diff --git a/pygrad/nn.py b/pygrad/nn.py
index a06366c..3a11e17 100644
--- a/pygrad/nn.py
+++ b/pygrad/nn.py
@@ -1,38 +1,43 @@
 # Neural networks from scratch with numpy.
 
 import numpy as np
-import pygrad.tensor as tensor
+from pygrad.tensor import tensor, Tensor
 
 def mean_absolute_error(x, y):
   return np.mean(np.abs(x - y))
 
-def mean_squared_error(x, y):
-  return np.mean(np.power(x - y, 2))
+def mean_squared_error(x: Tensor, y: Tensor):
+  return x.sub(y).expt(2).div(tensor([[2.0]]))
 
-def cross_entropy_loss(x, y):
-  return -np.log(np.exp(y) / np.sum(np.exp(x)))
+def cross_entropy_loss(x: Tensor, y: Tensor):
+  return y.exp().div(np.sum(x.exp())).log().neg()
 
 # prepare inputs and outputs
-x = np.array([[1, 0]])
-y = np.array([[1]])
+x = tensor(np.array([[1, 0]]))
+y = tensor(np.array([[1]]))
 
 # we're doing xavier initialisation - see <http://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf>
-w1 = np.random.randn(2, 3) / np.sqrt(2)
-w2 = np.random.randn(3, 1) / np.sqrt(3)
+w1 = tensor(np.random.randn(2, 3) / np.sqrt(2))
+w2 = tensor(np.random.randn(3, 1) / np.sqrt(3))
 
 def single_pass():
+  global w1, w2
+
   # forward pass
-  h = np.matmul(x, w1)
-  h_hat = np.tanh(h)
-  j = np.matmul(h_hat, w2)
-  print("prediction {}".format(j))
+  h = x.mul(w1)
+  h_hat = h.tanh()
+  j = h_hat.mul(w2)
+  print(f"prediction {j}")
 
   # loss calculation
-  loss = cross_entropy_loss(j, y)
-  print("loss {}".format(loss))
+  loss = mean_squared_error(j, y)
+  print(f"loss {loss}")
 
-  # TODO Backward pass.
-  return
+  loss.backward()
+  print(w1.grad, w2.grad)
+
+  w1.value -= 0.1 * w1.grad
+  w2.value -= 0.1 * w2.grad
 
 # initialise layers
 #   self.lin1 = nn.Linear(2, 3)