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Maria88
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What is "Negative Gradient" ? and what is "Gradient Descent Method" ? What is the difference and relationship between them ?
What is the benefit each of them ?
What is the benefit each of them ?
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thanks a lotjtbell said:Do you know how to calculate the gradient of a function, in vector calculus, and what it means geometrically?
A negative gradient is a slope that is decreasing in the direction of the steepest descent. It is the opposite of a positive gradient, which represents an increasing slope. In mathematics and science, a gradient is a vector that points in the direction of the steepest increase of a function.
The negative gradient is an essential component of the gradient descent method. It is used to find the minimum value of a function by iteratively adjusting the parameters of the function in the direction of the negative gradient. By following the negative gradient, the algorithm can reach the minimum value of the function and find the optimal solution.
The negative gradient is directly related to the convergence of the gradient descent method. As the algorithm approaches the minimum value of the function, the magnitude of the negative gradient decreases, indicating that the algorithm is getting closer to the optimal solution. Eventually, the negative gradient becomes zero when the algorithm reaches the minimum value, and the convergence is achieved.
Yes, a negative gradient can lead to overshooting in gradient descent if the learning rate is too high. The learning rate determines the size of the steps taken in the direction of the negative gradient. If the learning rate is too high, the algorithm may overshoot the minimum value and oscillate around it, making it difficult to converge.
The negative gradient is calculated by taking the derivative of the objective function with respect to each of the parameters. This results in a vector that points in the direction of the steepest decrease of the function. The negative gradient is then multiplied by the learning rate and subtracted from the current parameter values to update them in the direction of the negative gradient.