The Gradient Function

Gradient function We are trying to find a formula (gradient function) for calculating the slope of an arbitrary line, but probably it is the simplest equation, so in simple cases such as g = c 2, g = c, g = c 3 Start with. Since they may not be that complicated, I would like to see an official former formula that is easier to find more complicated equations. Let's first look at g = c 2 lines. g = c 2 c 1 2 3 4 g 1 4 9 16 Look at the chart on the other sheet One of the most obvious things I noticed is that the gradation increases as the coordinates increase.

Back-prop is a way to calculate the partial derivative (or slope) of a function. It has the form of a combination of functions (as in the case of a neural network). If you solve the optimization problem using a gradient-based approach (gradient descent is one of them), calculate the function gradient at each iteration. In the case of a neural network, the objective function takes a join form. How do you calculate the gradient? There are two general ways to do this. (I) Analyze differentiation. You know the format of the function. Only the chain rule (basic calculation) is necessary to calculate the derivative. (Ii) Approximate differentiation using finite differences. In this method, since the number of function evaluations is O (N), calculation cost is required. Where N is the number of parameters. This is more expensive than analyzing the difference. However, limited differences are often used to verify the implementation of reverse support during debugging.

The gradient descent is the first-order iterative optimization algorithm used to find the minimum of the function. In order to find the minimum value of a function using gradient descent, a step size proportional to the negative value (or approximate slope) of the slope of the function at the current point is needed. Conversely, if you use a step size proportional to the positive value of the gradient, it approaches the maximum of the function and the process is called a gradient rise. So I hope the sequence converges to the required minimum value. The allowable step size value changes from iteration to iteration. Certain assumptions about functions (eg convex and Lipschitz) and specific choices (eg choice of line search or Barzilai-Borwein method satisfying Wolfe condition)