SlowGuess/ACL_2020_OCR huggingface dataset:
where  $\delta$  is Kronecker delta and  $\cdot^{-1}$  denotes matrix inversion. Eq. 19 is suitable for multi-root setting. In the case of single-root setting, it is replaced by:
$$
[ \hat {\boldsymbol {L}} ^ {(t)} ] _ {i j} = \left\{ \begin{array}{l l} r _ {j} ^ {(t)} & \text {i f} i = 1, \\ [ \boldsymbol {L} ^ {(t)} ] _ {i j}, & \text {o t h e r w i s e .} \end{array} \right. \tag {21}
$$
During training, a cross-entropy loss is used to each layer's root probability  $\alpha_{i}^{(t)}$ , similar to  $\hat{y}_i^{\mathrm{emo}}$ .
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