  Jammed soft disks exhibit avalanches of particle rearrangements under
quasistatic shear. We follow the avalanches using steepest descent to decompose
them into individual localized rearrangements. We characterize the local
structural environment of each particle by a machine-learned quantity,
softness, designed to be highly correlated with rearrangements, and analyze the
interplay between softness, rearrangements and strain. Our findings form the
foundation of an augmented elastoplastic model that includes local structure.
