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How to obtain the parameter update for the multiclass classification (general loss and activation function)?

Consider the feature space $\mathcal{X}=\mathbb R^{d}$ and $\mathcal{Y}=\{1,...,c\}$ such that $c > 2$. We consider some activation function $\alpha: \mathbb R^{c} \to \mathbb R^{c}$ and out weight ...
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