where w(x i ) is the weight of element i, x i is the frequency of element i and ϵ (ϵ ≥ 1) is a parameter to adjust the weight distribution which was set to 1.1 to avoid extremely large weights. The resolution of the persistence image during training was set to 50 × 50 with a patch size of 5 × 5 in accordance to previous studies . For fine-tuning, all datasets (except for ∆-E) were randomly split with a train-validation-test ration of 80%:10%:10%. The ∆-E dataset was split according to the original paper . By initializing a single dense layer to the [CLS] token, all model weights are fine-tuned to predict desired properties for 50 epochs with a batch size of 32. All other settings are the same as in the pre-training step.