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(also backward propagation of errors, backprop)

Backpropagation definition

Backpropagation is an algorithm used in machine learning. It is applied in training feedforward neural networks (artificial neural networks wherein a circle is not formed out of connections between nodes) as well as other parameterized networks that contain differentiable nodes. Backpropagation is an example of efficient application of the Leibniz chain rule to such networks.

A method employed for training artificial neural networks in the context of supervised learning. Backpropagation computes the gradient of the loss function concerning each weight utilizing the chain rule, determining the gradient for each layer sequentially and iterating in reverse from the final layer to reduce the discrepancy between the predicted and actual outputs. This modification of weights enables the neural network to enhance its learning capabilities and overall performance.

See also: artificial intelligence, machine learning

Backpropagation examples

  • Image recognition: Backpropagation is applied to train deep learning models like convolutional neural networks (CNNs) for recognizing objects within images.
  • Natural language processing: Backpropagation is used to train recurrent neural networks (RNNs) and transformer-based models for various language tasks, such as translation, sentiment analysis, and text generation.

Backpropagation vs. other optimization algorithms

Gradient descent and its variants, like stochastic gradient descent (SGD) and mini-batch gradient descent, are optimization algorithms that use backpropagation to compute gradients. Other optimization algorithms, like genetic algorithms and particle swarm optimization, do not rely on backpropagation for training neural networks.

Pros and cons of backpropagation


  • Efficient: It calculates gradients in a computationally efficient manner, making it suitable for large-scale problems.
  • Widely used: Backpropagation is a well-established technique and forms the basis for many state-of-the-art machine learning models.


  • Local minima: The algorithm can get stuck in local minima (a point where the objective value of the function is lower than the one of its neighbors but still higher than the global minimum), resulting in suboptimal solutions.
  • Vanishing gradients: For deep neural networks, gradients can become very small, slowing down learning or causing it to stop altogether.

Tips for using backpropagation

  • Experiment with different activation functions to avoid issues like vanishing gradients.
  • Use adaptive learning rate optimizers like Adam or RMSprop to speed up convergence.

Further reading

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