Traceback (most recent call last):
  File "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/jupyter_cache/executors/utils.py", line 51, in single_nb_execution
    executenb(
  File "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/nbclient/client.py", line 1204, in execute
    return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute()
  File "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/nbclient/util.py", line 84, in wrapped
    return just_run(coro(*args, **kwargs))
  File "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/nbclient/util.py", line 62, in just_run
    return loop.run_until_complete(coro)
  File "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/asyncio/base_events.py", line 642, in run_until_complete
    return future.result()
  File "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/nbclient/client.py", line 663, in async_execute
    await self.async_execute_cell(
  File "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/nbclient/client.py", line 965, in async_execute_cell
    await self._check_raise_for_error(cell, cell_index, exec_reply)
  File "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/nbclient/client.py", line 862, in _check_raise_for_error
    raise CellExecutionError.from_cell_and_msg(cell, exec_reply_content)
nbclient.exceptions.CellExecutionError: An error occurred while executing the following cell:
------------------
# to categorical turns our integer vector into a onehot representation
from sklearn.metrics import accuracy_score

# one-hot in numpy
def to_categorical_numpy(integer_vector):
    n_inputs = len(integer_vector)
    n_categories = np.max(integer_vector) + 1
    onehot_vector = np.zeros((n_inputs, n_categories))
    onehot_vector[range(n_inputs), integer_vector] = 1
    
    return onehot_vector

#Y_train_onehot, Y_test_onehot = to_categorical(Y_train), to_categorical(Y_test)
Y_train_onehot, Y_test_onehot = to_categorical_numpy(Y_train), to_categorical_numpy(Y_test)

def feed_forward_train(X):
    # weighted sum of inputs to the hidden layer
    z_h = np.matmul(X, hidden_weights) + hidden_bias
    # activation in the hidden layer
    a_h = sigmoid(z_h)
    
    # weighted sum of inputs to the output layer
    z_o = np.matmul(a_h, output_weights) + output_bias
    # softmax output
    # axis 0 holds each input and axis 1 the probabilities of each category
    exp_term = np.exp(z_o)
    probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
    
    # for backpropagation need activations in hidden and output layers
    return a_h, probabilities

def backpropagation(X, Y):
    a_h, probabilities = feed_forward_train(X)
    
    # error in the output layer
    error_output = probabilities - Y
    # error in the hidden layer
    error_hidden = np.matmul(error_output, output_weights.T) * a_h * (1 - a_h)
    
    # gradients for the output layer
    output_weights_gradient = np.matmul(a_h.T, error_output)
    output_bias_gradient = np.sum(error_output, axis=0)
    
    # gradient for the hidden layer
    hidden_weights_gradient = np.matmul(X.T, error_hidden)
    hidden_bias_gradient = np.sum(error_hidden, axis=0)

    return output_weights_gradient, output_bias_gradient, hidden_weights_gradient, hidden_bias_gradient

print("Old accuracy on training data: " + str(accuracy_score(predict(X_train), Y_train)))

eta = 0.01
lmbd = 0.01
for i in range(1000):
    # calculate gradients
    dWo, dBo, dWh, dBh = backpropagation(X_train, Y_train_onehot)
    
    # regularization term gradients
    dWo += lmbd * output_weights
    dWh += lmbd * hidden_weights
    
    # update weights and biases
    output_weights -= eta * dWo
    output_bias -= eta * dBo
    hidden_weights -= eta * dWh
    hidden_bias -= eta * dBh

print("New accuracy on training data: " + str(accuracy_score(predict(X_train), Y_train)))
------------------

---------------------------------------------------------------------------
RuntimeWarning                            Traceback (most recent call last)
Input In [26], in <cell line: 54>()
     53 lmbd = 0.01
     54 for i in range(1000):
     55     # calculate gradients
---> 56     dWo, dBo, dWh, dBh = backpropagation(X_train, Y_train_onehot)
     58     # regularization term gradients
     59     dWo += lmbd * output_weights

Input In [26], in backpropagation(X, Y)
     32 def backpropagation(X, Y):
---> 33     a_h, probabilities = feed_forward_train(X)
     35     # error in the output layer
     36     error_output = probabilities - Y

Input In [26], in feed_forward_train(X)
     18 z_h = np.matmul(X, hidden_weights) + hidden_bias
     19 # activation in the hidden layer
---> 20 a_h = sigmoid(z_h)
     22 # weighted sum of inputs to the output layer
     23 z_o = np.matmul(a_h, output_weights) + output_bias

Input In [25], in sigmoid(x)
      3 def sigmoid(x):
----> 4     return 1/(1 + np.exp(-x))

RuntimeWarning: overflow encountered in exp
RuntimeWarning: overflow encountered in exp