I've recently become interested in LSTMs and I was surprised to learn that the weights are shared across time.
I know that if you share the weights across time, then your input time sequences can be a variable length.
With shared weights you have many fewer parameters to train.
From my understanding, the reason one would turn to an LSTM vs. some other learning method is because you believe there is some sort of temporal/sequential structure/dependence in your data that you would like to learn. If you sacrifice the variable length ‘luxury’, and accept long computation time, wouldn’t an RNN/LSTM without shared weights (i.e. for every time step you have different weights) perform way better or is there something I’m missing?