fix(train): fix an error in computing layer's error

feat(examples): add an example (xor)

examples/xor.hs

@@ -0,0 +1,32 @@
+module Main where
+  import Lib
+  import Numeric.LinearAlgebra
+  import Data.List
+  import Debug.Trace
+
+  -- 1x2
+  -- 2x3 + 1x3
+  -- 3x1 + 1x1
+
+  -- main :: IO [()]
+  main =
+    let learning_rate = 0.5
+        (iterations, epochs) = (2, 1000)
+        ih = randomLayer 0 (2, 8)
+        ho = randomLayer 1 (8, 1)
+        network = ih :- O ho
+
+        inputs = [vector [0, 1], vector [1, 0], vector [1, 1], vector [0, 0]]
+        labels = [vector [1], vector [1], vector [0], vector [0]]
+
+        updated_network = session inputs network labels learning_rate (iterations, epochs)
+        results = map (`forward` updated_network) inputs
+        rounded = map (map round) $ map toList results
+    in sequence [putStrLn "",
+                 putStrLn $ "inputs: " ++ show inputs,
+                 putStrLn $ "labels: " ++ show labels,
+                 putStrLn $ "learning rate: " ++ show learning_rate,
+                 putStrLn $ "iterations/epochs: " ++ show (iterations, epochs),
+                 putStrLn $ "...",
+                 putStrLn $ "rounded result: " ++ show rounded,
+                 putStrLn $ "actual result: " ++ show results]