What is the significance of underflow during parameter update using stochastic gradient descent?
Underflow is happening because the result of that calculation is a number of smaller absolute value than your computer can actually represent in memory.
Underflow is not directly related to the performance of the model (e.g., learning rate or local minimum). Underflow is the interplay between computer software and hardware.
I suggest rescaling the data. For example, batch normalization often stops underflow errors.