As far as I understand, gradients are supposed to tell us 1) the magnitude and 2) direction, to update a parameter such as to minimize the loss function.

Regarding saliency maps, which use gradients with respect to the input, do the gradients give us the same information?

Consider vanilla saliency maps [1] (i.e. gradients-only) and integrated-gradients [2] (using a baseline image), with grayscale images.

Do the (vanilla) gradients give us the amount and direction a pixel-value needs to change? OR does the magnitude tell us for the amount of in loss based on a minimal change in pixel-value?

In simpler terms: does magnitude signify:

  1. amount of change required in a pixel-value to have some change (in loss?) or

  2. amount of change in (loss?) based on a minimal/local change in pixel-value?

  • $\begingroup$ Saliency Map: arxiv.org/abs/1312.6034 (Specifically section 3) Integrated Gradients: arxiv.org/abs/1703.01365 $\endgroup$
    – user452306
    Commented Dec 6, 2021 at 13:12
  • 1
    $\begingroup$ I believe the magnitude will be related to how sensitive that input variable is. That is: If you only look at the gradient of the output with respect to the input: then a change of a specific input feature, then the gradient is how much it will affect the output. So: a small change in input could be a large change in output. If you want more interpretation on what it means, it would vastly change based on implementation and is problem specific. $\endgroup$ Commented Dec 7, 2021 at 13:30


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