This paper presents the engineering implementation methods of the SKG inference framework and provides complete case studies across four domains.
Case Studies
Case 1: 2D Dissipative Mechanical System
- OOD MSE is 1.69 to 4.12 times lower than the best neural baseline
- State-dependent metric yields a 10^8-order improvement under controlled conditions
Case 2: Target Detection Sim-to-Real
- Real-machine mAP increases from 0.2564 to 0.4964 (+24.00 points, single-run experiment, 32 images, point estimate)
- AP75 increases from 0.1736 to 0.5765 (+40.29 points)
- No real-machine retraining required
Case 3: Sequence Modeling (sine to square)
- OOD MSE: 0.0296 vs Transformer 0.0641 (mean of 5 seeds, p=0.024)
Case 4: Molecular Dynamics (MD17)
- ID@100 ADE: 0.0285 vs ESTAG 0.1467
- OOD@100: 0.0316 vs 0.1411 (single seed)
Methodology
For each case, we present:
- Objective definition
- Applied SKG theory
- Parameter settings
- Baseline comparison protocol
- Data results
- Sources of advantage
Complete methodology includes:
- Pre-validation
- Task invariant construction
- Three-stage training
- Residual training
- Four theorems and one proposition supporting these methods
Key Contributions
- Demonstrates effective SKG configurations across four domains
- Honestly reports:
- Variance of single-run experiments
- Limitations of single-seed results
- Negative updates caused by parameterization mismatch
- Provides practical experience on using engineering thresholds as diagnostic signals (not hard constraints)