Fig. 2

Learning of PF00014 at equilibrium We show in a the evolution over the iterations of the three overlaps used to monitor the quality of the sampling together with the waiting time T_wait. b We plot, for all iterations, the fitting errors (red, orange and brown markers) associated with the one-site, two-site (connected and non-connected) frequencies computed as defined by \(\varepsilon _{f}\), \(\varepsilon _{s}\) and \(\varepsilon _{c}\) in Sect. 2.4. Using a blue marker we show the Pearson correlation coefficient between the two-site connected frequencies of the natural sequences and of the configurations generated during training. c We plot the projections of the natural sequences into the space of the first two principal components (PC1, PC2) of the covariance matrix associated with the natural sequences while in d we project the configurations obtained by the re-sampling of the converged model into PC1 and PC2 associated with the natural sequences. e Depicts the behavior of the positive predictive value (PPV) versus the number of non-trivial contact predictions, i.e. those associated with site indices \(|i-j|>4\), for adabmDCA, plmDCA [33] and Mi3-GPU [31]. f We instead plot the contact maps used for the comparison in e: gray blocks are associated with the ground-truth obtained by Pfam-interactions [35], while the colored markers indicate whether the Frobenius norms computed using the parameters retrieved by the three methods are larger than 0.20