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.
--------
Question: Just as introduced in sec:introduction, it is intractable to compute similarity exactly, as involving INLINEFORM0 computation. Hence, we consider the monte-carlo approximation: DISPLAYFORM0

where INLINEFORM0 is a list of entity pairs sampled from INLINEFORM1 . We use sequential sampling to gain INLINEFORM6 , which means we first sample INLINEFORM7 given INLINEFORM8 from INLINEFORM9 , and then sample INLINEFORM10 given INLINEFORM11 and INLINEFORM12 from INLINEFORM13 .
Question: Which sampling method do they use to approximate similarity between the conditional probability distributions over entity pairs?

Answer: monte-carlo sequential sampling

Question: An acoustic word embedding is a function that takes as input a speech segment corresponding to a word, INLINEFORM0 , where each INLINEFORM1 is a vector of frame-level acoustic features, and outputs a fixed-dimensional vector representing the segment, INLINEFORM2 .
Question: How do they represent input features of their model to train embeddings?

Answer: a vector of frame-level acoustic features

Question: While $eta $-VAE offers regularizing the ELBO via an additional coefficient $eta \in {
m I\!R}^+$, a simple extension BIBREF16 of its objective function incorporates an additional hyperparameter $C$ to explicitly control the magnitude of the KL term,

where $C\!\! \in \!\! {
m I\!R}^+$ and $| . |$ denotes the absolute value.
Question: How does explicit constraint on the KL divergence term that authors propose looks like?

Answer:
Answer with content missing: (Formula 2) Formula 2 is an answer:
ig \langle\! \log p_ heta({x}|{z}) ig
angle_{q_\phi({z}|{x})} - eta |D_{KL}ig(q_\phi({z}|{x}) || p({z})ig)-C|