Nesterov momentum, or Nesterov Accelerated Gradient (NAG), is a slightly modified version of Momentum with stronger theoretical convergence guarantees for convex functions. In practice, it has produced slightly better results than classical Momentum.

In the standard Momentum method, the gradient is computed using current parameters (* θt*). Nesterov momentum achieves stronger convergence by applying the velocity (

*) to the parameters in order to compute interim parameters (*

**vt**

**θ̃ = θt+μ*vt***)*, where μ is the decay rate. These interim parameters are then used to compute the gradient, called a "lookahead" gradient step or a Nesterov Accelerated Gradient.

The reason this is sometimes referred to as a "lookahead" gradient is that computing the gradient based on interim parameters allow NAG to change velocity in a faster and more responsive way, resulting in more stable behavior than classical Momentum in many situations, particularly for higher values of *μ. *NAG is the correction factor for classical Momentum method.

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### Further reading

CS231n Convolutional Neural Networks for Visual Recognition

Stanford Computer Science

Web

Momentum Method and Nesterov Accelerated Gradient - Konvergen - Medium

Roan Gylberth

Web

On the importance of initialization and momentum in deep learning

Ilya Sutskever, James Martens, George Dahl, Geoffrey Hinton