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Introduction to recurrent neural networks


Recurrent neural networks (RNN) is one of the most popular neural networks. If you hear about LSTM ( Long-short term memory), it is one of types of RNN. Specially, the RECURSIVE neural networks is a general of Recurrent neural networks. The different between them is shared weights. In Recursive neural network, shared weights are put in every node, however in recurrent neural networks, shared weights are put through sequences.



Problem:
Could you know what word will be filled in the sentence: “I like French … ” ?. Let represent the sentence in numberic of words, based on dictionary, we are facing with a sequences problem: predicting the next word given by previous words. RNN does not only dare with sequence problem, It also build a neural network that can remmember. It is exactly what the brain does regularily.
Normally, a feedforward neural networks only process information through layers and forget information in the previous layers. In RNN, the information can be remembered, updated, forgotten.

Model:
$$ s_{k} = s_{k-1}*w_{rec} + x * w_{x} $$
$s_{k}, s_{k-1} $: can be a unit or a layer

let see with another intuition of RNN:




 

Training
Autoregressive model:
In the autoregressive model, t-2 and t-1 previous input neural output will be trained to neural t.


Feedforward neural net:
To training with RNN, we have to unrolded it. We can think of RNN as a feedforward neural net with many hidden layers with shared weights. We also can think of this training algorithm in the time domain.


Regularization 
One of the most downside of RNN is vanshing/exploding problem. Beside using some common techniques like penalty and dropout, LSTM is a RNN networks that can avoid this problem. Will talk about it in the next section.

Example
The simplest RNN networks is the sum of one (1) number that appeared in the list of ones, zeros (1,0).

[0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1] à sum = 5

Forward 
$$ s_{k} = s_{k-1}*w_{rec} + x * w_{x} $$

Backward
$$ \frac{\partial{E}}{\partial{w_{rec}}} = \frac {\partial{(\sum_{k=1}^{n}{E_{k}}})} {\partial{s_{k}}} * \frac{\partial{s_{k}}}{\partial{w_{rec}}} = \sum_{k=1}^{n}{\frac{\partial{E_{k}}}{\partial{s_{k}}} } * s_{k-1} $$
$$ \frac{\partial{E}}{\partial{w_{x}}} = \frac {\partial{(\sum_{k=1}^{n}{E_{k}}})} {\partial{s_{k}}} * \frac{\partial{s_{k}}}{\partial{w_{x}}} = \sum_{k=1}^{n}{\frac{\partial{E_{k}}}{\partial{s_{k}}} } * x_{k} $$



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