Extended Data Fig. 3: FlexConsensus error histograms computed for the EMPIAR 10028 dataset.

The error metric corresponds to the standard Root Mean Squared Error between every original space and the spaces decoded by FlexConsensus from the consensus space, as well as the consensus error derived from the consensus space. The three images presented show a similar error tendency for all the decoders: the two HetSIREN executions remain more similar, meaning that the two independent estimations have similar characteristics and are reliable for most particles. In contrast, Zernike3D deviates more from HetSIREN, an effect mainly occurring due to the differences in the approximation followed by each method and the differences in the type of variability they can estimate. Apart from these differences, one can see that the distribution of the errors is similar in the three cases, and it allows us to easily identify and exclude those particles on the right tail of the distributions, which are the ones estimated with lower reliability based on these three executions.