Detailed Instructions: In this task, you will be presented with a context from an academic paper and you have to write an answerable question based on the context. Your questions can be extractive, abstractive, or yes-no questions.
Problem:For the overlapped speech recognition problem, the conditional independence assumption in the output label streams is still made as in Equation ( 5 ). Then the cross-entropy based PIT can be transformed to sequence discriminative criterion based PIT as below,

$$egin{split} \mathcal {J}_{ ext{SEQ-PIT}}=\sum _u \min _{s^{\prime }\in \mathbf {S}}
rac{1}{N} \sum _{n\in [1,N]}-\mathcal {J}_{ ext{SEQ}}(\mathbf {L}_{un}^{(s^{\prime })},\mathbf {L}_{un}^{(r)}) \end{split}$$ (Eq. 44)

Different from Equation ( 7 ), the best permutation is decided by $\mathcal {J}_{ ext{SEQ}}(\mathbf {L}_{un}^{(s^{\prime })},\mathbf {L}_{un}^{(r)})$ , which is the sequence discriminative criterion of taking the $s^{\prime }$ -th permutation in $n$ -th output inference stream at utterance $u$ . Similar to CE-PIT, $\mathcal {J}_{ ext{SEQ}}$ of all the permutations are calculated and the minimum permutation is taken to do the optimization.
Solution:
How is the discriminative training formulation different from the standard ones?