Same as Fig. 3, but HALOSCOPE has been trained with different input properties. In the top left panel, random uncorrelated inputs are used for training HALOSCOPE and when we apply our algorithm to the LR haloes, LR+HALOSCOPE, no halo AB is measured. In the top middle panel, we train HALOSCOPE with properties from LR haloes. For the other panels, HALOSCOPE is trained with the input properties indicated in the legend. In all the panels, the blue and red triangles correspond to the upper and lower 25% of (c_vir, λ, c/a, b/a) HR haloes. This is our reference. To recover the multi-dimensional halo AB, HALOSCOPE needs to be trained with haloes’ environmental properties; in particular b₁, α_4R, and a combination of the two give the best results.