The prior is wrong

[Abraham0912541]

The prior is wrong

[Abraham0912541]

Yes, I understand you，but you just implement the maximization procedure，and I think you lost the minimization in the code. In my opinion，you just implement this
max EV[log Dφ(y)] + EP[log(1 − Dφ(Eψ(x)))] this is the PRIOR in the code
but you lost this
min EV[log Dφ(y)]
because the GAN is a minimax two-play game. Is it right?

[DuaneNielsen]

Thanks for the comments. I'll take a look this weekend. Translation below for those that don't speak Chinese.

zhaoxingwudy: It should be correct, the original two E (logD (y)) maximization and E (1-D (E (x))) maximize, min-max is the two are maximized, and finally take a negative plus To total loss while maximizing three items

SuJingZhi:
I think maybe not. As with the original generation of the anti-network, when optimizing the discriminator, the generator parameters are fixed, maximizing E(logD(y))+E(1-D(E(x))), in order to make the discriminator easier. Distinguish between true and false samples; when optimizing the generator, fix the discriminator parameters and minimize E(1-D(E(x))) in order to make the sample generated by the generator easier to confuse the discriminator. Here are the two processes. , one maximizes, one minimizes, so this code should be problematic.

zhaoxingwidy:
Here G is E, this formula is training D, train.py 97 98 lines are the code to train E and D respectively. But I am very curious for this loss general... all three are added up This loss training encoder and deepMInetwork

[DuaneNielsen]

I understand your point, and it could be the case, as the results are not as expected. The research team has new code out, so I'll take a look and compare.

[aflyingnoob]

应该是对的, 原始两项E(logD(y))最大化和E(1-D(E(x)))最大化, min-max就是两项都最大化, 最后取了个负号加到总的loss,同时最大化三项

[Abraham0912541]

我觉得可能不是。和原始的生成对抗网络一样，优化判别器的时候，固定生成器参数，最大化E(logD(y))+E(1-D(E(x)))，是为了使得判别器可以更容易区分真假样本;优化生成器时，固定判别器参数，最小化E(1-D(E(x)))，是为了使生成器所生成的样本更容易迷惑判别器，这里是两个过程，一个最大化，一个最小化，所以这个代码应该是有问题的。

[aflyingnoob]

这里的G就是E, 这个式子就是训练D, train.py 97 98行就分别是训练E和D的代码了. 不过我很好奇为啥这个loss通用...三项加起来的全部都是这个loss训练encoder和deepMInetwork

[Abraham0912541]

OK，thank you very much.

[aflyingnoob]

emmmm.....in the orignal paper , the appendix said:

Here we provide architectural details for our experiments. Example code for running Deep Infomax (DIM) can be found at REDACTED.

what's the meaning of REDACTED ?thanks

[DuaneNielsen]

Redacted means the information was removed before publication. It's a bit weird, normally redaction would be done for security or legal reasons, but I don't see that applying here.

[DuaneNielsen]

Ok, so I finally got around to looking at this.

From the paper..

DIM imposes statistical constraints onto learned
representations by implicitly training the encoder so that the push-forward distribution, Uψ,P, matches
a prior, V. This is done (see Figure 6 in the App. A.1) by training a discriminator, Dφ : Y → R, to
estimate the divergence, D(V||Uψ,P), then training the encoder to minimize this estimate:

(ˆω, ψˆ)P = arg min ψ arg max φ Dbφ(V||Uψ,P) = EV[log Dφ(y)] + EP[log(1 − Dφ(Eψ(x)))] (7)

And the code..

        prior = torch.rand_like(y)

        term_a = torch.log(self.prior_d(prior)).mean()
        term_b = torch.log(1.0 - self.prior_d(y)).mean()
        PRIOR = - (term_a + term_b) * self.gamma

In words..

Make a uniform random bunch of numbers of same shape as the output.
Feed them through a discriminator network to estimate the probability of noise.
Feed the output, y through the same network.
Take the inverse probability of the output.
Take the expectation(mean) of the log probability of both.
Add them together and multiply by -1 and the gamma hyper parameter.

I think this works. The maximization would occur because we have multiplied by -1 at the end.

Thoughts?

[Abraham0912541]

I think that you can have a look at the paper 'Adversarial Autoencoder' and it may be helpful.

[ccchang0111]

Thank you for such a clean and neat code. I have learned a lot from it!

Back to this prior question, I think @SuJingZhi is correct. However I am not familiar with PyTorch, but I guess we probably need to take these line into a separate loss function (e.g. prior_loss), which is for updating PriorDiscriminator first.

And then come back to DeepInfoMaxLoss, replace the PRIOR with something like

class DeepInfoMaxLoss(nn.Module):
    ...
    y_rescaled = nn.Sigmoid(y) # original author has this 'nonlinearity' set
    ENCLOSS = -prior_loss(y_rescaled) * self.gamma # minus sign is to "trick" PriorDiscriminator
    return LOCAL + GLOBAL + ENCLOSS

This is how the original author implements it (which is a bit complicated, because he is trying to make everything fits into his 'cortext' framework).
https://github.com/rdevon/DIM/blob/bac4765a8126746675f517c7bfa1b04b88044d51/cortex_DIM/models/prior_matching.py#L70-L75