17. Training a Neural Network with Python

By Bernd Klein. Last modified: 19 Apr 2024.

Introduction

In the chapter Running Neural Networks, we programmed a class in Python code called 'NeuralNetwork'. The instances of this class are networks with three layers. When we instantiate an ANN of this class, the weight matrices between the layers are automatically and randomly chosen. It is even possible to run such a ANN on some input, but naturally it doesn't make a lot of sense exept for testing purposes. Such an ANN cannot provide correct classification results. In fact, the classification results are in no way adapted to the expected results. The values of the weight matrices have to be set according the the classification task. We need to improve the weight values, which means that we have to train our network. To train it we have to implement backpropagation in the train method. If you don't understand backpropagation and want to understand it, we recommend to go back to the chapter Backpropagation in Neural Networks.

After knowing und hopefully understanding backpropagation, you are ready to fully understand the train method.

The train method is called with an input vector and a target vector. The shape of the vectors can be one-dimensional, but they will be automatically turned into the correct two-dimensional shape, i.e. reshape(input_vector.size, 1) and reshape(target_vector.size, 1). After this we call the run method to get the result of the network output_vector_network = self.run(input_vector). This output may differ from the target_vector. We calculate the output_error by subtracting the output of the network output_vector_network from the target_vector.

%%writefile neural_networks1.py
import numpy as np
from scipy.special import expit as activation_function
from scipy.stats import truncnorm

def truncated_normal(mean=0, sd=1, low=0, upp=10):
    return truncnorm(
        (low - mean) / sd, (upp - mean) / sd, loc=mean, scale=sd)

class NeuralNetwork:
    
    def __init__(self, 
                 no_of_in_nodes, 
                 no_of_out_nodes, 
                 no_of_hidden_nodes,
                 learning_rate):
        self.no_of_in_nodes = no_of_in_nodes
        self.no_of_out_nodes = no_of_out_nodes
        self.no_of_hidden_nodes = no_of_hidden_nodes
        self.learning_rate = learning_rate 
        self.create_weight_matrices()
        
    def create_weight_matrices(self):
        """ A method to initialize the weight matrices of the neural network"""
        rad = 1 / np.sqrt(