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]: Later, BIBREF8 introduced an RNN with an external stack memory to learn simple context-free languages, such as $a^n b^m$ , $a^nb^ncb^ma^m$ , and $a^{n+m} b^n c^m$ . Similar studies BIBREF15 , BIBREF16 , BIBREF17 , BIBREF10 , BIBREF11 have explored the existence of stable counting mechanisms in simple RNNs, which would enable them to learn various context-free and context-sensitive languages BIBREF9 , on the other hand, proposed a variant of Long Short-Term Memory (LSTM) networks to learn two context-free languages, $a^n b^n$ , $a^n b^m B^m A^n$ , and one strictly context-sensitive language, $a^n b^n c^n$ .
[A]: How do they get the formal languages?


[Q]: As Garimella et al. BIBREF23 have made their code public , we reproduced their best method Randomwalk on our datasets and measured the AUC ROC, obtaining a score of 0.935. An interesting finding was that their method had a poor performance over their own datasets. This was due to the fact (already explained in Section SECREF4) that it was not possible to retrieve the complete discussions, moreover, in no case could we restore more than 50% of the tweets. So we decided to remove these discussions and measure again the AUC ROC of this method, obtaining a 0.99 value. Our hypothesis is that the performance of that method was seriously hurt by the incompleteness of the data. We also tested our method on these datasets, obtaining a 0.99 AUC ROC with Walktrap and 0.989 with Louvain clustering.
[A]:
What are the state of the art measures?