An alternative is processing the context words in addition to each target word:
This naive approach works, but is computationally intensive. Additionally, for questions of content, a few words of context is not sufficient. In the above example if asked the question "What is fun?", the model would have no way of knowing that the answer is "Deep Learning", because "fun" does not include that context.
Recurrent Neural Networks
Recurrent Neural Networks (RNN's) attempt to solve the problem of storing context by having their own output fed back into them. By doing this for each processed word, information is preserved and passed along.
This can take various forms, LSTM's being the most popular.
A very simple NN that feeds the output of its middle layer to a "recurrent" layer, and then gets it back