How to reduce dimensionality of encoder decoder output?

Question

I have an encoder decoder architecture where the output $ \bar{\bf{y}}_t $ is a sequence of integers of maximum length $n$. Each integer in the sequence is representative of a category so the sequence $ {0 ,1 ,3 ,4 ,6} $ could mean $\text{Car , Train , Plane , House , Dog}$. There are $m$ possible categories. The current output of the network is an $n \times m$ matrix where the entry $(i,j)$ is meant to represent the probability that the $i^\text{th}$ element of the output sequence belongs to category $j$. I was wondering is there a way to reduce the dimensionality of this problem by sharing weights among the rows of the output matrix. I was thinking there may be a way of predicting the outputs sequentially so there is weight sharing among the rows