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arXiv Machine Learning By Jian An, Chaoshi Wu, Jinhui Wu

SKG: A Law-Induced Engine from Inference to Induction

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The paper introduces SKG (Symplectic‑Kernel Gradient), a reasoning engine that integrates symplectic geometry, GENERIC, kernel methods, RKHS, group‑equivariant networks, and constrained mechanics into a unified framework for law‑induced inference and induction. It defines an octuple S = (M, g, ω, H, S, G, Δ, Π) capturing conservation laws, constitutive relations, symmetry groups, and axiom systems, and presents several theoretical results on metric reconstruction, kernel bandwidth determination, error decomposition, and function‑space reconstruction. The authors validate SKG on a 1‑D damped oscillator and a 2‑D rotation‑invariant system, reporting significant statistical performance (p < 0.01) across six unit tests and ten experiments.

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