As you can see, the gradient is perfectly well defined without coordinates. What Alice and Bob will not agree on, is the coordinate expression of their gradients.

In my AI textbook there is this paragraph, without any explanation. The sigmoid function is defined as follows $$\\sigma (x) = \\frac{1}{1+e^{-x}}.$$ This function is easy to differentiate

In sum, the gradient is a vector with the slope of the function along each of the coordinate axes whereas the directional derivative is the slope in an arbitrary specified direction.

We just learned what the gradient of a function is. It means the largest change in a function. It is the directional derivative. However I have also seen notation that lists the gradient squared ...

Mar 17, 2021 · Could anyone explain in simple words (and maybe with an example) what the difference between the gradient and the Jacobian is? The gradient is a vector with the partial …

the gradient is a vector, whose components are derivatives of your function in variable $x_i$. So the first component of your gradient is $2 (x_1-a)$

Sep 11, 2020 · The Dirac Delta is simply NOT a function (it is a Generalized Function). And use of an integral operator symbol to represent the functional $\langle \delta,\phi\rangle$ is abuse of …

Mar 20, 2015 · Gradient function of a circle Ask Question Asked 10 years, 7 months ago Modified 5 years, 5 months ago

May 13, 2020 · From my understanding, The gradient is the slope of the most rapid descent. Modifying your position by descending along this gradient will most rapidly cause your cost …

Sep 5, 2019 · The function is two-dimensional, as in, it takes in two real numbers as input. The domain of the function is the plane, so the gradient also lives in the plane. Yes, the graph is …