Timeline for Is there a full and precise formulation of Theorem 1 in the Integrated Gradients paper?
Current License: CC BY-SA 4.0
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| Aug 15, 2021 at 21:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 17, 2021 at 20:48 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 18, 2021 at 20:30 | answer | added | mlerma54 | timeline score: 1 | |
| Mar 11, 2021 at 1:52 | comment | added | mlerma54 | Back to Proposition 1, for univariate functions the condition should be "absolutely continuous" (rather than differentiable almost everywhere) - this leads to a suitable generalization of the Fundamental Theorem of Calculus that can be applied to functions occurring in deep networks, but I am still wondering how to generalize the gradient theorem in a similar way so it can be applied to functions implemented by deep networks. That generalization would contain premises to be used in the formulation of Theorem 1. | |
| Mar 10, 2021 at 16:51 | comment | added | mlerma54 | Well, I just realized that Proposition 1 in the paper cannot be correct as stated either. In one dimension that proposition is just the (second) Fundamental Theorem of Calculus stated for functions that verify Lebesgue’s integrability criterion, but Cantor's staircase function is a well known counter-example showing that such condition is not enough to ensure the conclusion of the FTC. The premises of the proposition would need to be relaxed somehow, but still keeping them strong enough to be applied to deep networks with functions such as ReLu and max pooling. | |
| Mar 8, 2021 at 9:55 | history | edited | nbro | CC BY-SA 4.0 |
added 76 characters in body; edited tags; edited title
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| Mar 7, 2021 at 19:11 | review | First posts | |||
| Mar 8, 2021 at 5:21 | |||||
| Mar 7, 2021 at 19:10 | history | asked | mlerma54 | CC BY-SA 4.0 |