Fig. 4: Information theoretical quantities correlate with error and chemical trends in the TM23 dataset.

a Information entropy of the full TM23 training set for each element⁴⁷. b Force errors (in %) for NequIP models²¹ trained on the full training set, obtained from Owen et al.⁴⁷. c These two quantities exhibit strong correlation, as indicated by the Pearson correlation coefficient of ρ = 0.79 for transition metals with incomplete d-shell. d The difference between the final forces error (in %) and the initial forces errors (in %) (denoted as ΔError) is explained by the dataset overlap obtained by computing the differential entropies \(\delta {{{\mathcal{H}}}}(0.75{T}_{m}| 0.25{T}_{m})\) or \(\delta {{{\mathcal{H}}}}(1.25{T}_{m}| 0.25{T}_{m})\), as demonstrated by the Pearson correlation coefficient of ρ = − 0.85. Red and blue dots indicate error differences for models trained on the “cold” subset of TM23 (sampled at 0.25 T_m, where T_m is the melting temperature) and tested on the “warm” (0.75 T_m) and “melt” (1.25 T_m), respectively.