System I: Soft Repulsive Disks.

This computer-simulated 2D soft-disk system is polydisperse (49). Disks interact via 1/rd12 pairwise repulsions, where rd is the separation, and samples are prepared using swap Monte-Carlo methods (49). System IA is equilibrated at Ta=0.2, while for IB Ta=0.025. Initial states for IB may not be completely equilibrated, but this does not affect interpretation of the results. After energy minimization to T=0, these configurations are sheared athermally and quasistatically by repeatedly applying a small simple shear strain of δϵ=10−5 and minimizing the potential energy, up to total strain ϵend=0.1. Energy minimization is carried out using the steepest descent algorithm with a very conservative step size to simulate overdamped dynamics (SI Appendix in ref. 37). During minimization, we study intermediate configurations using the same protocol as ref. 37 to investigate the course of an avalanche.