What is backpropagation?
by Stephen M. Walker II, CoFounder / CEO
What is backpropagation?
Backpropagation is a widelyused algorithm for training artificial neural networks (ANNs) by adjusting their weights and biases to minimize a loss function, which measures the difference between the predicted and actual output values. The name "backpropagation" refers to the fact that the algorithm propagates error signals backwards through the network, from the output layer to the input layer, in order to update the weights of each neuron based on their contribution to the overall error.
The basic steps of backpropagation are as follows:
 Forward pass — Given an input
x
and a set of weights and biases for each layer of the network, the forward pass computes the activations of all neurons in the network by applying nonlinear activation functions to their weighted sums (also known as "preactivations"). The output of the final layer is then compared with the desired target valuey
.  Error calculation — The difference between the predicted output
y_pred
and the actual target valuey
is computed using a loss function, such as mean squared error (MSE) or crossentropy loss. This loss value represents the overall error of the network for that specific input example.  Gradient computation — The gradient of the loss function with respect to each weight and bias in the network is calculated using the chain rule of calculus, which allows us to backpropagate the error signal from the output layer all the way to the input layer by multiplying the partial derivatives of the activation functions at each neuron.
 Weight update — The calculated gradients are then used to update the weights and biases of each neuron in the network using a learning rate
α
, which controls the step size of the weight update. This is done according to the following formula:
wherew_new = w_old  α * gradient_w b_new = b_old  α * gradient_b
w_old
andb_old
represent the old weights and biases, respectively, andgradient_w
andgradient_b
represent the gradients of the loss function with respect to each weight and bias, respectively.  Repeat — Steps 14 are repeated for all input examples in a training dataset, typically using stochastic gradient descent (SGD) or one of its variants, such as minibatch SGD or Adam. The network's weights and biases are updated iteratively after each pass through the entire dataset, which is called an "epoch".
Backpropagation is a crucial component of many deep learning architectures, including convolutional neural networks (CNNs), recurrent neural networks (RNNs), and transformers. It enables these models to learn complex representations of data by adjusting their internal parameters in response to feedback from the environment, leading to improved performance on various tasks, such as image classification, speech recognition, and natural language processing.
What are the benefits of backpropagation?
Backpropagation is a widelyused method for training artificial neural networks, and it offers several benefits. These include:
 Efficient computation: Backpropagation efficiently computes the gradient of the loss function with respect to the weights in a neural network. This makes it suitable for large networks and complex data sets.
 Automatic differentiation: The method allows for automatic differentiation, which is important when dealing with complex functions. It reduces the need for manual calculations and helps minimize errors that may occur during this process.
 Flexibility in model design: Backpropagation can be applied to various types of neural networks, such as feedforward networks, recurrent networks, and convolutional networks, allowing researchers and developers to experiment with different architectures.
 Convergence properties: In many cases, backpropagation converges to a minimum or nearminimum of the loss function, leading to improved performance in terms of prediction accuracy.
 Computational efficiency: Backpropagation can be implemented efficiently using gradient descent algorithms, making it faster and more computationally efficient than other training methods.
What are the drawbacks of backpropagation?
Some drawbacks of backpropagation include:

Gradient vanishing or exploding: Backpropagation can suffer from the issue of either gradient values becoming too small (vanishing gradients) or too large (exploding gradients), making it difficult for the algorithm to learn effectively.

Sensitivity to initial weights: The performance of backpropagation is highly dependent on the initial weight values assigned to the network. If these values are poorly chosen, the algorithm may get stuck in local minima or fail to converge.

Lack of generalization: Backpropagation can lead to overfitting, where the model learns the training data too well but performs poorly on new, unseen data. This is due to its focus on minimizing the error for each individual training example, rather than considering the overall performance on the entire dataset.

Slow convergence: Backpropagation can be computationally intensive and slow to converge, especially in large networks with many layers or weights.

Difficulty in handling discrete data: Backpropagation is mainly designed for continuous input and output values, making it less suitable for tasks involving discrete or categorical data.
How can backpropagation be improved?
There are several ways to improve the performance of backpropagation and address some of its drawbacks:
 Regularization techniques: Techniques like dropout, weight decay, and early stopping can help prevent overfitting by limiting the complexity of the learned model and improving its ability to generalize to new data.
 Normalization methods: Batch normalization or layer normalization can help stabilize the learning process by standardizing input values across batches or layers, reducing the risk of gradient vanishing or exploding.
 Better initialization strategies: Using techniques like Xavier initialization or He initialization can help ensure that the initial weights are chosen in a way that promotes efficient learning and avoids getting stuck in local minima.
 Adaptive learning rates: Algorithms like Adam, AdaGrad, and RMSprop adjust the learning rate dynamically during training, allowing for faster convergence and better overall performance.
 Improved optimization methods: Using advanced optimization techniques like stochastic gradient descent with momentum or Nesterov accelerated gradient can help speed up the training process and improve the quality of the learned model.