In this task, you will be presented with a context from an academic paper and you have to write an answerable question based on the context. Your questions can be extractive, abstractive, or yes-no questions.

[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 $\frac{(1-p)p}{1+(1-p)p}$ 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 $(1-p)^{\beta }$ factor, leading the final loss to be $(1-p)^{\beta }\log p$.
[A]: How are weights dynamically adjusted?


[Q]: The resulting set of 46 documents makes up our base corpus. Note that these documents vary greatly in size, which means the resulting corpus is varied, but not balanced in terms of size (Table TABREF43).
[A]: How big PIE datasets are obtained from dictionaries?


[Q]: We pair 11'248 standard German written words with their phonetical representations in six different Swiss dialects: Zürich, St. Gallen, Basel, Bern, Visp, and Stans (Figure FIGREF1).
[A]:
How many words are coded in the dictionary?


