Detailed Instructions: In this task, you will be presented with a context from an academic paper and a question separated with a
. You have to answer the question based on the context.
Q: Comparing Eq.DISPLAY_FORM14 with Eq.DISPLAY_FORM22, we can see that Eq.DISPLAY_FORM14 is actually a soft form of $F1$, using a continuous $p$ rather than the binary $\mathbb {I}( p_{i1}>0.5)$. This gap isn't a big issue for balanced datasets, but is extremely detrimental if a big proportion of training examples are easy-negative ones: easy-negative examples can easily dominate training since their probabilities can be pushed to 0 fairly easily. Meanwhile, the model can hardly distinguish between hard-negative examples and positive ones, which has a huge negative effect on the final F1 performance.

To address this issue, we propose to multiply the soft probability $p$ with a decaying factor $(1-p)$, changing Eq.DISPLAY_FORM22 to the following form:

One can think $(1-p_{i1})$ as a weight associated with each example, which changes as training proceeds. The intuition of changing $p_{i1}$ to $(1-p_{i1}) p_{i1}$ is to push down the weight of easy examples. For easy examples whose probability are approaching 0 or 1, $(1-p_{i1}) p_{i1}$ makes the model attach significantly less focus to them. Figure FIGREF23 gives gives an explanation from the perspective in derivative: the derivative of $
rac{(1-p)p}{1+(1-p)p}$ with respect to $p$ approaches 0 immediately after $p$ approaches 0, which means the model attends less to examples once they are correctly classified.

A close look at Eq.DISPLAY_FORM14 reveals that it actually mimics the idea of focal loss (FL for short) BIBREF16 for object detection in vision. Focal loss was proposed for one-stage object detector to handle foreground-background tradeoff encountered during training. It down-weights the loss assigned to well-classified examples by adding a $(1-p)^{eta }$ factor, leading the final loss to be $(1-p)^{eta }\log p$.
Question: How are weights dynamically adjusted?
A:
One can think $(1-p_{i1})$ as a weight associated with each example, which changes as training proceeds. The intuition of changing $p_{i1}$ to $(1-p_{i1}) p_{i1}$ is to push down the weight of easy examples. For easy examples whose probability are approaching 0 or 1, $(1-p_{i1}) p_{i1}$ makes the model attach significantly less focus to them. Figure FIGREF23 gives gives an explanation from the perspective in derivative: the derivative of $
rac{(1-p)p}{1+(1-p)p}$ with respect to $p$ approaches 0 immediately after $p$ approaches 0, which means the model attends less to examples once they are correctly classified.