human
Solve the following python programming problem given the following code:
# Linear feed-forward that takes a params pytree.
def predict_pytree(params, x):
  return jnp.dot(x, params['W']) + params['b']

# Loss function: Mean squared error.
def mse_pytree(params, x_batched,y_batched):
  # Define the squared loss for a single pair (x,y)
  def squared_error(x,y):
    y_pred = predict_pytree(params, x)
    return jnp.inner(y-y_pred, y-y_pred) / 2.0
  # We vectorize the previous to compute the average of the loss on all samples.
  return jnp.mean(jax.vmap(squared_error)(x_batched, y_batched), axis=0)

# Initialize estimated W and b with zeros. Store in a pytree.
params = {'W': jnp.zeros_like(W), 'b': jnp.zeros_like(b)}
Given the above code, generate some markdown instructions for it.
assistant
#Here is Python program to compute the average of the loss on all samples.

Linear regression with Pytrees
Whereas our previous example was perfectly fine, we can see that when things get more complicated (as they will with neural networks), it will be harder to manage parameters of the models as we did.
Here we show an alternative based on pytrees, using the same data from the previous example.
Now, our params is a pytree containing both the W and b entries.