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$NLL = -\log(\hat{p}_{y_i})$

$CCE = -\sum_{i=1}^N \sum_{c=1}^M y_{ic} \log(p_{ic})$

$MSE = \frac{1}{N} \sum_{i=1}^N (y_i - \hat{y}_i)^2$

$MAE = \frac{1}{N} \sum_{i=1}^N |y_i - \hat{y}_i|$

$L_{\delta} (y, \hat{y}) = \begin{cases} \frac{1}{2}(y - \hat{y})^2 & \text{for } |y - \hat{y}| \le \delta, \\ \delta |y - \hat{y}| - \frac{1}{2}\delta^2 & \text{otherwise} \end{cases}$

$L(y) = \max(0, 1 - y_i \cdot f(x_i))$

$H(y,p) = -\sum_{i} y_i \log(p_i)$

$D_{KL}(P \parallel Q) = \sum p(x)\log(\frac{p(x)}{q(x)})$

$logistic = \log(1 + e^{-y_i f(x_i)})$