Is there a good reference as to what a "parameter" is in this context? I've looked a few times, but the explanations don't make any sense to me.
In any case, during training (where the model is run in possibly large batches), and even during inference, the size of the parameters is completely dwarfed by the intermediate tensor representations.
What makes you say this?
Something similar applies for RNNs (same weights applied at each element of a sequence), GNNs and transformers (same weights applied at each pair of data).