Wrong derivation of negative gradient of sigmoid+BCE

[GeraldHan]

Sorry for the wrong derivation of the negative gradient for Sigmoid+BCE loss.
The correct negative gradient is

$$ \nabla \mathcal{H}_i= y_i - \sigma(\mathcal{H}_i) $$

In theory, as long as the pseudo label has a negative correlation with the bias model prediction, it is able to mine the hard examples.
The wrong gradient in the paper is actually an approximation of $\nabla \mathcal{H}_i$. That's why it still works well.

[Murphyzc]

What's reason about this statement "In theory, as long as the pseudo label has a negative correlation with the bias model prediction, it is able to mine the hard examples."?