Route queries through 62 semantic primitives with verified mathematical properties.
The framework achieves 100% precision on routing benchmarks - it never sends a query to the wrong specialist. This isn't optimization; it's guaranteed by the structure (Hadamard orthogonality ensures primitives don't interfere).
Current interpretability methods rely on learned representations:
- Trained linear probes overfit to specific tasks
- SAE features are emergent, not semantically grounded
- Activation patching is costly and hard to interpret systematically
Alternative: Project representations into a pre-defined semantic basis with known mathematical properties. The basis is constructed a priori from Wierzbicka's 62 cross-culturally validated primitives. No training required.
| Property | Result |
|---|---|
| Intra-dimension orthogonality | 229/229 pairs at cos = 0.000 |
| Bipolar opposition | 14/14 pairs at cos = -1.000 |
| Cross-dimension independence | mean |
Antonyms are structurally opposed (cos = -1.0 exactly), not just distant.
| Metric | Result |
|---|---|
| Precision | 100.00% |
| Recall | 85.62% |
| False Positives | 0 |
The router abstains when uncertain rather than guessing. 31.5% abstention rate on ambiguous queries.
| Operation | Latency |
|---|---|
| Sentence encoding | 273 μs |
| Cosine similarity | 59 μs |
Memory: 21 KB for entire basis. 10,000-100,000× faster than LLM inference for equivalent semantic operations.
pip install -e .from semantic_probing import HadamardBasis
basis = HadamardBasis().generate()
# Antonyms have cosine = -1.0 (exact, not approximate)
good = basis.get_primitive("GOOD")
bad = basis.get_primitive("BAD")
print(f"cos(GOOD, BAD) = {good.cosine(bad)}") # -1.0from semantic_probing.routing import route_query
result = route_query("If A implies B and B implies C, what about A and C?")
print(result) # LOGICAL (conf=0.78)
result = route_query("asdfgh qwerty")
print(result) # ABSTAIN: Insufficient dimension evidence8,192-dimensional space partitioned into 8 semantic dimensions (1024d each)
SUBSTANTIVES | QUANTITY | EVALUATORS | MENTAL | ACTION | TEMPORAL | SPATIAL | LOGICAL
Hadamard partitions → exact orthogonality within dimensions
Bipolar pairs → cos(GOOD, BAD) = -1.0 exactly
Operations:
⊗ Bind - role-filler binding
⊕ Bundle - superposition
ρ Permute - positional encoding
| Dimension | Primitives |
|---|---|
| SUBSTANTIVES | I, YOU, SOMEONE, SOMETHING, PEOPLE, BODY, KIND, PART |
| QUANTITY | ONE, TWO, QUANTITY, NUMBER |
| EVALUATORS | GOOD/BAD, BIG/SMALL |
| MENTAL | THINK, KNOW, WANT, FEEL, SEE, HEAR |
| ACTION | SAY, DO, HAPPEN, MOVE, BE, HAVE, EXIST |
| TEMPORAL | MOMENT, WHEN, BEFORE/AFTER, NOW/THEN |
| SPATIAL | WHERE, HERE, ABOVE/BELOW, NEAR/FAR, INSIDE/OUTSIDE |
| LOGICAL | NOT, MAYBE, CAN, MUST, BECAUSE, IF, TRUE/FALSE |
pytest tests/test_headline_results.py -v # Mathematical properties
python -m tests.benchmarks.routing_test_suite # Routing benchmark- Natural Semantic Metalanguage (NSM): Wierzbicka's universal primitives
- Hyperdimensional Computing: Kanerva's sparse distributed representations
- Hadamard Matrices: Walsh-Hadamard transform for guaranteed orthogonality
MIT License