Loss Functions

# Focal Loss

Introduced by Lin et al. in Focal Loss for Dense Object Detection

A Focal Loss function addresses class imbalance during training in tasks like object detection. Focal loss applies a modulating term to the cross entropy loss in order to focus learning on hard misclassified examples. It is a dynamically scaled cross entropy loss, where the scaling factor decays to zero as confidence in the correct class increases. Intuitively, this scaling factor can automatically down-weight the contribution of easy examples during training and rapidly focus the model on hard examples.

Formally, the Focal Loss adds a factor $(1 - p_{t})^\gamma$ to the standard cross entropy criterion. Setting $\gamma>0$ reduces the relative loss for well-classified examples ($p_{t}>.5$), putting more focus on hard, misclassified examples. Here there is tunable focusing parameter $\gamma \ge 0$.

$${\text{FL}(p_{t}) = - (1 - p_{t})^\gamma \log\left(p_{t}\right)}$$

#### Papers

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