PhysSAE: Mechanistic Interpretability of PINNs with Sparse Autoencoders

תקציר מקורי באנגליתarXiv:2609.07061v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) embed PDE residuals into neural network training, but their internal representations remain opaque: it is unknown what physical features their hidden layers encode or whether those features have a localized causal role. We present PhysSAE, a mechanistic interpretability framework that trains overcomplete sparse autoencoders (SAEs) on PINN penultimate-layer activations and evaluates dictionary atoms through direct causal intervention in the original frozen hidden state: $h_{\mathrm{cf}} = h - \alpha z_k d_k$, bypassing the SAE decoder entirely. Across six PDE families, with 3 PINN seeds and 3 SAE seeds each---we show that (i) Our discovered SAE atoms align with independently-defined physical observa