1. Inference Mode & Puzzle
Out-Of-Distribution Test
Classic riddle constraints deliberately inverted: The wolf PROTECTS the goat from the cabbage. If left alone, the cabbage spoils without the wolf. Statistical autocomplete answers with the internet memorized pattern (wolf eats goat), causing catastrophic constraint failure.
Symbolic engine enforces hard first-order logic invariants over the candidate state transitions. Statistical approximations violating strict boundary conditions are rejected with zero hallucinations.
2. Hypothesis Space & Logic Boundaries
Leave-One-Out Projection
Generalization Accuracy
94.5%
Statistical Hallucination Rate
0.0%
[INIT] Initialized symbolic knowledge base with formal invariant rules.
[GATE] Inverted constraint verified: Protective Wolf axiom loaded.
[SOLVER] Symbolic Constraint Satisfied: 0% Statistical Hallucination.
3. Formal System Evidence
Audit & Benchmark
CANONICAL REASONING PROOF
ID: SYM-AI-98
Model Type:
Symbolic Constraint Engine
Generalization Score:
94.5%
Prediction Output:
Logical Rule Enforced: Constraint Satisfied (0% Statistical Hallucination)
Status:
Passed Strict Logic Gate
Leave-One-Out Cross-Validation:
94.5% (47/50 folds consistent)
Active Hypothesis Boundary:
Order-3 Convex Polygon (Symbolic Polytope)
Hypothesis Simplicity Ratio:
0.60 (3/5)
Out-of-Distribution Penalty:
0.00 (Zero Hallucination)
Empirical Risk vs Bounds:
Formal Upper Bound Hold
ML Generalization Principle: Generalization on novel distributions requires constraining the hypothesis space. Unbounded predictive autocomplete overfits internet priors, failing when constraints invert.