Mathematical Formulation of Objective Function about glow-pytorch HOT 4 OPEN

As far as I am concerned, the GLOW (or normalization flow) model try to max likelihood of training data, which means max the log probability (the var objective in my code) and thus means min the -objective.

logdet += float(-np.log(256.) * pixels)

About this line, I cannot recall the details. It is supposed to handle some extra multiplication factor out of det().

• -np.log(256.) is used to approx intergration for discrete pixel values.
• pixels handles the (width, height) dimension of input.

from glow-pytorch.

Well, from my reading in another paper "Generative Flow via n * n Convolution: Thanh-Dat Truong et al.".
The data is added with a random uniform noise, which is the discretization level of the data, making the input continuous.

Could you get some hint? (I'm still confused...)

from glow-pytorch.

float(-np.log(256.) * pixels)

discretized level is a number denote the range of 8 bit pixel (2^8=256). So, glow paper mentioned c=-M x log a, where a=256 in Eq(2), while M is the number of total pixels in your image (i.e. 32 * 32 image, M=32*32).

from glow-pytorch.

@chaiyujin i wonder why the objectives will need to divided by float(np.log(2.) * pixels ? what is that means ?

from glow-pytorch.