Loss (Eq. (5)) on held-out test data as a function of the number of Quijote LH simulations. The loss asymptotes to the Cramér-Rao bound (ℒ_CR) via the power law decay ∝N^−0.39 (see Eq. (7)). We mark on the abscissa the asymptotic regime, defined as where the test loss becomes e times the Cramér-Rao bound. Based on our initial training set of 1500, we predict that the information extracted by the neural summary is not yet optimal and that several thousand simulations are needed to reach the asymptotic regime. This prediction is verified in Fig. 5.