Question: What assumption is EqEmb based on?
Evidence: Given a dataset of words and equations the goal of the EqEmb models is to derive a semantic representation of each equation. EqEmb model equations in the context of words. EqEmb is based on the idea that a good semantic representation of equations could be discovered by expanding the original word context to include any equations that appear in a possibly larger window around it.
We assign embeddings to words ( INLINEFORM0 , INLINEFORM1 ) and equations ( INLINEFORM2 , INLINEFORM3 ). The objective function contains conditionals over the observed words and equations: DISPLAYFORM0 
This is a sum of two sets of conditional distributions, the first over observed words ( INLINEFORM0 ) and the second over observed equations ( INLINEFORM1 ). In word embedding models, INLINEFORM2 and INLINEFORM3 are referred to as embedding and context vectors. Here we use a different terminology: the interaction INLINEFORM4 and feature vector INLINEFORM5 .
In word embeddings, the context of the word INLINEFORM0 is defined to index the surrounding words in a small window around it. Here the context of the word INLINEFORM1 will be the original context ( INLINEFORM2 ) and any equations ( INLINEFORM3 ) that are in a possibly larger window around it. This is referred to as the word-equation context window.
Both conditionals are Bernoulli distributions. The first conditional is defined over the words in the collection. It has the following parameter: DISPLAYFORM0 
The word context function is: DISPLAYFORM0 
This function encompasses the words in the original word context ( INLINEFORM0 ) and any equations ( INLINEFORM1 ) that appear in a possibly larger window ( INLINEFORM2 ) around it.
The second term in the objective corresponds to the sum of the log conditional probabilities of each equation. Its parameter is: DISPLAYFORM0 
Similar to word embeddings, equation context INLINEFORM0 contains words that are in a context window around the equation: DISPLAYFORM0 
The equation context can have a larger window than the word context. Equation feature vectors ( INLINEFORM0 ) are only associated with the first term of the objective function. This function contains the words where the equation appears in their larger context INLINEFORM1 .
The left side of Figure FIGREF1 shows an example equation in a scientific article. With a word context of size INLINEFORM0 we model the words in the article while ignoring equations. For example when modeling the word "embedding" (highlighted in green) with context window size of 4 (i.e. INLINEFORM1 ), the context contains the words that appear two words before ("current" and "word") and after ("recurrent" and "version") this word. With a word-equation context window of size INLINEFORM2 =16, the term for the word "embedding" would have the feature vector of the equation as one of its components.
Given a dataset of words and equations the goal of the EqEmb models is to derive a semantic representation of each equation. EqEmb model equations in the context of words. EqEmb is based on the idea that a good semantic representation of equations could be discovered by expanding the original word context to include any equations that appear in a possibly larger window around it.
Answer: A good semantic representation of equations could be discovered by expanding the original word context to include any equations that appear in a possibly larger window around it.