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Delta rule

Delta rule

(also delta learning rule, delta rule algorithm)

Delta rule definition

The delta rule represents a gradient descent learning technique employed in artificial neural networks, particularly for instructing single-layer perceptrons. This method modifies the network’s weights by evaluating the disparity between the expected outcome and the genuine outcome. Commonly utilized in supervised learning scenarios, the delta rule lays the foundation for more sophisticated algorithms such as backpropagation.

See also: artificial intelligence, machine learning

Delta rule examples

  • Linear regression: In a simple linear regression problem, the delta rule can be used to adjust the weights for a single-layer perceptron to fit the data and minimize the error.
  • XOR problem: The delta rule is incapable of solving the XOR problem using a single-layer perceptron, demonstrating its limitations in solving nonlinear problems.

Comparing the delta rule with other learning algorithms

  • Backpropagation: Backpropagation extends the delta rule to multi-layer perceptrons, allowing for the training of more complex neural networks. It uses a similar weight adjustment mechanism but accounts for the hidden layers in the network.
  • Hebbian learning: Unlike the delta rule, Hebbian learning is an unsupervised learning algorithm based on the idea that neurons that fire together wire together. It does not rely on the comparison between desired and actual outputs to adjust weights.

Pros and cons of the delta rule


  • Simple and easy to implement.
  • Suitable for linearly separable problems.
  • Forms the basis for more advanced learning algorithms.


  • Limited to single-layer perceptrons.
  • Ineffective for nonlinearly separable problems.
  • Can get stuck in local minima.

Tips for using the delta rule

  • Apply the delta rule when dealing with linearly separable problems.
  • For nonlinear problems, consider using backpropagation or other advanced learning algorithms.
  • Experiment with different learning rates to avoid getting stuck in local minima.

Further reading

Ultimate digital security