Full fine-tuning updates every weight in the model. For each weight it keeps the weight itself in fp16 (2 bytes), a gradient in fp16 (2 bytes), and, with the common Adam optimizer, three fp32 copies (12 bytes): a running average of gradients, a running average of their squares, and a full-precision master copy. That is 16 bytes per weight.
For Llama-2-7B, which has 6.74 billion weights, 16 bytes each comes to about 108 GB before activations. That is more than a single 80 GB A100 holds, so you rent a multi-GPU machine. Activations, the values each layer keeps for the backward pass, come on top and grow with batch size and sequence length.
The second bill arrives when you deploy. Each fully fine-tuned model is a complete copy, about 14 GB for a 7B model in fp16. Ten teams with ten fine-tunes means ten large copies to store, load and serve. Parameter-efficient fine-tuning, PEFT for short, reduces both bills with one idea: freeze the base model, add a small number of new trainable parameters, and train only those.