(Optional) Focal Loss

Class Imbalance Problem of One-Stage Detector

• A much larger set of candidate object locations is regularly sampled across an image (~100k locations), which densely cover spatial positions, scales and aspect ratios.

• The training procedure is still dominated by easily classified background examples. It is typically addressed via bootstrapping or hard example mining. But they are not efficient enough.

alpha-Balanced CE Loss

$$CE(p_t) = - \alpha_t t_i log(p_t)$$

• To address the class imbalance, one method is to add a weighting factor $\alpha$ for class 1 and $1 - \alpha$ for class -1. $\alpha$ may be set by inverse class frequency or treated as a hyperparameter to set by cross validation.

Focal Loss

$$FL = -\sum_{i=1}^{C=n}(1 - p_{i})^{\gamma }t_{i} log (p_{i})$$

• The loss function is reshaped to down-weight easy examples and thus focus training on hard negatives. A modulating factor $(1-p_{t})^{\gamma}$ is added to the cross entropy loss where $\gamma$ is tested from $[0,5]$ in the experiment.

• There are two properties of the FL:

• When an example is misclassified and $p_{t}$ is small, the modulating factor is near 1 and the loss is unaffected. As $p_{t} \rightarrow 1$, the factor goes to 0 and the loss for well-classified examples is down-weighted.

• The focusing parameter $\gamma$ smoothly adjusts the rate at which easy examples are down-weighted. When $\gamma = 0$, FL is equivalent to CE. When $\gamma$ is increased, the effect of the modulating factor is likewise increased. ($\gamma = 2$ works best in experiment.)

alpha-Balanced Variant of FL

$$FL = -\sum_{i=1}^{C=n} - \alpha_t (1 - p_{i})^{\gamma }t_{i} log (p_{i})$$

• The above form is used in experiment in practice where α is added into the equation, which yields slightly improved accuracy over the one without α. And using sigmoid activation function for computing p resulting in greater numerical stability.

• $\gamma$: Focus more on hard examples.
• $\alpha$: Offset class imbalance of number of examples.