ML Loss Functions
MSE, cross-entropy, hinge, KL divergence, contrastive — formatted for slides.
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\text{MSE:}\quad \mathcal L = \frac{1}{N}\sum_{i=1}^{N}(y_i - \hat y_i)^2
\text{Binary cross-entropy:}\quad \mathcal L = -\frac{1}{N}\sum_{i} \left[ y_i \log \hat y_i + (1-y_i)\log(1-\hat y_i) \right]
\text{Categorical cross-entropy:}\quad \mathcal L = -\sum_{c=1}^{C} y_c \log \hat y_c
\text{Hinge:}\quad \mathcal L = \max(0, 1 - y \hat y)
\text{KL divergence:}\quad D_{\mathrm{KL}}(p \| q) = \sum_x p(x) \log\frac{p(x)}{q(x)}
\text{InfoNCE / contrastive:}\quad \mathcal L = -\log \frac{\exp(s(q,k^+)/\tau)}{\sum_{i} \exp(s(q,k_i)/\tau)}