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Pixel Recurrent Neural Networks

2016 · paper · AI and machine learning

Presents a deep neural network that predicts image pixels one at a time along two spatial dimensions, modelling raw pixel values. It reports log-likelihood scores considerably better than prior results, ImageNet benchmarks, and coherent generated samples.

Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.

1 finding

Wording Section 5.1: "a constant value for every interval [i, i + 1], i = 1, 2, . . . 256"; with pixel values 0–255 and noise in [0, 1] the index should run i = 0, 1, …, 255.
  • p. 6 Section 5.1, first paragraph
    every interval [i, i + 1], i = 1, 2, . . . 256
  • p. 6 Section 5.3
    values 0 and 255 often get a much higher probability
  • p. 6 Section 5.3
    mass lying outside the interval [0, 255]

Judge's note: Read on p6. The same page uses pixel values 0 and 255, the interval [0, 255], Figure 6 axes of 0–255, and noise 'in the interval [0, 1]'. Dequantised data therefore lie in [0, 256], while the printed intervals cover [1, 257], omitting [0, 1]. This is an off-by-one in the index range. Indexing categories from 1 would not fit, because the interval is written in pixel-value units.

Second check: another model agreed

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12 minor (typos and the like; most checked by the judge only)
Wording The Section 3 roadmap says "In Section 3.4 we describe the softmax layer that computes the discrete joint distribution of the colors and the masking technique", but Section 3.4 ("Masked Convolution") describes only the masking.
  • p. 3 Section 3, opening paragraph
    In Section 3.4 we describe the softmax layer that computes the discrete joint distribution
  • p. 4 Section 3.4 heading
    3.4. Masked Convolution

Judge's note: Read Section 3 opening on p3 and Section 3.4 on p4-5. Section 3.4 covers the RGB feature split and masks A and B, with no description of a softmax layer. The softmax is covered in Section 2.2, Table 1 and Section 5.3. The masking half of the pointer is correct, so this is a partly inaccurate roadmap sentence.

Second check: another model agreed

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Wording Table 1 lists the Diagonal BiLSTM state-to-state kernel as "s-s: 1 × 2 no mask", whereas Section 3.2 and the Figure 3 caption give "a kernel of size 2 × 1".
  • p. 5 Table 1, Diagonal BiLSTM column
    s-s: 1 × 2 no mask
  • p. 4 Section 3.2
    convolution Kss that has a kernel of size 2 × 1
  • p. 3 Figure 3 caption
    uses a kernel of size 2 × 1
  • p. 3 Figure 3 caption
    uses a kernel of size 2 × 1.

Only the authors can say what is right here.

Judge's note: Table 1 on p5 prints '1 × 2'. Section 3.2 on p4 prints '2 × 1' three times and the Figure 3 caption on p3 prints '2 × 1'. The Row LSTM kernel is 'k × 1' in the text and '3 × 1' in the table, so the table does not simply use a flipped convention throughout. The orientation is not explained; the authors should say which is intended.

Second check: another model agreed

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Wording Section 3.2 says skewing "results in a map of size n × (2n − 1). At this point we can compute the input-to-state ..." via a 1 × 1 convolution, yet "the operation generates a 4h × n × n tensor".
  • p. 4 Section 3.2, second paragraph
    results in a map of size n × (2n − 1). At this point we can
  • p. 4 Section 3.2, second paragraph
    eration generates a 4h × n × n tensor

Only the authors can say what is right here.

Judge's note: Read on p4. A 1 × 1 convolution keeps spatial size, so applied to the skewed n × (2n − 1) map as the text's order of operations states, it would give 4h × n × (2n − 1). The map returns to n × n only after the later skew-back step. The authors may be counting only valid positions or applying the 1 × 1 convolution before skewing, so this is a query on a dimension statement and does not affect results.

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Wording Section 5.5 says "In Table 4 we report the performance of the Diagonal BiLSTM model" and Section 4 specifies only "a Diagonal BiLSTM with 7 layers and a value of h = 16" for MNIST, but Table 4 also reports PixelCNN (81.30), Row LSTM (80.54) and a 1-layer h = 32 Diagonal BiLSTM (80.75) whose settings are not given.
  • p. 7 Section 5.5
    we report the performance of the Diagonal BiLSTM model
  • p. 7 Table 4
    PixelCNN: 81.30
  • p. 5 Section 4
    For MNIST we use a Diagonal BiLSTM with 7 layers and a value of h = 16

Judge's note: Checked Section 4 on p5 and Section 5.5 with Table 4 on p7. The MNIST PixelCNN and Row LSTM configurations are not specified anywhere in the text. The 1-layer h = 32 variant is described only by its table label. This is an omission in the description, with no numeric conflict.

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Typo Figure 3 caption: "the input map is skewed by offseting each row"; "offseting" should be "offsetting".
  • p. 3 Figure 3 caption
    the input map is skewed by offseting each
  • p. 3 Figure 3 caption
    offseting each

Judge's note: The misspelling is visible in the Figure 3 caption on the p3 page image.

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Typo Table 2 caption: "evaluated on the Cifar-10 validation set"; the dataset is written "CIFAR-10" everywhere else.
  • p. 6 Table 2 caption
    evaluated on the Cifar-10 validation set

Judge's note: The Table 2 caption on p6 prints 'Cifar-10'. The body text, the Table 3 and Table 5 captions and the section headings all use 'CIFAR-10'. This is a capitalisation inconsistency only.

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Typo Section 5.7: "Although to our knowledge the are no published results on the ILSVRC ImageNet dataset"; "the are" should be "there are".
  • p. 7 Section 5.7, first sentence
    Although to our knowledge the are no published results on
  • p. 7 Section 5.7, first sentence
    Although to our knowledge the are no published results

Judge's note: The typo is visible on the p7 page image at the start of Section 5.7.

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Typo Figure 9 caption: "textures such as water, wood and shrubbery are also inputed relative well (see Figure 1)"; "inputed" should be "imputed"/"inpainted" and "relative well" should be "relatively well".
  • p. 8 Figure 9 caption, last sentence
    are also inputed relative well (see Figure 1)
  • p. 8 Figure 9 caption
    are also inputed relative well

Judge's note: Both wording errors are visible in the Figure 9 caption on the p8 page image. The pointer to Figure 1 (image completions) is appropriate.

Second check: none (judge only)

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Typo Section 5.7 prints "Note that the ImageNet models are in general less compressible than the CIFAR-10 images"; the subject should be "ImageNet images", since the comparison term and the following sentences are about images.
  • p. 8 Section 5.7, second paragraph
    Note that the ImageNet models are in general less com-
  • p. 8 Section 5.7, paragraph beginning 'Note that'
    Note that the ImageNet models are in general less com-pressible than the CIFAR-10 images.

Judge's note: Read on the page 8 image. The sentence compares "models" with "images", and the next sentences ("ImageNet has greater variety of images", "The ImageNet images are less blurry") show that images are meant. Wrong word with an evident fix; the meaning is recoverable, so cosmetic.

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Typo Section 5.7 prints "The main constraint on model size are currently computation time and GPU memory": singular subject with plural verb.
  • p. 8 Section 5.7, first paragraph
    straint on model size are currently computation time and

Judge's note: Read on the page 8 image, left column. Subject-verb disagreement as printed; should be "constraints ... are" or "constraint ... is". Meaning is unaffected.

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Typo The reference entry "Bengio, Yoshua and Bengio, Samy. Modeling high-dimensional discrete data with multi-layer neural networks. pp. 400–406. MIT Press, 2000." gives pages and publisher but no book or proceedings title.
  • p. 9 References, first entry
    works. pp. 400–406. MIT Press, 2000.

Judge's note: Read on the crop of the page 9 reference list. The entry runs from the paper title straight to "pp. 400–406. MIT Press, 2000" with no venue, whereas the Murray & Salakhutdinov entry in the same list carries "In Advances in Neural Information Processing Systems". The omission is visible on the page; the entry is incomplete rather than wrong. I did not verify what the missing venue is, as that is not in the files.

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Typo The Figure 10 caption prints "Additional samples from a model trained on ImageNet 32x32 (right) images." although the figure is a single panel with no left or right.
  • p. 11 Figure 10 caption
    trained on ImageNet 32x32 (right) images
  • p. 11 Figure 10 caption
    Additional samples from a model trained on ImageNet 32x32 (right) images.
  • p. 11 Figure 10 caption
    ImageNet 32x32 (right) images

Judge's note: Read on the page 11 image: Figure 10 is one 16x16 grid of samples. The "(right)" matches the Figure 7 caption wording "CIFAR-10 (left) and ImageNet 32x32 (right) images" (text extract, line 629) and looks carried over from it. Stray panel label; delete it.

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