arXiv:2608. 01582v1 Announce Type: cross Abstract: Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling.
By Shida Liu, Abhishek Gupta, Sumit Sinha, L. Mahadevan
The paper presents a data-driven method for discovering intrinsic Lie point symmetries of differential equation systems directly from sampled jet-space data. By formulating symmetry discovery as an operator-theoretic problem, the approach identifies admissible generators, separates them from redundant or trivial directions, and reconstructs the full symmetry algebra, including its Lie-bracket structure, on benchmark systems. The method demonstrates that explicit continuous-symmetry generators can be recovered from data generated by both exact and approximate differential systems.
By Ilker Gurcan, Kadir Ustun, Ramazan Gokberk Cinbis
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.
By Jian An, Chaoshi Wu, Jinhui Wu
The paper presents an energy‑based reduced‑order model for micromagnetic magnetization dynamics that couples a convolutional autoencoder with a latent neural ODE. The latent dynamics are driven by a learned scalar potential via an antisymmetric operator and a symmetric dissipative operator, ensuring monotonic energy decrease while allowing motion along level sets. The model is trained solely on short trajectory windows without explicit physical labels, and shows that antisymmetric‑dissipative and deep‑quadratic energy formulations yield superior long‑term trajectory predictions compared to purely dissipative models.
By Sebastian Schaffer, Lukas Exl
arXiv:2606. 05957v1 Announce Type: new Abstract: Singular learning theory and information geometry have studied the same parameter spaces in mostly separate vocabularies: the former computes Bayesian invariants in resolved coordinates, the latter works in original coordinates under a non-degeneracy assumption that overparameterised models routinely violate.
By Tejas Pradeep Shirodkar
arXiv:2607. 28939v1 Announce Type: new Abstract: Structure-preserving neural networks are essential for the long-term prediction of Hamiltonian systems from data.
By Vakhtang Putkaradze