When does local structure play a role in sheared jammed packings?

In jammed packings, it is usually assumed that local structure only plays a significant role in specific regimes. For instance, it is known that in jammed packings the variance of the relative excess coordination, δΖ/Ζ_c, decays like 1/d, so that local structure should play no role at high spatial dimensions. Furthermore, in any fixed dimension d >= 2, lowering the pressure results in a diverging length scale, again suggesting that local structure should not be sufficient to describe response. Here we address the validity of the assumption that local structure does not matter in these cases. Focusing on jammed packings under athermal, quasistatic shear, we utilize machine learning to identify a local structural variable, softness, that has been shown to be strongly predictive of rearrangements in many disordered systems. We apply the softness analysis to plastic events in jammed packings across many dimensions and pressures, and find that local structure is perhaps more predictive than one might have guessed.