Triadic Neurosymbolic Engine¶
A deterministic algebraic framework for neurosymbolic validation, semantic projection, and AI model auditing.
The Problem with Cosine Similarity¶
Cosine similarity tells you "King and Queen are 0.87 similar" — a black-box number.
The Triadic Engine tells you "King = 2x3x5 and Queen = 2x5x7. They share {2,5} (Royalty). King has {3} (Male) that Queen lacks. Queen has {7} (Female) that King lacks." — fully transparent, deterministic decomposition.
| Cosine Similarity | Triadic Engine | |
|---|---|---|
| Speed (50K pairs) | baseline | 28.4x faster |
| Explainability | Black box | Prime factor proof |
| Subsumption (A contains B?) | Approximation | Exact: phi(A) mod phi(B) == 0 |
| Composition (A union B) | Geometric average | lcm(phi(A), phi(B)) |
| Gap analysis | Not possible | gcd + quotient decomposition |
| Determinism | Seed-dependent | PCA / contrastive modes |
| AI model audit | Not supported | Topological discrepancy |
How It Works¶
Text --> Neural Embedding --> LSH Hyperplanes --> Composite Prime Integer
(R^384) (k projections) (phi(x) = prod p_i)
Each concept becomes a single integer whose prime factors are its semantic features. This enables three operations impossible under cosine similarity:
| Operation | Math | What it answers |
|---|---|---|
| Subsumption | phi(A) mod phi(B) == 0 |
"Does A contain every feature of B?" |
| Composition | lcm(phi(A), phi(B)) |
"What concept has all features of both A and B?" |
| Gap Analysis | gcd(phi(A), phi(B)) + quotients |
"Which features do they share? Which are unique?" |
Core Modules¶
| Module | Description |
|---|---|
neurosym.encoder |
Multi-backend embedding encoder (HuggingFace, OpenAI, Cohere) + 4-mode LSH-to-Prime projection |
neurosym.triadic |
Algebraic validation: subsumption, composition, abductive gap analysis |
neurosym.graph |
Scalable graph builder with inverted prime index (avoids O(N^2)) |
neurosym.storage |
SQLite persistence for prime indices and audit results |
neurosym.reports |
Exportable reports in HTML, JSON, and CSV formats |
neurosym.ingest |
DataFrame ingestion with inverted prime index and semantic search |
neurosym.anomaly |
Multiplicative anomaly detection for tabular data |
Built-in Tools¶
Interactive Dashboard¶
pip install "triadic-engine[dashboard]"
triadic-dashboard
Six tabs: Ingestion & Encoding, Semantic Graph, Logic & Search, AI Auditor, Anomaly Detection, Benchmarks.
REST API¶
pip install "triadic-engine[api]"
uvicorn api.server:app --host 0.0.0.0 --port 8000
| Endpoint | Method | Description |
|---|---|---|
/health |
GET | Engine status and loaded concepts count |
/encode |
POST | Encode concepts into composite prime integers |
/audit |
POST | Compare two embedding models topologically |
/search |
POST | GCD-based semantic search over indexed concepts |
/report |
GET | Export engine state as HTML, JSON, or CSV |
Interactive docs at http://localhost:8000/docs (Swagger UI).
Ecosystem¶
The Engine is the foundation of the Triadic research program:
- TriadicGPT — 40M-parameter GPT that learns prime signatures end-to-end
- reptimeline — Tracks how discrete representations evolve during training