Neural networks are the core of deep learning, a field that has practical applications in many different areas. Today neural networks are used for image classification, speech recognition, object detection, etc. Now, Let’s try to understand the basic unit behind all these states of art techniques.
A single neuron transforms given input into some output. Depending on the given input and weights assigned to each input, decide whether the neuron fired or not. Let’s assume the neuron has 3 input connections and one output.
We will be using tanh activation function in a given example.
The end goal is to find the optimal set of weights for this neuron that produces correct results. Do this by training the neuron with several different training examples. At each step calculate the error in the output of the neuron, and backpropagate the gradients. The step of calculating the output of a neuron is called forward propagation while the calculation of gradients is called back propagation.
Below is the implementation :
Python3
# Python program to implement a # single neuron neural network# import all necessary librariesfrom numpy import exp, array, random, dot, tanh# Class to create a neural # network with single neuronclass NeuralNetwork(): def __init__(self): # Using seed to make sure it'll # generate same weights in every run random.seed(1) # 3x1 Weight matrix self.weight_matrix = 2 * random.random((3, 1)) - 1 # tanh as activation function def tanh(self, x): return tanh(x) # derivative of tanh function. # Needed to calculate the gradients. def tanh_derivative(self, x): return 1.0 - tanh(x) ** 2 # forward propagation def forward_propagation(self, inputs): return self.tanh(dot(inputs, self.weight_matrix)) # training the neural network. def train(self, train_inputs, train_outputs, num_train_iterations): # Number of iterations we want to # perform for this set of input. for iteration in range(num_train_iterations): output = self.forward_propagation(train_inputs) # Calculate the error in the output. error = train_outputs - output # multiply the error by input and then # by gradient of tanh function to calculate # the adjustment needs to be made in weights adjustment = dot(train_inputs.T, error * self.tanh_derivative(output)) # Adjust the weight matrix self.weight_matrix += adjustment# Driver Codeif __name__ == "__main__": neural_network = NeuralNetwork() print ('Random weights at the start of training') print (neural_network.weight_matrix) train_inputs = array([[0, 0, 1], [1, 1, 1], [1, 0, 1], [0, 1, 1]]) train_outputs = array([[0, 1, 1, 0]]).T neural_network.train(train_inputs, train_outputs, 10000) print ('New weights after training') print (neural_network.weight_matrix) # Test the neural network with a new situation. print ("Testing network on new examples ->") print (neural_network.forward_propagation(array([1, 0, 0]))) |
Output :
Random weights at the start of training [[-0.16595599] [ 0.44064899] [-0.99977125]] New weights after training [[5.39428067] [0.19482422] [0.34317086]] Testing network on new examples -> [0.99995873]
