bias.py

import math
import random

class NeuralNetwork():
	def __init__(self):

		# Seed the random number generator, so we get the same random numbers each time
		random.seed(1)

		# Create 3 weights and set them to random values in the range -1 to +1
		self.weights = [random.uniform(-1, 1), random.uniform(-1, 1), random.uniform(-1, 1)]

		# Create a bias and set it to a random value in the range -1 to +1
		self.bias = random.uniform(-1, 1)

	# Make a prediction
	def think(self, neuron_inputs):
		sum_of_weighted_inputs = self.__sum_of_weighted_inputs(neuron_inputs)
		neuron_output = self.__sigmoid(sum_of_weighted_inputs + self.bias) 
		return neuron_output

	# Adjust the weights of the neural network to minimise the error for the training set
	def train(self, training_set_examples, number_of_iterations):
		for iteration in range(number_of_iterations):
			for training_set_example in training_set_examples:

				# Predict the output based on the training set example inputs
				predicted_output = self.think(training_set_example["inputs"])

				# Calculate the error as the difference between the desired output and the predicted output
				error_in_output = training_set_example["output"] - predicted_output

				# Iterate through the weights and adjust each one
				for index in range(len(self.weights)):

					# Get the neuron's input associated with this weight
					neuron_input = training_set_example["inputs"][index]

					# Calculate how much to adjust the weights by using the delta rule (gradient descent)
					adjust_weight = neuron_input * error_in_output * self.__sigmoid_gradient(predicted_output)

					# Adjust the weight
					self.weights[index] += adjust_weight

				# Adjust the bias
				self.bias += error_in_output * self.__sigmoid_gradient(predicted_output)


	# Calculate the sigmoid (our activation function)
	def __sigmoid(self, sum_of_weighted_inputs):
		return 1 / (1 + math.exp(-sum_of_weighted_inputs))

	# Calculate the gradient of the sigmoid using its own output	
	def __sigmoid_gradient(self, neuron_output):
		return neuron_output * (1 - neuron_output)

	# Multiply each input by its own weight, and then sum the total
	def __sum_of_weighted_inputs(self, neuron_inputs):
		sum_of_weighted_inputs = 0
		for index, neuron_input in enumerate(neuron_inputs):
			sum_of_weighted_inputs += self.weights[index] * neuron_input
		return sum_of_weighted_inputs

neural_network = NeuralNetwork()

print("Random starting weights: " + str(neural_network.weights))
print("Random starting bias: " + str(neural_network.bias))

# The neural network will use this training set of 4 examples, to learn the pattern
training_set_examples = [{"inputs": [0, 0, 1], "output": 0},
						{"inputs": [1, 1, 1], "output": 1},
						{"inputs": [1, 0, 1], "output": 1},
						{"inputs": [0, 1, 1], "output": 0}]

# Train the neural network using 10,000 iterations
neural_network.train(training_set_examples, number_of_iterations=10000)

print("New weights after training: " + str(neural_network.weights))
print("New bias after training: " + str(neural_network.bias))

# Make a prediction for a situation
new_situation = [0, 0, 0]
prediction = neural_network.think(new_situation)

print("Prediction for the situation " + str(new_situation) + " -> ? " + str(prediction))