We study how neural emulators of partial differential equation solution operators internalize physical symmetries by introducing an influence-based diagnostic that measures the propagation of parameter updates between symmetry-related states, defined as the metric-weighted overlap of loss gradients evaluated along group orbits. This quantity probes the local geometry of the learned loss landscape and goes beyond forward-pass equivariance tests by directly assessing whether learning dynamics couple physically equivalent configurations. Applying our diagnostic to autoregressive fluid flow emulators, we show that orbit-wise gradient coherence provides the mechanism for learning to generalize over symmetry transformations and indicates when training selects a symmetry compatible basin. The result is a novel technique for evaluating if surrogate models have internalized symmetry properties of the known solution operator.
XBreaking: Understanding how LLMs security alignment can be broken
Department of Electrical, Computer；Biomedical Engineering, University of Pavia, Italy\ .；Department of Computer Applications,\ University of Science \& Technology, India\ .
Align, then memorise: the dynamics of learning with feedback alignment
Ecole Normale Supérieure（巴黎高等师范学院）；EPFL（洛桑联邦理工学院）；Facebook AI Research（脸书人工智能研究院）；LightOn；International School of Advanced Studies (SISSA)（国际高等研究学院（SISSA））
