In the original FOFE with just a single forgetting factor, we would have to determine the best trade-off between these two benefits.
the dual-FOFE does not face such issues since it is composed of two FOFE codes: the half of the dual-FOFE code using a smaller forgetting factor is solely optimized and responsible for representing the positional information of all words in the sequence; meanwhile the other half of the dual-FOFE code using a larger forgetting factor is optimized and responsible for maintaining the long-term dependency of past context.