L3 Flow Models -- CS294-158-SP20 Deep Unsupervised Learning -- UC Berkeley -- Spring 2020

[@not_a_human_being]

This is some great content - very easy to follow, nicely paced, not rushed, and not more complex than it has to be!

[@user-or7ji5hv8y]

These videos should have a million view. Worth more than Bitcoin.

[@rj-nj3uk]

42:28 that student almost stumped Pieter with that question. That was a nice question.

[@rj-nj3uk]

and Pieter gave a great explanation too.

[@rj-nj3uk]

Bu the still got confused on "why a Mixture of Gaussian is a valid flow" argument.

[@PaxiKaksi]

Woah. Thanks for making the lecture publicly available :3

[@Michael-vs1mw]

How do we work with Gaussian mixtures at 56:40? What does it mean for the flow for x1 to be the CDF of a Gaussian mixture? These CDFs require integration, since the Normal CDF is an integral. But here we're somehow obtaining mixture CDFs without any integration whatsoever. How does this work?

[@huaijinwang6908]

I cannot understand how neural nets is related to the gaussian mixture model at kzbin.info/www/bejne/gHPFZqaJeJV9pbs. How can we impose the f \theta to be a Gaussian mixture CDF (maybe some assumption here with kl divergence in the objective function, I'm not sure)?

[@AbhinavKumar-tr7ww]

When we are manipulating in the latent space, (at 1:43:04), we add the smile vector to the latent representation of the image we want to modify. Is the latent space still euclidean where such addition is valid?

[@shuminghu]

I suppose for euclidean space you were referring to property like "P + (v + w) = (P + v) + w" (P being a point, v, w being vectors) rather than distance metric like L2-norm. My feeling is that, in this case, they are not asserting the space is euclidean but P + (v + w) = (P + v) + w is true for w that orthogonal to v so that the order doesn't matter, i.e. they found an independent vector/direction in latent space, to represent smile for example.

[@saihemanthiitkgp]

At 1:06:30, if we condition z2 on x1 instead of z1, then training can be parallelized, isn't it? In that way, both training and sampling can be faster

[@saihemanthiitkgp]

oh, then sampling will be slower as x2 will depend on x1.

[@rangugoutham7249]

@@saihemanthiitkgp w.r.t your actual question conditioning z2 on x1 is what happens in AF modelling, and you are right inherently then x2 will depend on x1 making the sampling slower.

[@shuminghu]

For 2D autogressive flow, z2 is conditioned on x1. Doesn't that mean dz2/dx1 should also be included in the loss?

[@shuminghu]

Ah it's not needed. dz1/dx2 is 0 so when only dz1/dx1 and dz2/dx2 survive when evaluating the determinant of the Jacobian.

[@shuminghu]

This also generalizes to N-D autoregressive flows since the Jacobian is a lower triangular matrix.

[@SimonSlangen]

Was just wondering this while watching the video, so thanks for being one of the rare people who comes back to answer their own question.

[@SimonSlangen]

On second thought, showing equivalence to the determinant formula just shows that the decomposition formula likely wasn't in error. But it doesn't answer the question of why we don't need a |dz2/dx1| term. -- I believe it's by construction because f2(x2; x1) != f2(x2, x1). i.e. f2 is parametrised in x1. Another way to write it would be f2_{x1}(x2).

[@leoguti85]

Thanks for this excellent material. How does the flow model would work in the case we have data with mixed-type variables, i.e., continuous + discrete variables? should we have a different invertible transformation for each type of variable?.. Thank you!

[@sinancalsr726]

Hi, thanks a lot for sharing the course and the materials. There is a jump in the video around 1:09:22 I was okay until that time but it became harder to follow after that. I couldn't understand especially the volume part.

[@Shottedsheriff]

I guess it was just before the pizza break (take a look on the slides from this lecture, after the jump it is just the next slide). However, the content might be more challenging

[@GenerativeDiffusionModel_AI_ML]

it is log(exp(sigma))?

[@bender2752]

So flow is one kind of latent variable model right? Since it have a Gaussian (or other kind) distribution based latent space.

[@shuminghu]

People usually refer to latent variable models as the ones with latent space having less dimensions that data. Flow's latent space has the same dimension as data. Lecture 4 has more details.

[@LucaPuggini]

is there any reference paper for flow models?

[@tingchen6586]

the last page of lecture slides docs.google.com/presentation/d/1WqEy-b8x-PhvXB_IeA6EoOfSTuhfgUYDVXlYP8Jh_n0/edit#slide=id.g4f883b39d8_2_34