Up and Down Variables

[gwmdunda]

Dear Authors,

Thank you for your works. May I ask why we need up and down variables in the model?

[zbh2047]

Hi, thanks for your interest in our work. Here we add up and down variables in order to support the interval bound propagation in computing the certified radius for L-infinity distance layers. You may not use it if the certified radius is computed simply based on the Lipschitz property. You will need up and down variables for hybrid architectures, e.g., a MLP is built on top of an L-infinity distance net. Hope this can address your question.

[gwmdunda]

Thank you for your answer. May I also ask why there is a negative sign in the forward() function (x, lower, upper = -x, -upper, -lower)

[zbh2047]

Hi, could you please provide the location of this line of code?

[gwmdunda]

It is in ell_inf_models.py line 43

[zbh2047]

The model implemented in this repo follows the original ICML paper, where in Section 3.2 g(x) = (−x_1^{(L)}, −x_2^{(L)}, ..., −x_M^{(L)}). So this line of code takes negative for x, lower, upper variables.

[gwmdunda]

I am a bit confused since in ICML paper you need to take the negative sign, but in your ICLR paper, the negative sign is not needed.