SKG: A Law-Induced Engine from Inference to Induction
This paper proposes the SKG (Symplectic-Kernel Gradient) reasoning engine for law-induced inference and induction. Laws are a priori; data provide instances. Inference is geometric evolution under law constraints. We organize symplectic geometry, GENERIC, kernel methods, RKHS, group-equivariant networks, and constrained mechanics into a unified, analyzable, implementable, verifiable framework. We propose the SKG octuple S = (M, g, omega, H, S, G, Delta, Pi), whose four components correspond to four levels of laws: conservation laws, constitutive relations, symmetry groups, and axiom systems. Main results: (1) Invariants enter metric construction via the Jacobian: g = J^T Sigma^-1 J + epsi...
| Authors | Jian An, Chaoshi Wu, Jinhui Wu |
|---|---|
| Primary category | cs.LG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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