rnn update

doc/src/Recurrent/Recurrent.do.txt

@@ -6,10 +6,9 @@ DATE: today
 !split
 ===== Recurrent neural networks: Overarching view =====
 
-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.
+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 that it also has connections pointing
@@ -24,7 +23,7 @@ example, they can take sentences, documents, or audio samples as
 input, making them extremely useful for natural language processing
 systems such as automatic translation and speech-to-text.
 
-_The text here is under development_. Planned finished Jan 2020.
+_The text here is under development_. Planned finished mid Jan 2020.
 
 
 !split
@@ -36,18 +35,27 @@ 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 $y_t$.   The figure here shows an example of a simple RNN.
-
-
-Add figures and bring up equations. 
+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 $y_t$.  The figure here shows an
+example of a simple RNN.
 
 
 
 !split
 ===== Solving differential equations and eigenvalue problems with RNNs =====
 
-Have example with eigenvalues solvers as well.
+
+
+In our discussions of ordinary differential equations and partial
+differential equations using neural networks. Here we will discuss how
+we can solve say ordinary differential equations and eigenvalue
+problems using RNNs. Eigenvalue problems can be solved using RNNs by
+rewriting such a problems as a non-linear differential equation.
+
+Instead of starting with a well-known ordinary differential equation,
+we start directly with an eigenvaule problem.
+
 
 
 !split