## The Vation Ventures Glossary

# Backpropagation: Definition, Explanation, and Use Cases

Backpropagation, a term that is frequently used in the field of artificial intelligence (AI), is a method used in training artificial neural networks. This method is fundamental to the operation of many AI systems, and it is crucial to understand its definition, explanation, and use cases to fully comprehend the intricacies of AI. This article will delve into the depths of backpropagation, providing a comprehensive understanding of this critical concept.

Backpropagation is an abbreviation for "backward propagation of errors," and it is a method used to calculate the gradient of a loss function in a neural network. It is a crucial part of the learning process for neural networks, as it is the mechanism that updates the weights of the network, based on the error rate (the difference between the network's output and its expected output). The backpropagation algorithm uses these error rates to go backwards through the network, from the output layer to the input layer, adjusting the weights as it goes.

## Definition of Backpropagation

The term backpropagation refers to a specific algorithm for how weights in a neural network are updated in reverse order at the end of each training epoch. It is a two-step process: propagation and weight update. During propagation, the input data is passed forward through the network, and the output is compared with the expected result. This produces an error value for each neuron in the output layer. During the weight update, this error value is distributed back through the network, giving each neuron an error value that reflects its contribution to the original output. This error value is then used to adjust the weights of each neuron during the next training epoch.

Backpropagation is a gradient descent algorithm, which means it finds the minimum of a function (in this case, the error function) by moving in the direction of steepest descent as defined by the negative of the function's gradient. In the context of neural networks, the gradient is the change in error with respect to the change in weights, and the steepest descent is the direction that will reduce the error the most.

### Propagation

In the propagation phase, the input data is passed forward through the network. Each neuron takes the weighted sum of its input, applies a function (usually a non-linear function like a sigmoid or ReLU), and passes the result to the next layer. This process continues until the output layer is reached. The output of the network is then compared to the expected output, and an error value is calculated for each neuron in the output layer. This error value is a measure of how much the actual output of the network deviates from the expected output.

The error value for each neuron in the output layer is then used to calculate the error value for each neuron in the hidden layers. This is done by distributing the error values back through the network, in reverse order of the layers. The error value for each neuron in the hidden layers is a weighted sum of the error values of the neurons in the layer below it, where the weights are the weights of the connections between the neurons. This process continues until an error value has been calculated for every neuron in the network.

### Weight Update

Once the error values have been calculated for all neurons in the network, the weights of the network can be updated. The change in weight for a connection between two neurons is proportional to the product of the error value of the neuron at the end of the connection, and the output of the neuron at the start of the connection. This means that if a neuron has a high error value, the weights of its incoming connections will be adjusted more than if it had a low error value. Similarly, if a neuron has a high output, the weights of its incoming connections will be adjusted more than if it had a low output.

The proportionality constant for the weight update is the learning rate. The learning rate is a hyperparameter that determines how much the weights are adjusted at each update. A high learning rate means the weights are adjusted a lot, which can lead to faster learning, but also to overshooting the minimum of the error function. A low learning rate means the weights are adjusted a little, which can lead to slower learning, but also to more precise convergence to the minimum of the error function.

## Explanation of Backpropagation

Backpropagation is a way of training a neural network by adjusting its weights to minimize the error of its output. The error of the output is a measure of how far the actual output of the network is from the expected output. By adjusting the weights in the direction that reduces the error, the network can learn to produce more accurate outputs.

The backpropagation algorithm is based on the chain rule of calculus. The chain rule states that the derivative of a composite function is the product of the derivatives of the functions that make up the composite function. In the context of a neural network, the composite function is the function that takes the input to the network and produces the output, and the functions that make up the composite function are the functions applied by each neuron in the network.

### Chain Rule

The chain rule is a fundamental concept in calculus that is used to calculate the derivative of a composite function. A composite function is a function that is composed of two or more other functions. For example, if we have a function f(x) = g(h(x)), then f is a composite function composed of g and h.

In the context of backpropagation, the chain rule is used to calculate the derivative of the error function with respect to the weights. The error function is a composite function that is composed of the functions applied by each neuron in the network. The derivative of the error function with respect to the weights tells us how much the error changes when we change the weights. This is the information we need to adjust the weights in the direction that reduces the error.

### Gradient Descent

Gradient descent is a method for finding the minimum of a function. It works by starting at a random point on the function, calculating the gradient of the function at that point, and then taking a step in the direction of steepest descent. The size of the step is determined by the learning rate. This process is repeated until the minimum of the function is found.

In the context of backpropagation, gradient descent is used to find the weights that minimize the error function. The error function is a measure of how far the actual output of the network is from the expected output. By adjusting the weights in the direction of steepest descent of the error function, the network can learn to produce more accurate outputs.

## Use Cases of Backpropagation

Backpropagation is used in a wide range of applications in the field of artificial intelligence. It is the standard method for training artificial neural networks, which are used in everything from image recognition to natural language processing to autonomous driving. Any application that uses a neural network likely uses backpropagation to train that network.

For example, in image recognition, a neural network is trained to recognize images of certain objects. The network is trained by showing it images of the objects and adjusting the weights of the network using backpropagation until the network can accurately recognize the objects. Similarly, in natural language processing, a neural network is trained to understand and generate human language. The network is trained by showing it examples of human language and adjusting the weights of the network using backpropagation until the network can accurately understand and generate human language.

### Image Recognition

Image recognition is a common application of artificial neural networks, and by extension, backpropagation. In image recognition, a neural network is trained to recognize certain objects or features in images. The network is trained by showing it images of the objects or features it is supposed to recognize, and adjusting the weights of the network using backpropagation until the network can accurately recognize the objects or features.

For example, a neural network might be trained to recognize images of cats. The network would be shown images of cats and other animals, and the weights of the network would be adjusted using backpropagation until the network could accurately distinguish images of cats from images of other animals. Once the network is trained, it can be used to recognize cats in new images that it has not seen before.

### Natural Language Processing

Natural language processing (NLP) is another common application of artificial neural networks, and by extension, backpropagation. In NLP, a neural network is trained to understand and generate human language. The network is trained by showing it examples of human language, and adjusting the weights of the network using backpropagation until the network can accurately understand and generate human language.

For example, a neural network might be trained to translate English to French. The network would be shown pairs of English and French sentences, and the weights of the network would be adjusted using backpropagation until the network could accurately translate English sentences into French. Once the network is trained, it can be used to translate new English sentences that it has not seen before.

### Autonomous Driving

Autonomous driving is a cutting-edge application of artificial neural networks, and by extension, backpropagation. In autonomous driving, a neural network is trained to control a vehicle. The network is trained by showing it examples of good driving, and adjusting the weights of the network using backpropagation until the network can accurately control a vehicle.

For example, a neural network might be trained to control a self-driving car. The network would be shown video footage of human drivers controlling a car, and the weights of the network would be adjusted using backpropagation until the network could accurately control a car in a similar way. Once the network is trained, it can be used to control a self-driving car in real-world conditions.

## Conclusion

Backpropagation is a fundamental concept in the field of artificial intelligence. It is the method used to train artificial neural networks, which are the basis for many AI systems. Understanding backpropagation is crucial for anyone who wants to understand how these systems work.

Backpropagation is a complex algorithm, but it can be understood by breaking it down into its components: propagation, weight update, the chain rule, and gradient descent. By understanding these components, one can gain a deep understanding of backpropagation and its role in training neural networks.

The use cases of backpropagation are vast and varied, ranging from image recognition to natural language processing to autonomous driving. Any application that uses a neural network likely uses backpropagation to train that network. As such, understanding backpropagation is not only important for understanding how these applications work, but also for developing new applications.

In conclusion, backpropagation is a key concept in artificial intelligence that is worth understanding in depth. It is the backbone of many AI systems, and its understanding can open the door to a deeper understanding of artificial intelligence as a whole.