From Density Matrices to Phase Transitions in Deep Learning: Spectral Early Warnings and Interpretability

arXiv:2603.29805v1 Announce Type: cross Abstract: A key problem in the modern study of AI is predicting and understanding emergent capabilities in models during training. Inspired by methods for studying reactions in quantum chemistry, we present the ``2-datapoint reduced density matrix". We show that this object provides a computationally efficient, unified observable of phase transitions during training. By tracking the eigenvalue statistics of the 2RDM over a sliding window, we derive two com