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In jammed packings, it is usually thought that local structure only plays asignificant role in specific regimes. The standard deviation of the relativeexcess coordination, $\sigma_Z/ Z_\mathrm{c}$, decays like $1/\sqrt{d}$, sothat local structure should play no role in high spatial dimensions.Furthermore, in any fixed dimension $d \geq 2$, there are diverging lengthscales as the pressure vanishes approaching the unjamming transition, againsuggesting that local structure should not be sufficient to describe response.Here we challenge the assumption that local structure does not matter in thesecases. In simulations of jammed packings under athermal, quasistatic shear, weuse machine learning to identify a local structural variable, softness, thatcorrelates with rearrangements in dimensions $d=2$ to $d=5$. We find thatsoftness - and even just the coordination number $Z$ - are quite predictive ofrearrangements over a wide range of pressures, all the way down to unjamming,in all $d$ studied. This result provides direct evidence that local structurecan play a role in higher spatial dimensions.

Correlation of plastic events with local structure in jammed packings across spatial dimensions