
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self.coordinator.phase.store(SharedCoordinator::PHASE_COMPUTE, Ordering::Release);
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// Each core processes independently
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// Work stealing if some cores finish early
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while !self.coordinator.all_completed() {
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// Idle cores steal from busy cores
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self.work_stealing_pass();
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}
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// Phase 3: Collect results
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self.coordinator.phase.store(SharedCoordinator::PHASE_COLLECT, Ordering::Release);
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let global_min = self.coordinator.global_min_cut.load(Ordering::Acquire);
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}
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/// Work stealing for load balancing
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fn work_stealing_pass(&mut self) {
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for core_id in 0..256u8 {
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if self.executors[core_id as usize].is_idle() {
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// Find busy core to steal from
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if let Some(victim) = self.find_busy_core() {
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let work = self.executors[victim].steal_work();
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self.executors[core_id as usize].accept_work(work);
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}
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}
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}
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}
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}
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```
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**Performance Target**: Near-linear speedup up to 256× for independent level updates
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---
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## Component 5: Streaming Sketch Fallback
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For graphs with n > 100K vertices:
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```rust
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/// Semi-streaming cut sketch for massive graphs
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pub struct StreamingCutSketch {
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/// Two edges per vertex (reservoir sampling)
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sampled_edges: HashMap<VertexId, [Option<Edge>; 2]>,
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/// Total vertices seen
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vertex_count: usize,
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/// Reservoir sampling state
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reservoir: ReservoirSampler,
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}
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impl StreamingCutSketch {
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/// Process edge in streaming fashion: O(1) per edge
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pub fn process_edge(&mut self, edge: Edge) {
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// Update reservoir for source vertex
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self.reservoir.sample(edge.source, edge);
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// Update reservoir for target vertex
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self.reservoir.sample(edge.target, edge);
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}
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/// Approximate min-cut from sketch: O(n) query
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pub fn approximate_min_cut(&self) -> ApproximateCut {
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// Build sparse graph from sampled edges
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let sparse = self.build_sparse_graph();
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// Run exact algorithm on sparse graph
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// O(n log n) edges → tractable
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let cut = exact_min_cut(&sparse);
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ApproximateCut {
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value: cut.value,
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approximation_factor: 1.0 + self.epsilon(),
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partition: cut.partition,
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}
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}
|
||
|
||
/// Memory usage: O(n log n)
|
||
pub fn memory_bytes(&self) -> usize {
|
||
self.vertex_count * 2 * std::mem::size_of::<Edge>()
|
||
}
|
||
}
|
||
|
||
/// Adaptive system that switches between full j-tree and streaming
|
||
pub struct AdaptiveJTree {
|
||
full_jtree: Option<LazyJTreeHierarchy>,
|
||
streaming_sketch: Option<StreamingCutSketch>,
|
||
threshold: usize, // Switch point (default: 100K vertices)
|
||
}
|
||
|
||
impl AdaptiveJTree {
|
||
pub fn new(graph: &DynamicGraph) -> Self {
|
||
if graph.vertex_count() > 100_000 {
|
||
Self {
|
||
full_jtree: None,
|
||
streaming_sketch: Some(StreamingCutSketch::from_graph(graph)),
|
||
threshold: 100_000,
|
||
}
|
||
} else {
|
||
Self {
|
||
full_jtree: Some(LazyJTreeHierarchy::build(graph)),
|
||
streaming_sketch: None,
|
||
threshold: 100_000,
|
||
}
|
||
}
|
||
}
|
||
}
|
||
```
|
||
|
||
**Performance Target**: Handle 1M+ vertex graphs in <1GB memory
|
||
|
||
---
|
||
|
||
## Performance Comparison
|
||
|
||
| Metric | ADR-002 Baseline | SOTA Optimized | Improvement |
|
||
|--------|------------------|----------------|-------------|
|
||
| **Update Time** | O(n^ε) | O(n^ε) / 256 cores | ~100× |
|
||
| **Query Time (approx)** | O(log n) | O(1) cached | ~10× |
|
||
| **Query Time (exact)** | O(n^{o(1)}) | O(n^{o(1)}) lazy | ~5× |
|
||
| **Memory** | O(n log n) | O(active × n) | ~3× |
|
||
| **Prediction Accuracy** | N/A | 80%+ | New |
|
||
| **Edge Reduction** | 1 - ε | 90% neural | ~9× |
|
||
| **Max Graph Size** | ~100K | 1M+ streaming | ~10× |
|
||
|
||
---
|
||
|
||
## Integration with Existing Codebase
|
||
|
||
### SNN Integration Points
|
||
|
||
```rust
|
||
// Use existing SNN components from src/snn/
|
||
use crate::snn::{
|
||
PolicySNN, // For prediction engine
|
||
ValueNetwork, // For TD learning
|
||
NeuralGraphOptimizer, // For neural sparsification
|
||
compute_synchrony, // For stability detection
|
||
compute_energy, // For attractor dynamics
|
||
};
|
||
|
||
// Connect j-tree to SNN energy landscape
|
||
impl PredictiveJTree {
|
||
pub fn snn_energy(&self) -> f64 {
|
||
let mincut = self.hierarchy.approximate_min_cut().value;
|
||
let synchrony = compute_synchrony(&self.policy.recent_spikes(), 10.0);
|
||
compute_energy(mincut, synchrony)
|
||
}
|
||
}
|
||
```
|
||
|
||
### Parallel Architecture Integration
|
||
|
||
```rust
|
||
// Use existing parallel components from src/parallel/
|
||
use crate::parallel::{
|
||
SharedCoordinator, // Atomic coordination
|
||
CoreExecutor, // Per-core execution
|
||
CoreDistributor, // Work distribution
|
||
ResultAggregator, // Result collection
|
||
NUM_CORES, // 256 cores
|
||
};
|
||
|
||
// Extend CoreExecutor for j-tree levels
|
||
impl CoreExecutor {
|
||
pub fn process_jtree_level(&mut self, level: &JTree) -> CoreResult {
|
||
// Process assigned level within 8KB memory budget
|
||
self.state.process_compact_jtree(level)
|
||
}
|
||
}
|
||
```
|
||
|
||
### SONA Integration
|
||
|
||
```rust
|
||
// Connect to SONA hooks for continuous adaptation
|
||
const SONA_HOOKS: [usize; 4] = [8, 16, 24, 28];
|
||
|
||
impl PredictiveJTree {
|
||
pub fn enable_sona(&mut self) {
|
||
for &hook in &SONA_HOOKS {
|
||
self.policy.enable_hook(hook);
|
||
}
|
||
// Adaptation latency: <0.05ms per hook
|
||
}
|
||
}
|
||
```
|
||
|
||
---
|
||
|
||
## Implementation Priority
|
||
|
||
| Phase | Component | Effort | Impact | Dependencies |
|
||
|-------|-----------|--------|--------|--------------|
|
||
| **P0** | Degree-based presparse | 1 week | High | None |
|
||
| **P0** | 256-core distribution | 2 weeks | High | parallel/mod.rs |
|
||
| **P1** | Lazy hierarchy | 2 weeks | High | ADR-002 base |
|
||
| **P1** | Warm-start cut-matching | 2 weeks | High | Lazy hierarchy |
|
||
| **P2** | SNN prediction | 3 weeks | Medium | snn/optimizer.rs |
|
||
| **P2** | Neural sparsifier | 3 weeks | Medium | SNN prediction |
|
||
| **P3** | Streaming fallback | 2 weeks | Medium | None |
|
||
| **P3** | SONA integration | 1 week | Medium | SNN prediction |
|
||
|
||
---
|
||
|
||
## References
|
||
|
||
### New Research (2024-2026)
|
||
|
||
1. **SpecNet**: "Spectral Neural Graph Sparsification" (arXiv:2510.27474)
|
||
2. **DSpar**: "Degree-based Sparsification" (OpenReview)
|
||
3. **Warm-Start**: "Faster Weak Expander Decomposition" (arXiv:2511.02943)
|
||
4. **Parallel Expander**: "Near-Optimal Parallel Expander Decomposition" (SODA 2025)
|
||
5. **Semi-Streaming**: "Semi-Streaming Min-Cut" (Dudeja et al.)
|
||
|
||
### Existing Codebase
|
||
|
||
- `src/snn/mod.rs` - SNN integration (triple isomorphism)
|
||
- `src/snn/optimizer.rs` - PolicySNN, ValueNetwork, R-STDP
|
||
- `src/parallel/mod.rs` - 256-core architecture
|
||
- `src/compact/mod.rs` - 8KB per-core state
|
||
|
||
---
|
||
|
||
## Appendix: Complexity Summary
|
||
|
||
| Operation | Baseline | + Prediction | + Neural | + Parallel | + Streaming |
|
||
|-----------|----------|--------------|----------|------------|-------------|
|
||
| Insert Edge | O(n^ε) | O(n^ε) × 0.2 | O(n^ε) × 0.1 | O(n^ε / 256) | O(1) |
|
||
| Delete Edge | O(n^ε) | O(n^ε) × 0.2 | O(n^ε) × 0.1 | O(n^ε / 256) | O(1) |
|
||
| Approx Query | O(log n) | O(1) cached | O(1) | O(1) | O(n) |
|
||
| Exact Query | O(n^{o(1)}) | O(n^{o(1)}) × 0.2 | - | - | - |
|
||
| Memory | O(n log n) | O(n log n) | O(n log n / 10) | O(n log n) | O(n log n) |
|
||
|
||
**Combined**: Average case approaches O(1) for queries, O(n^ε / 256) for updates, with graceful degradation to streaming for massive graphs.
|