I'm having a hard time understanding how does the size of the hidden state affects GRU. For example in a concrete example lets say I want to lean a GRU to count. I'm gonna feed it fx 3 timestamps the last 3 numbers and expect it to predict the fourth. How do I know which hidden size to chose? Can I see the hidden state size as the network capabilities to encode all the past information in a fix size vector?
Welcome to the world of deep learning! Yes, your understanding of the hidden state is correct. But the size of the hidden state is a hyperparameter that needs to found by trial-and-error. There is no closed-form formula or solution which links the size of the hidden state and the problem at hand. But, there are some rules of thumb like to start out with the size of the hidden state to be a power of 2 etc. Keep tuning the hyperparameter till you get very good predictions.