# Intuition behind using the inverse of a Hessian matrix for automatically estimating the learning rate (aggression parameter) in gradient descent.

I am reviewing some course material where the lecturer suggests that instead of guessing the learning rate parameter in gradient descent implementation, one could use the inverse of the Hessian multiplied by the negative of the Jacobian, to determine the step-size.

Any help with the intuition behind using the inverse of the Hessian would be much appreciated.

Say you have $$f(x)=f(x_n+\Delta x)=f(x_n)+f'(x_n)\Delta x + f''(x_n)\Delta x^2$$ and you want to get to a point where $$f'(x) = 0$$, then you will use $$\Delta x=-\frac{f'(x_n)}{f''(x_n)}$$.
Generalizing to n dimension, $$f''$$ is the Hessian of the equation.