Hi datistiquo,
when you fine-tune BERT, you can choose whether to freeze the BERT layers or not.   Do you want BERT to learn to embed the words in a slightly different way, based on your new data, or do you just want to learn to classify the texts in a new way (with the standard BERT embedding of the words)?
I wanted to use BertViz visualisation to see what effect the classification tuning had on the attention heads, so I did fine-tuning with the first 8 layers of BERT frozen and the remaining 4 layers unfrozen.
Some people suggest doing gradual unfreezing of the BERT layers, ie finetuning with BERT frozen, then finetuning a bit more with just one layer unfrozen, etc.
I believe it should be possible to use the main BertModel together with your own neural network achitecture afterwards, and fine tune the weights in that way too (but I couldn’t make that work).
By the way, are you using BertForSequenceClassification (in pytorch) or TFBertForSequenceClassification (in tensorflow)?
BertForSequenceClassification is a "Bert Model transformer with a sequence classification/regression head on top (a linear layer on top of the pooled output) ".    If you want to use a different kind of output, you might consider using BertModel instead.