human
I am working on the file "1_dlnd-your-first-neural-network/dlnd-your-first-neural-network.ipynb".
The first task is:
Time to build the network
Below you'll build your network. We've built out the structure and the backwards pass. You'll implement the forward pass through the network. You'll also set the hyperparameters: the learning rate, the number of hidden units, and the number of training passes.
The network has two layers, a hidden layer and an output layer. The hidden layer will use the sigmoid function for activations. The output layer has only one node and is used for the regression, the output of the node is the same as the input of the node. That is, the activation function is $f(x)=x$. A function that takes the input signal and generates an output signal, but takes into account the threshold, is called an activation function. We work through each layer of our network calculating the outputs for each neuron. All of the outputs from one layer become inputs to the neurons on the next layer. This process is called forward propagation.
We use the weights to propagate signals forward from the input to the output layers in a neural network. We use the weights to also propagate error backwards from the output back into the network to update our weights. This is called backpropagation.

Hint: You'll need the derivative of the output activation function ($f(x) = x$) for the backpropagation implementation. If you aren't familiar with calculus, this function is equivalent to the equation $y = x$. What is the slope of that equation? That is the derivative of $f(x)$.

Below, you have these tasks:
1. Implement the sigmoid function to use as the activation function. Set self.activation_function in __init__ to your sigmoid function.
2. Implement the forward pass in the train method.
3. Implement the backpropagation algorithm in the train method, including calculating the output error.
4. Implement the forward pass in the run method.
Can you write Python program for it?

Can you provide a the slope of that equation?
assistant
#Here is the slope of that equation.

class NeuralNetwork(object):
    def _forward_pass(self, inputs):
        outputs = {}
        # Hidden layer
        hidden_inputs = np.dot(self.weights_input_to_hidden, inputs)
        outputs['hidden'] = self.activation_function(hidden_inputs)

        # Output layer
        final_inputs = np.dot(self.weights_hidden_to_output, outputs['hidden'])
        outputs['final'] = final_inputs # Activation function: f(x) = x
        
        return outputs
    
    def _backward_pass(self, targets, outputs):
        
        output_errors = targets - outputs['final'] # 1x1
        
        # Calculate error gradients
        errors = {}
        errors['final'] = output_errors # Activation function: f(x) = x
        errors['hidden'] = np.dot(self.weights_hidden_to_output.T, errors['final']) * \
                                           outputs['hidden'] * (1-outputs['hidden']) 
        
        return errors
            
    def _weight_update(self, errors, inputs, outputs):
        self.weights_hidden_to_output += self.lr * np.dot(errors['final'], outputs['hidden'].T)
        self.weights_input_to_hidden += self.lr * np.dot(errors['hidden'], inputs.T)
    
    def __init__(self, input_nodes, hidden_nodes, output_nodes, learning_rate):
        
        # Set number of nodes in input, hidden and output layers.
        self.input_nodes = input_nodes
        self.hidden_nodes = hidden_nodes
        self.output_nodes = output_nodes

        # Initialize weights
        self.weights_input_to_hidden = np.random.normal(0.0, self.hidden_nodes**-0.5, 
                                       (self.hidden_nodes, self.input_nodes))

        self.weights_hidden_to_output = np.random.normal(0.0, self.output_nodes**-0.5, 
                                       (self.output_nodes, self.hidden_nodes))
        self.lr = learning_rate
        
        # Activation function is the sigmoid function
        self.activation_function = lambda x : 1/(1+np.exp(-x))
    
    def train(self, inputs_list, targets_list):
        
        # Using...