神经网络前向传播python编程练习

神经网络

1.Coding the single forward propagation algorithm

本文的PPT你可以从这里下载

In this exercise, you'll write code to do forward propagation (prediction) for your first neural network:

Each data point is a customer. The first input is how many accounts they have, and the second input is how many children they have. The model will predict how many transactions the user makes in the next year. You will use this data throughout the first 2 chapters of this course.

The input data has been pre-loaded as input_data, and the weights are available in a dictionary called weights. The array of weights for the first node in the hidden layer are in weights['node_0'], and the array of weights for the second node in the hidden layer are in weights['node_1']

The weights feeding into the output node are available in weights ['output'].

NumPy will be pre-imported for you as np in all exercises

Calculate the value in node 0 by multiplying input_data by its weights weights['node_0'] and computing their sum. This is the 1st node in the hidden layer.
Calculate the value in node 1 using input_data and weights['node_1']. This is the 2nd node in the hidden layer.
Put the hidden layer values into an array. This has been done for you.
Generate the prediction by multiplying hidden_layer_outputs by weights['output'] and computing their sum.

In [1]: import numpy as np
In [2]: input_data = np.array([2, 3])
In [3]: weights = {'node_0': np.array([1, 1]),
 ...:              'node_1': np.array([-1, 1]),
 ...:              'output': np.array([2, -1])}
In [4]: node_0_value = (input_data * weights['node_0']).sum()
In [5]: node_1_value = (input_data * weights['node_1']).sum()
# Calculate node 0 value: node_0_value
node_0_value = (input_data * weights['node_0']).sum()
# Calculate node 1 value: node_1_value
node_1_value = (input_data * weights['node_1']).sum()
# Put node values into array: hidden_layer_outputs
hidden_layer_outputs = np.array([node_0_value, node_1_value])
# Calculate output: output
output = (hidden_layer_outputs * weights['output']).sum()
# Print output
print(output)

Activation function Relu

def relu(input):
    '''Define your relu activation function here'''
    # Calculate the value for the output of the relu function: output
    output = max(input, 0)
    # Return the value just calculated
    return(output)
# Calculate node 0 value: node_0_output
node_0_input = (input_data * weights['node_0']).sum()
node_0_output = relu(node_0_input)
# Calculate node 1 value: node_1_output
node_1_input = (input_data * weights['node_1']).sum()
node_1_output = relu(node_1_input)
# Put node values into array: hidden_layer_outputs
hidden_layer_outputs = np.array([node_0_output, node_1_output])
# Calculate model output (do not apply relu)
model_output = (hidden_layer_outputs * weights['output']).sum()
# Print model output
print(model_output)

Execution of the FP Network

# Define predict_with_network()
def predict_with_network(input_data_row, weights):
    # Calculate node 0 value
    node_0_input = (input_data_row * weights['node_0']).sum()
    node_0_output = relu(node_0_input)
    # Calculate node 1 value
    node_1_input = (input_data_row * weights['node_1']).sum()
    node_1_output = relu(node_1_input)
    # Put node values into array: hidden_layer_outputs
    hidden_layer_outputs = np.array([node_0_output, node_1_output])
    # Calculate model output
    input_to_final_layer = (hidden_layer_outputs * weights['output']).sum()
    model_output = relu(input_to_final_layer)
    # Return model output
    return(model_output)
# Create empty list to store prediction results
results = []
for input_data_row in input_data:
    # Append prediction to results
    results.append(predict_with_network(input_data_row, weights))
# Print results
print(results)

2.Coding the multi-hidden-layer forward propagation

Multi-layer neural networks

In this exercise, you'll write code to do forward propagation for a neural network with 2 hidden layers. Each hidden layer has two nodes. The input data has been preloaded as input_data. The nodes in the first hidden layer are called node_0_0 and node_0_1. Their weights are pre-loaded as weights['node_0_0'] and weights['node_0_1'] respectively.

The nodes in the second hidden layer are called node_1_0 and node_1_1. Their weights are pre-loaded as weights['node_1_0'] and weights['node_1_1'] respectively.

We then create a model output from the hidden nodes using weights pre-loaded as weights['output'].

def predict_with_network(input_data):
    # Calculate node 0 in the first hidden layer
    node_0_0_input = (input_data * weights['node_0_0']).sum()
    node_0_0_output = relu(node_0_0_input)
    # Calculate node 1 in the first hidden layer
    node_0_1_input = (input_data * weights['node_0_1']).sum()
    node_0_1_output = relu(node_0_1_input)
    # Put node values into array: hidden_0_outputs
    hidden_0_outputs = np.array([node_0_0_output, node_0_1_output])
    # Calculate node 0 in the second hidden layer
    node_1_0_input = (hidden_0_outputs * weights['node_1_0']).sum()
    node_1_0_output = relu(node_1_0_input)
    # Calculate node 1 in the second hidden layer
    node_1_1_input = (hidden_0_outputs * weights['node_1_1']).sum()
    node_1_1_output = relu(node_1_1_input)
    # Put node values into array: hidden_1_outputs
    hidden_1_outputs = np.array([node_1_0_output, node_1_1_output])
    # Calculate model output: model_output
    model_output = relu((hidden_1_outputs * weights['output']).sum())
    # Return model_output
    return(model_output)
output = predict_with_network(input_data)
print(output)