chore(README): simple neural network

README.md

@@ -5,8 +5,45 @@ A simple Machine Learning library.
 notMNIST dataset, cross-entropy loss, learning rate decay and sgd:
 ![notMNIST](https://github.com/mdibaiee/sibe/blob/master/notmnist.png?raw=true)
 
-See examples:
+## Simple neural network
+```haskell
+    let a = (sigmoid, sigmoid') -- activation function
+        -- random network, seed 0, values between -1 and 1,
+        -- two inputs, two nodes in hidden layer and a single output
+        rnetwork = randomNetwork 0 (-1, 1) 2 [(2, a)] (1, a)
+
+        -- inputs and labels
+        inputs = [vector [0, 1], vector [1, 0], vector [1, 1], vector [0, 0]]
+        labels = [vector [1], vector [1], vector [0], vector [0]]
+
+        -- define the session which includes parameters
+        session = def { network = rnetwork
+                      , learningRate = 0.5
+                      , epochs = 1000
+                      , training = zip inputs labels
+                      , test = zip inputs labels
+                      } :: Session
+
+        initialCost = crossEntropy session
+
+    -- run gradient descent
+    -- you can also use `sgd`, see the notmnist example
+    newsession <- run gd session
+
+    let results = map (`forward` newsession) inputs
+        rounded = map (map round . toList) results
+
+        cost = crossEntropy newsession
+    
+    putStrLn $ "- initial cost (cross-entropy): " ++ show initialCost
+    putStrLn $ "- actual result: " ++ show results
+    putStrLn $ "- rounded result: " ++ show rounded
+    putStrLn $ "- cost (cross-entropy): " ++ show cost
 ```
+
+
+## Examples
+```bash
 # neural network examples
 stack exec example-xor
 stack exec example-424