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We analyze the limits inherent to the inverse reconstruction of a pairwiseIsing spin glass based on susceptibility propagation. We establish theconditions under which the susceptibility propagation algorithm is able toreconstruct the characteristics of the network given first- and second-orderlocal observables, evaluate eventual errors due to various types of noise inthe originally observed data, and discuss the scaling of the problem with thenumber of degrees of freedom.

Intrinsic limitations of inverse inference in the pairwise Ising spin glass