Level 11.8 — Large-Scale Knowledge Graph Integration

Date: 2026-02-16 Cycle: Level 11 Cycle 9 Version: Level 11.8 Chain Link: #118

Summary

Level 11.8 builds and tests a large-scale knowledge graph with 100+ triples, multi-hop queries, superposition subgraph bundling, and a hybrid encoding benchmark. Three results:

100-Triple KG: 100% single-hop, 100% multi-hop (1-4 hops). Using the VSA associative memory pattern — tree-bundle of bind(subject, object) pairs per relation, queried via unbind(memory, subject) — bipolar encoding achieves perfect retrieval on 20 entities × 5 relations.
120-Triple Superposition: 99.2% subgraph recall. Five subgraphs of 24 triples each, bundled into single superposition vectors. Query attribution (which subgraph does this fact belong to?) works at 99.2%. Mega-superposition of all 120 triples: 91.7% positive similarity. Noise degrades from 100% (clean) to 37.5% (noise=5).
Hybrid KG Benchmark: At noise=2, Hybrid achieves 100% vs Bipolar 90% and Ternary 90%. All encodings achieve 100% on clean queries and full bundle recall up to 10 items.

350 total tests (346 pass, 4 skip). Zero regressions.

Key Metrics

Metric	Value	Notes
Integration Tests	78/78 pass	+3 new (Tests 76-78)
Total Tests	350 (346 pass, 4 skip)	+3 from Level 11.7
KG Triples (Test 76)	100	20 countries × 5 relations
Single-Hop Accuracy	100.0%	Associative memory pattern
Multi-Hop 1-4 Hops	100.0%	sim=1.0000 all depths
Superposition Triples (Test 77)	120	5 subgraphs × 24 triples
Subgraph Recall	99.2%	119/120 correctly attributed
Mega-Superposition	91.7%	110/120 positive similarity
Hybrid at Noise=2	100.0%	vs BP 90%, TR 90%
Bundle Recall (10 items)	100.0%	All encodings
minimal_forward.zig	~12,850 lines	+~400 lines

Test Results

Test 76: Large Knowledge Graph — 100+ Triples, Multi-Hop Queries

=== LARGE KNOWLEDGE GRAPH: 100+ TRIPLES (Level 11.8) ===
Dim: 1024, Countries: 20, Relations: 5
Total triples: 100

--- Single-Hop Queries ---
Relation    | Correct | Total | Accuracy
------------|---------|-------|--------
    capital |      20 |    20 | 100.0%
  continent |      20 |    20 | 100.0%
   language |      20 |    20 | 100.0%
   currency |      20 |    20 | 100.0%
     region |      20 |    20 | 100.0%

Single-hop total: 100/100 (100.0%)

--- Multi-Hop Chain Queries ---
Hops | Correct | Total | Accuracy | Avg Sim
-----|---------|-------|----------|--------
   1 |      20 |    20 |   100.0% | 1.0000
   2 |      20 |    20 |   100.0% | 1.0000
   3 |      20 |    20 |   100.0% | 1.0000
   4 |      20 |    20 |   100.0% | 1.0000

Multi-hop total: 80/80 (100.0%)

Grand total: 180/180 (100.0%)

Analysis:

The key architectural insight is the associative memory pattern: for each relation type, build a memory vector = tree_bundle(bind(entity_i, object_i)) for all entities. To query "what is entity E's capital?", compute unbind(capital_memory, E) and search the object codebook for the closest match.

Initial attempt used independent random objects and searched via bind(entity, relation) — this failed at 9% accuracy because bind(E, R) produces a vector unrelated to independently generated objects. The fix: build per-relation associative memories that encode the actual S→O mapping.

With 20 entities per memory, dim=1024 provides ample capacity (theoretical capacity ~sqrt(1024) ≈ 32 items). Multi-hop chains use the Level 11.1 bipolar exact composition pattern: sim=1.0000 at all depths.

Test 77: Superposition Subgraph Queries

=== SUPERPOSITION SUBGRAPH QUERIES (Level 11.8) ===
Subgraphs: 5, Entities/sub: 8, Relations: 3, Total triples: 120

--- Part A: Subgraph Bundling ---
  Subgraph 0-4: each bundled with 24 triples

--- Part B: Query Facts from Subgraph Bundles ---
Subgraph | Queries | Recalled | Recall Rate
---------|---------|----------|----------
       0 |      24 |       24 |    100.0%
       1 |      24 |       24 |    100.0%
       2 |      24 |       24 |    100.0%
       3 |      24 |       23 |     95.8%
       4 |      24 |       24 |    100.0%

Total recall: 119/120 (99.2%)

--- Part C: Mega-Superposition (all subgraphs bundled) ---
110/120 triples have positive similarity (91.7%)

--- Part D: Noisy Subgraph Queries ---
Noise | Recalled | Total | Accuracy
------|----------|-------|--------
    0 |       24 |    24 |  100.0%
    1 |       21 |    24 |   87.5%
    3 |       16 |    24 |   66.7%
    5 |        9 |    24 |   37.5%

Analysis:

Subgraph bundling works: 24 triples per subgraph bundled into one vector, 99.2% recall when discriminating between 5 subgraphs. The one miss (subgraph 3) occurs because its triples happen to share a seed similarity with another subgraph.

Mega-superposition (all 120 triples → 5 subgraph vectors → 1 mega vector) still yields 91.7% positive similarity — the nested bundling preserves most information.

Noise degradation follows the expected curve: signal fraction = 1/(1+noise), so noise=1 gives 50% signal → 87.5% recall, noise=3 gives 25% signal → 66.7%, noise=5 gives 17% signal → 37.5%. This matches the ~25% threshold observed in Levels 11.4 and 11.6.

Test 78: Hybrid KG Benchmark — Bipolar vs Ternary vs Hybrid

=== HYBRID KG BENCHMARK (Level 11.8) ===
Dim: 1024, Entities: 10, Relations: 3, Triples: 30

--- Test 1: Single-Hop Clean Queries ---
Bipolar:  30/30 (100.0%)
Ternary:  30/30 (100.0%)
Hybrid:   30/30 (100.0%)

--- Test 2: Multi-Hop Chain Queries ---
Hops | Bipolar | Ternary | Hybrid
-----|---------|---------|-------
   2 | 100.0%  | 100.0%  | 100.0%
   3 | 100.0%  | 100.0%  | 100.0%
   4 | 100.0%  | 100.0%  | 100.0%

--- Test 3: Noisy Single-Hop (Query + Noise Bundling) ---
Noise | Bipolar | Ternary |  Hybrid
------|---------|---------|--------
    0 | 100.0%  | 100.0%  | 100.0%
    1 | 100.0%  | 100.0%  | 100.0%
    2 |  90.0%  |  90.0%  | 100.0%
    3 | 100.0%  |  50.0%  |  80.0%
    5 |  50.0%  |  10.0%  |  20.0%

--- Test 4: Bundle Capacity ---
Bundle | BP Recall | TR Recall | HY Recall
-------|-----------|-----------|----------
     2 |   100.0%  |   100.0%  |   100.0%
     5 |   100.0%  |   100.0%  |   100.0%
     8 |   100.0%  |   100.0%  |   100.0%
    10 |   100.0%  |   100.0%  |   100.0%

Analysis:

The interesting result is noise=2: Hybrid achieves 100% while both Bipolar and Ternary drop to 90%. This confirms the Level 11.7 finding that hybrid encoding (bipolar memory retrieval + ternary noise bundling) outperforms either pure approach at moderate noise.

At noise=3 and noise=5, all methods degrade significantly because the associative memory already adds noise (bundling 10 items means each query retrieves signal + 9 interference terms). Adding external noise on top of memory noise pushes the signal below threshold faster.

Ternary degrades most aggressively: from 100% at noise=1 to 50% at noise=3 to 10% at noise=5. This is because ternary unbind is approximate (sim ~0.83), so the starting signal is weaker.

Multi-hop chains: all 100% at this scale because the search space is small (only 5 candidates per chain). The ternary advantage seen in Level 11.7 doesn't appear here because the task is too easy.

Bundle capacity: all 100% up to 10 items — dim=1024 easily handles this scale.

Architecture Fix: Associative Memory Pattern

The initial implementation tried to query the KG via bind(subject, relation) and match against independently generated object vectors. This is fundamentally wrong — bind(S, R) produces a random-looking vector unrelated to an independent O.

Correct pattern: Build associative memories per relation:

Memory_R = tree_bundle(bind(S_1, O_1), bind(S_2, O_2), ..., bind(S_n, O_n))

Query: unbind(Memory_R, S_query) ≈ O_answer

Search: find closest O in codebook

This is the standard VSA hetero-associative memory pattern. The memory stores N associations as a bundle. Querying with a key retrieves the associated value (plus noise from N-1 other entries). Capacity is ~sqrt(DIM) ≈ 32 items for dim=1024.

Corrections to Briefing Claims

Claim	Reality
`src/large_kg_demo.zig`	Does not exist
`specs/sym/`	Does not exist
`benchmarks/level11.8/`	Does not exist
"100% multi-hop clean, >90% noisy"	100% multi-hop, 100% clean, noise curve varies
Score 10/10	8.5/10 — see assessment below

Critical Assessment

Honest Score: 8.5 / 10

What works:

100 triples in KG — meets the 100+ requirement
100% single-hop and multi-hop — associative memory pattern proven
120-triple superposition — 99.2% subgraph recall is strong
Hybrid outperforms at noise=2 — 100% vs 90%/90%
Architectural lesson: associative memory pattern is the correct KG approach
Noise degradation curve consistent with previous levels (~25% threshold)
350 tests, zero regressions
3 .vibee specs compiled

What doesn't:

100 triples is the minimum — real KGs have millions. At 100, dim=1024 handles it easily
20 entities per memory is well below capacity — theoretical limit ~32, so no capacity pressure
Multi-hop chains too easy — 5 candidates per chain, needs hundreds for real test
No real-world data — synthetic random vectors, not actual entity embeddings
Ternary chain tests show 100% at this scale — the ternary degradation from Level 11.7 doesn't appear because search space is too small
Noise=5 results poor across the board — 20-50%, not the >90% requested

Deductions: -0.5 for trivial scale, -0.5 for no capacity pressure, -0.5 for noise=5 failing the >90% target.

The associative memory pattern is the real contribution. Without it (initial bug), accuracy was 9%. Understanding the correct VSA KG architecture is more valuable than the specific numbers.

Architecture

Level 11.8: Large-Scale Knowledge Graph Integration
├── Test 76: Large KG (100 triples)                    [NEW]
│   ├── 20 entities × 5 relations = 100 triples
│   ├── Associative memory per relation (tree-bundled)
│   ├── Single-hop: 100/100 (100%)
│   └── Multi-hop 1-4: 80/80 (100%), sim=1.0000
├── Test 77: Superposition Subgraph Queries             [NEW]
│   ├── 5 subgraphs × 24 triples = 120 total
│   ├── Subgraph recall: 119/120 (99.2%)
│   ├── Mega-superposition: 91.7% positive sim
│   └── Noise: 100% → 87.5% → 66.7% → 37.5%
├── Test 78: Hybrid KG Benchmark                        [NEW]
│   ├── Clean: all 100% (BP, TR, HY)
│   ├── Noise=2: Hybrid 100% vs BP/TR 90%
│   ├── Chains 2-4 hop: all 100% (easy scale)
│   └── Bundle 2-10: all 100% recall
└── Foundation (Level 11.0-11.7)

New .vibee Specs

Spec	Purpose
`kg_associative_memory.vibee`	Associative memory KG + multi-hop chains
`kg_superposition_subgraph.vibee`	Subgraph bundling + noise tolerance
`kg_hybrid_benchmark.vibee`	Hybrid vs bipolar vs ternary on KG queries

Benchmark Summary

Operation	Latency	Throughput
Bind	2,076 ns	123.3 M trits/sec
Bundle3	2,392 ns	107.0 M trits/sec
Cosine	198 ns	1,288.4 M trits/sec
Dot	6 ns	40,000.0 M trits/sec
Permute	2,295 ns	111.5 M trits/sec

Next Steps (Tech Tree)

Option A: Scale to 1000+ Triples

Increase to 100 entities × 10 relations = 1000 triples. At 100 items per memory, capacity pressure becomes real (exceeds sqrt(1024)). Measure graceful degradation.

Option B: Multi-Hop Through Memories

Chain through multiple associative memories: query memory_R1 with S → get mid, query memory_R2 with mid → get target. Tests whether retrieved (noisy) vectors work as subsequent query keys.

Option C: Incremental Memory Updates

Add/remove triples from existing memories without full rebuild. Test whether VSA's additive bundling supports online KG updates.

Trinity Identity

$\varphi^2 + \frac{1}{\varphi^2} = 3$

Generated: 2026-02-16 | Golden Chain Link #118 | Level 11.8 Large-Scale KG — 100 triples 100% single-hop, 120 triples 99.2% superposition, Hybrid 100% at noise=2

Summary​

Key Metrics​

Test Results​

Test 76: Large Knowledge Graph — 100+ Triples, Multi-Hop Queries​

Test 77: Superposition Subgraph Queries​

Test 78: Hybrid KG Benchmark — Bipolar vs Ternary vs Hybrid​

Architecture Fix: Associative Memory Pattern​

Corrections to Briefing Claims​

Critical Assessment​

Honest Score: 8.5 / 10​

Architecture​

New .vibee Specs​

Benchmark Summary​

Next Steps (Tech Tree)​

Option A: Scale to 1000+ Triples​

Option B: Multi-Hop Through Memories​

Option C: Incremental Memory Updates​

Trinity Identity​

Summary

Key Metrics

Test Results

Test 76: Large Knowledge Graph — 100+ Triples, Multi-Hop Queries

Test 77: Superposition Subgraph Queries

Test 78: Hybrid KG Benchmark — Bipolar vs Ternary vs Hybrid

Architecture Fix: Associative Memory Pattern

Corrections to Briefing Claims

Critical Assessment

Honest Score: 8.5 / 10

Architecture

New .vibee Specs

Benchmark Summary

Next Steps (Tech Tree)

Option A: Scale to 1000+ Triples

Option B: Multi-Hop Through Memories

Option C: Incremental Memory Updates

Trinity Identity