IS-CAM formula error?
noobgrow opened this issue · 4 comments
🚀 Feature
https://frgfm.github.io/torch-cam/methods.html#activation-based-methods
Mk /ak formula of ISCAM in the link above is not the same as the original paper.
And I wonder if there is an original implement of ISCAM? Because I find that alpha calculated in paper is sumed by N time. But in your code it is sumed by k time.
Motivation & pitch
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Alternatives
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Additional context
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Hi @noobgrow 👋
Thanks for reporting this! So actually, the author reached out to me before the paper even came out to experiment with it. He validated the implementation back then, so I didn't question whether there would be some difference with the upcoming paper 😅
So let me check the difference you're talking about and get back to you 🙂
Cheers ✌️
So, this is going to be annoying without LaTex for math rendering, but let's try 😅
In the paper:
alpha_k^c = 1 / N * sum\limits_{i=0}^N (C(M_i))
# Let's expand M_i
alpha_k^c = 1 / N * sum\limits_{i=0}^N (C(sum\limits_{j=0}^{i-1} j / N * X_0 * A_l^k))
# Now we can simplify the sum
alpha_k^c = 1 / N * sum\limits_{i=0}^N (C(\frac{i * (i - 1)}{2N} * X_0 * A_l^k))
In the code, X_0 * A_l^k is stored as scored_inputs (cf. https://github.com/frgfm/torch-cam/blob/master/torchcam/methods/activation.py#L411-L414)
and \frac{i * (i - 1)}{2N} is stored as _coeff (cf. https://github.com/frgfm/torch-cam/blob/master/torchcam/methods/activation.py#L430)
So this line https://github.com/frgfm/torch-cam/blob/master/torchcam/methods/activation.py#L437 computes C(M_i) from the paper, they are summed in the following lines, and finally I divide by N here https://github.com/frgfm/torch-cam/blob/master/torchcam/methods/activation.py#L445
However, I realize that the docstring has some errors, I'll correct it to fix the documentation 👍
Let me know if some things are still unclear!