2172fde49301047270b2897085e4319d-Supplemental.pdf

We define a Gibbs distribution associated with the problem and evaluate its normalization constant -thepartition functionZ. The partition function, and in particular its logarithm divided by the temperature - the free energy -, contains all the information we aim to understand in the problem. By taking the proper derivatives, and possibly add an external field, we can compute relevant macroscopic properties such as: average overlapwiththegroundtruth,averagelossachieved. Indisordered systemwehavetoconsider the additional complication given by the randomness.