SKG in Practice: OOD Generalization Cases Across FourDomains

Abstract

This paper presents the engineering implementation methods of the SKG inference framework and provides complete case studies across four domains. Case 1, 2D Dissipative Mechanical System: OOD MSE is 1.69 to 4.12 times lower than the best neural baseline; the 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), and AP75 increases from 0.1736 to 0.5765 (+40.29 points), with no real-machine retraining required. Case 3, Sequence Modeling sine to square: OOD MSE is 0.0296 versus Transformer 0.0641 (mean of 5 seeds, p=0.024). Case 4, Molecular Dynamics MD17: ID@100 ADE is 0.0285 versus ESTAG 0.1467; OOD@100 is 0.0316 versus 0.1411 (single seed). For each case, we present the objective, applied SKG theory, parameter settings, baseline comparison protocol, data results, and sources of advantage. Following the cases, we provide the complete methodology: pre-validation, task invariant construction, three-stage training, residual training, and the four theorems and one proposition supporting these methods. This paper not only demonstrates effective configurations of SKG across four domains but also honestly reports the variance of single-run experiments, limitations of single-seed results, negative updates caused by parameterization mismatch, and practical experience of using engineering thresholds as diagnostic signals rather than hard constraints.