The presence of noise thus renders the minimum uncertainty non-zero, which means that the degeneracy can only be meaningfully determined up to the lower bound before adding additional points becomes irrelevant. Note that this statement holds on the condition that re-optimizing the GP hyperparameters with additional training points does not decrease the learned σ 2 n , which we found to be the case for the systems under study. Since the minimum uncertainty is learned in terms of c z 0 (R), it is propagated forward to ∆E(R) in the small value limit as 60