Backpropagation. How a neural network learns? Code backpropagation. single-neuron neural network

What is Backpropagation?
Welcome to this enlightening video, where I will guide you through the process of implementing a single-neuron neural network from scratch. Throughout this tutorial, we will explore the core concepts that drive neural network training, including the forward pass, cost function, gradient descent, and the pivotal backpropagation algorithm. By mastering these foundational ideas, you will be well-equipped to tackle more complex neural network architectures.

To facilitate your understanding, we will delve into the mathematics behind backpropagation, specifically focusing on the calculus principles involved. In particular, we will explore the chain rule and its role in backpropagation, unraveling how it enables neural networks to optimize their performance.

Furthermore, we will embark on a hands-on journey by writing Python code to construct a simple yet powerful neural network. This practical implementation will enable you to witness the translation of concepts into executable code, solidifying your understanding and empowering you to explore and experiment further.

For your convenience, the code will be made available on GitHub, ensuring easy access and the ability to refer back to it whenever needed. This comprehensive resource will serve as a valuable reference for your ongoing neural network endeavors.

Prepare yourself for an engaging and enlightening experience as we unravel the intricacies of a single-neuron neural network. By mastering the mathematics behind backpropagation, specifically the chain rule, and gaining practical coding skills, you will be well-prepared to tackle more complex neural network architectures and unleash the full potential of this powerful technology. Join me on this educational journey, and together, let's build and expand upon our understanding of neural networks.

Backpropagation is an algorithm commonly used in training artificial neural networks, including multi-layer perceptrons (MLPs), to adjust the weights and biases of the network based on the error between the predicted output and the desired output. It is a key component of the learning process in neural networks.

The backpropagation algorithm works by propagating the error from the output layer of the neural network back to the input layer, adjusting the weights and biases of each neuron along the way. The goal is to minimize the error or loss function between the predicted output and the actual output.

To illustrate the backpropagation algorithm, let's consider an example with a single neuron in a neural network. Assume we have a neuron with two inputs, x1 and x2, and corresponding weights w1 and w2, with a bias term b. The output of the neuron is calculated as follows:

Output = sigmoid(w1x1 + w2x2 + b)

The sigmoid function is a common activation function used in neural networks to introduce non-linearity.

Now, let's say we have a desired output, y, and we want to adjust the weights and bias of the neuron to minimize the error between the predicted output and the desired output.

Forward Propagation:
First, we feed the inputs x1 and x2 through the neuron and calculate the predicted output using the current weights and bias.

Calculate the Error:
Next, we calculate the error between the predicted output and the desired output using a suitable loss function, such as the mean squared error (MSE).

Error = 0.5 * (y - Output)^2

Backpropagation:
To update the weights and bias, we need to calculate how the error changes with respect to each weight and bias in the neuron. This is done through backpropagation.
a. Calculate the gradient of the error with respect to the output:
delta = (Output - y) * sigmoid_derivative(Output)

The sigmoid_derivative() function computes the derivative of the sigmoid function with respect to its input.

b. Calculate the partial derivatives of the error with respect to the weights and bias:
dE/dw1 = delta * x1
dE/dw2 = delta * x2
dE/db = delta

Update the Weights and Bias:
Finally, we update the weights and bias using a learning rate (alpha) to control the size of the weight update.
w1 = w1 - alpha * dE/dw1
w2 = w2 - alpha * dE/dw2
b = b - alpha * dE/db

This process is repeated iteratively for a number of training examples, adjusting the weights and bias in the direction that reduces the error. By updating the weights and biases using the gradients calculated through backpropagation, the neural network can learn to make better predictions over time.

Note that this example demonstrates the backpropagation algorithm for a single neuron, but in practice, backpropagation is used to train multi-layer neural networks with multiple neurons in each layer.

Видео Backpropagation. How a neural network learns? Code backpropagation. single-neuron neural network канала Computer Science with Dr. RCB