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Consider the sentence in the abstract of the paper at https://arxiv.org/abs/1610.09038.

Empirically we find that Professor Forcing acts as a regularizer, improving test likelihood on character level Penn Treebank and sequential MNIST.

I have used MNIST dataset. However, I could not find any Sequential MNIST or permuted MNIST datasets.

Are they standard datasets published anywhere or I can just permute by myself and call them permuted while the standard one is just called the Sequential one.

I guess the distinction in papers (of using the two versions -- permuted and sequential MNIST) must be due to some reason, what could be the reason? Is it some transfer learning thing?

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    $\begingroup$ Read section 4.3. $\endgroup$
    – Batman
    Jan 8 '17 at 2:12
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As in comment by @Batman, sequential MNIST is explained in section 4.3 of your link: https://arxiv.org/abs/1610.09038.

We evaluated Professor Forcing on the task of sequentially generating the pixels in MNIST digits.

As far as I am aware, sequential MNIST always implies the model does not get to see/generate the whole image at once (like for example a normal 2d-ConvNet would), but only one pixel at a time sequentially. So sequential MNIST should have the same meaning also in other non-generative contexts.

Also in section 4.3. they explain permuted mnist:

Applying a fixed random permutation to the pixels makes the problem even harder but IRNNs on the permuted pixels are still better than LSTMs on the non-permuted pixels.

The problem should be harder after permuting the pixels in all images with the same permutation, because you have to learn more long-range patterns: Distinctive shapes, like the horizontal bar of the 7 are typically more spread apart in the input after permutation compared to before.

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Permutated Sequential MNIST is introduced in the "A Simple Way to Initialize Recurrent Networks of Rectified Linear Units" paper from 2015 which has Hinton as a co-author.

Sequential MNIST: "classify the MNIST digits [21] when the 784 pixels are presented sequentially to the recurrent net"

Permutated Sequential MNIST: same thing with "a fixed random permutation of the pixels of the MNIST digits"

Permutated Sequential MNIST is not a real dataset, it's just a transformation of the MNIST dataset to evaluate recurrent neural networks.

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