Interpreting learning dynamics of autoencoders: Transient scaling and emerging concepts of the Ising model

תקציר מקורי באנגליתarXiv:2607.10285v2 Announce Type: replace Abstract: We study how unsupervised autoencoders trained on microscopic spin configurations from the Ising model learn macroscopic, theory-relevant variables underlying the data-generating process. We quantify learning across multiple spatial (coarse-graining) scales and reveal two distinct dynamical regimes that appear sequentially, controlled by the main hyperparameters (model depth, width, and learning rate): one in which magnetization and another in which energy is learned across scales. The first exhibits error fluctuations ordered to scale and learns global averages only; The second gradually resolves smaller scales relevant for the energy representation. Deep models trained at moderate and fast rates become arrested before reaching these reg