update on recurrent NN

doc/src/Recurrent/Recurrent.do.txt

@@ -6,15 +6,14 @@ DATE: today
 !split
 ===== Recurrent neural networks: Overarching view =====
 
-We have mostly looked at feedforward neural networks, where the
+Till now our focus has been, including convolutional neural networks as well, 
+on feedforward neural networks. The output or the
 activations flow only in one direction, from the input layer to the
 output layer.
 
 A recurrent neural network (RNN) looks very much like a feedforward
-neural network, except it also has connections pointing
-backward. Let’s look at the simplest possible RNN, composed of just
-one neuron receiving inputs, producing an output, and sending that
-output back to itself.
+neural network, except that it also has connections pointing
+backward. 
 
 RNNs are used to analyze time series data such as stock prices, and
 tell you when to buy or sell. In autonomous driving systems, they can
@@ -28,3 +27,12 @@ systems such as automatic translation and speech-to-text.
 
 !split
 =====  Set up of an RNN =====
+
+The figure here displays a simple example of an RNN, with inputs $x_t$
+at a given time $t$ and outputs $y_t$.  Introducing time as a variable
+offers an intutitive way of understanding these networks. In addition
+to the inputs $x_t$, the layer at a time $t$ receives also as input
+the output from the previous layer $t-1$, that is $y_{t1}$.
+
+This means also that we need to have weights that link both the inputs $x_t$ to the outputs $y_t$ as well as weights that link
+the output from the previous time $y_{t-1}$ and $y_t$.