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%ما هو (من)٪ 1 - تعريف
Gradient descent
![An animation showing the first 83 iterations of gradient descent applied to this example. Surfaces are [[isosurface]]s of <math>F(\mathbf{x}^{(n)})</math> at current guess <math>\mathbf{x}^{(n)}</math>, and arrows show the direction of descent. Due to a small and constant step size, the convergence is slow.](https://commons.wikimedia.org/wiki/Special:FilePath/Gradient Descent Example Nonlinear Equations.gif?width=200 "An animation showing the first 83 iterations of gradient descent applied to this example. Surfaces are [[isosurface]]s of <math>F(\mathbf{x}^{(n)})</math> at current guess <math>\mathbf{x}^{(n)}</math>, and arrows show the direction of descent. Due to a small and constant step size, the convergence is slow.")
![Illustration of gradient descent on a series of [[level set]]s](https://commons.wikimedia.org/wiki/Special:FilePath/Gradient descent.svg?width=200 "Illustration of gradient descent on a series of [[level set]]s")
.jpg?width=200 "Fog in the mountains")
![The steepest descent algorithm applied to the [[Wiener filter]]<ref>Haykin, Simon S. Adaptive filter theory. Pearson Education India, 2008. - p. 108-142, 217-242</ref>](https://commons.wikimedia.org/wiki/Special:FilePath/Steepest descent.png?width=200 "The steepest descent algorithm applied to the [[Wiener filter]]<ref>Haykin, Simon S. Adaptive filter theory. Pearson Education India, 2008. - p. 108-142, 217-242</ref>")
OPTIMIZATION ALGORITHM
Steepest descent; Gradient ascent; Gradient descent method; Steepest ascent; Gradient Descent; Gradient descent optimization; Gradient-based optimization; Gradient descent with momentum
In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent.
Stochastic gradient descent
OPTIMIZATION ALGORITHM
Gradient descent in machine learning; Incremental gradient descent; AdaGrad; Adagrad; Adam (optimization algorithm); Momentum (machine learning); RMSProp; Applications of stochastic gradient descent; Stochastic Gradient Descent; SGD optimizer; Adam optimizer; RMSprop
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g.
Gradient
![''f''(''x'',''y'') {{=}} −(cos<sup>2</sup>''x'' + cos<sup>2</sup>''y'')<sup>2</sup>}} depicted as a projected [[vector field]] on the bottom plane.](https://commons.wikimedia.org/wiki/Special:FilePath/3d-gradient-cos.svg?width=200 "''f''(''x'',''y'') {{=}} −(cos<sup>2</sup>''x'' + cos<sup>2</sup>''y'')<sup>2</sup>}} depicted as a projected [[vector field]] on the bottom plane.")
MULTI-VARIABLE GENERALIZATION OF THE DERIVATIVE
Gradient vector; Gradients; Gradient (calculus); Gradient of a scalar; Gradient Operator; Grad operator
·adj Moving by steps; walking; as, gradient automata.
II. Gradient ·adj Adapted for walking, as the feet of certain birds.
III. Gradient ·noun The rate of regular or graded ascent or descent in a road; grade.
IV. Gradient ·noun A part of a road which slopes upward or downward; a portion of a way not level; a grade.
V. Gradient ·adj Rising or descending by regular degrees of inclination; as, the gradient line of a railroad.
VI. Gradient ·noun The rate of increase or decrease of a variable magnitude, or the curve which represents it; as, a thermometric gradient.
