1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

## How can you use an RNN to predict grammatical errors in a sentence?

1. Suppose you are given an embedding found by word2vec of each of the d terms in the lexicon. You are also given an n × d document-term matrix D containing the term frequencies of each document in its rows with the same lexicon of size d. Propose a heuristic to find the coordinates of the documents in terms of this word embedding.

2. Suppose you have additional syntactic features of words such as the part-of-speech, orthography, and so on. Show how you would incorporate such features in word2vec.

3. How can you use an RNN to predict grammatical errors in a sentence?

4. Consider a d × d word-word context matrix C = [cij ] in which cij is the frequency of word j in the context of word i. The goal is to learn d × p and p × d matrices U and V , respectively, so that applying softmax to each row of UV matches the relative frequencies in the corresponding row of C. Create a loss function for this probabilistic factorization of C into U and V . Discuss the relationship with the skip-gram model.