Do not understand the computation of stdS apply_poe function

[vpellegrain]

Hi,

Thank you for your paper and released code.
I just wonder what is computed in the apply_poe function. Indeed, if we follow your paper (and math), the closed form of PoE distribution variance results in :

Other repo github (such as https://github.com/mhw32/multimodal-vae-public/blob/2a358eb3593e9942e0846eb0095519acef462fa6/vision/model.py) accordingly compute the resulting variance using this closed form.

However, I don't get what exactly you are computing in the apply_poe function for stdS, using also the logsumexp function.

If you can clear this for me, that would be great. Thank you in advance for your time.