Generative Adversarial Nets
NeurIPS, 2014 · paper · AI and machine learning
Proposes generative adversarial nets, a framework that trains a generative model and a discriminative model against each other in a minimax game. It needs no Markov chains or approximate inference, and experiments evaluate generated samples qualitatively and quantitatively.
Checked: PDF from proceedings.neurips.cc, fetched 4 Oct 2026. Page numbers are those of that PDF.
6 findings
Reference or label References [4] and [5] are both "Deep generative stochastic networks trainable by backprop" (ICML'14), labelled 2014a and 2014b; [5] adds Alain, G. as an author. The text cites the work as [4] ("Generative stochastic networks [4]", "[24, 3, 4]") and Table 1 cites it as "Deep GSN [5]".
- p. 8 References [4] and [5]
Deep generative stochastic networks trainable by backprop. In ICML’14.
- p. 8 Reference [5]
Bengio, Y., Thibodeau-Laufer, E., Alain, G., and Yosinski, J. (2014b)
- p. 8 References [4] and [5]
(2014a). Deep generative stochastic networks trainable by backprop. In ICML'14.
- p. 8 Reference [5]
Alain, G., and Yosinski, J. (2014b). Deep generative stochastic net-works trainable by backprop.
Only the authors can say what is right here.
Judge's note: I checked the page 8 reference list: both entries have the same title and the same venue, and their author lists differ. The citations are on page 2 (line 66 of the text), page 6 at Table 1 ([5]), and page 6 in Section 5 ([4]). Only the authors can say which author list is correct.
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Reference or label Algorithm 1 twice says "Sample minibatch of m noise samples {z(1), ..., z(m)} from noise prior pg(z)", but Section 3 defines the noise prior as pz(z) and uses pg for the generator's distribution over x.
- p. 4 Algorithm 1, first bullet inside the k-step loop
from noise prior pg(z)
- p. 4 Algorithm 1, generator-update bullet
Sample minibatch of m noise samples {z(1), . . . , z(m)} from noise prior pg(z).
- p. 3 Section 3
we define a prior on input noise variables pz(z)
- p. 4 Algorithm 1, discriminator and generator sampling steps
from noise prior pg(z).
Judge's note: The page 4 image shows p_g(z) in both sampling bullets: inside the k-step loop and before the generator update. Page 3 defines 'a prior on input noise variables p_z(z)' and p_g as 'the generator's distribution ... over data x'. The symbol should be p_z(z).
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Reference or label Reference [5] gives the venue as "Proceedings of the 30th International Conference on Machine Learning (ICML'14)"; the ordinal does not match the 2014 year.
- p. 8 Reference [5]
Proceedings of the 30th International Conference on Machine Learning (ICML’14)
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that ICML 2013 was the 30th conference and ICML 2014 the 31st. The page 8 image shows the entry exactly as quoted. The paper itself gives no ordinal for ICML'13 in [3], so the mismatch cannot be shown from the files alone.
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Reference or label Reference [15] (wake-sleep, Science) prints the page range as "268, 1558–1161", so the range ends before it starts.
- p. 9 Reference [15]
Science, 268, 1558–1161.
- p. 9 Reference [15]
Science, 268, 1558–1161
Judge's note: The page 9 image shows '1558–1161'. A page range that runs backwards is an error visible within the paper itself. The likely fix, 1158–1161, rests on outside knowledge of the real page range of the Science article.
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Wording Proof of Proposition 1: "For any (a, b) ∈ R2 \ {0, 0}, the function y → a log(y) + b log(1 − y) achieves its maximum in [0, 1] at a/(a+b)" — as printed, the claim holds only for nonnegative a and b.
- p. 5 Proof of Proposition 1, Eq. 3 first line
log(1 −D(g(z)))dz
- p. 5 Proof of Proposition 1, after Eq. 3
For any (a, b) ∈ R2 \ {0, 0}, the function y → a log(y) + b log(1 − y) achieves its maximum in [0, 1] at a/(a+b)
- p. 3 Eq. 1
V (D, G) = Ex∼pdata(x)
- p. 5 Eq. 3 and Eq. 4
log(1 −D(g(z)))
Only the authors can say what is right here.
Judge's note: Read on the page 5 image. My own working: f'(y)=a/y−b/(1−y). For a=2, b=−1, f'(y)=2/y+1/(1−y)>0 on (0,1), so f increases without bound as y→1, and a/(a+b)=2 lies outside [0,1]. For a=1, b=−1, a+b=0, so a/(a+b) is undefined. The step is therefore false on the stated domain. Proposition 1 still stands because the lemma is applied with a=p_data(x)≥0 and b=p_g(x)≥0, so severity is S3. Restricting the domain to nonnegative (a,b) repairs the step. The other points in this cluster are judged separately: lowercase g(z) in C017, capital Pdata in C012, the argument order of V in C005, and the {0,0} set notation in C014.
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Wording The undefined symbol p_x is used for the data distribution: the Proposition 2 proof ends "pg converges to px, concluding the proof" although the proposition states "pg converges to pdata", and the Figure 1 caption says "(black, dotted line) px".
- p. 5 Proof of Proposition 2, last sentence
pg converges to px, concluding the proof
- p. 5 Statement of Proposition 2
then pg converges to pdata
- p. 4 Figure 1 caption
dotted line) px from those of the generative distribution
- p. 5 Proof of Proposition 2
pg converges to px, concluding the proof.
Judge's note: On the page 5 image, the proof concludes p_x while the statement says p_data. On the page 4 image, the Figure 1 caption first writes p_x and later p_data for the same distribution. p_x is never defined; the intended symbol is p_data.
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13 minor (typos and the like; most checked by the judge only)
Wording Table 1 TFD column prints both "2110 ± 50" (Stacked CAE) and "2057 ± 26" (Adversarial nets) in bold, and the caption does not say what bold means; in the MNIST column only the highest value (225 ± 2) is bold.
- p. 6 Table 1, TFD column
2110 ± 50 ... 2057 ± 26
- p. 6 Table 1, TFD column
2110 ± 50
- p. 6 Table 1, TFD column
2057 ± 26
- p. 6 Table 1, Deep GSN row
Deep GSN [5]
Judge's note: I checked the page 6 image. Both TFD entries are bold, and 2110 is the higher of the two. The MNIST column bolds only the top value. The caption never defines the bold convention. Bold may mean 'within error of the best', which is a common convention, so this is an observation about the markup and not an error. The Deep GSN [5] citation point is handled in C025.
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Typo Introduction, p.1: "until the counterfeits are indistiguishable from the genuine articles" — 'indistiguishable' should be 'indistinguishable'.
- p. 1 Introduction, paragraph 2
indistiguishable from the genuine
- p. 1 Introduction, paragraph 2, last sentence
until the counterfeits are indistiguishable from the genuine
- p. 1 Introduction, counterfeiter analogy
counterfeits are indistiguishable from the genuine
Judge's note: The misspelling is visible in the typeset text on the page 1 image (last line of Introduction paragraph 2).
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Typo Introduction, p.1: "which have a particularly well-behaved gradient . Deep" — stray space before the full stop.
- p. 1 Introduction, paragraph 1
well-behaved gradient .
Judge's note: The crop shows a visible space between 'gradient' and the period. This is cosmetic.
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Typo Section 5, p.6: "We trained adversarial nets an a range of datasets" — 'an' should be 'on'.
- p. 6 Section 5, first sentence
We trained adversarial nets an a range of datasets
- p. 1 Introduction
indistiguishable
- p. 2 Related work
succesful
- p. 6 Section 5
trained adversarial nets an a range of datasets
Judge's note: Visible in crop C019-a. The other items bundled in this cluster are adjudicated elsewhere: 'indistiguishable' in C001, 'succesful' in C003, and 'networks has been' in C006.
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Typo Related work, p.2: "perhaps the most succesful is the deep Boltzmann machine" — 'succesful' should be 'successful'.
- p. 2 Section 2, paragraph 1
perhaps the most succesful is the deep Boltzmann
Judge's note: The misspelling is visible in the crop of Section 2, paragraph 1.
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Typo The value function's argument order is inconsistent: the text says "value function V(G, D)" and Eq. 3 and 4 use V(G, D), but Eq. 1 has "min_G max_D V(D, G)" and the Theorem 1 proof has "C(G) = V(D*_G, G)".
- p. 3 Section 3, Eq. 1 and the sentence before it
value function V (G, D):
- p. 5 Proof of Theorem 1
C(G) = V (D∗ G, G)
- p. 3 Section 3, text and Eq. 1
min G max D V (D, G)
- p. 3 Eq. 1
min G max D V (D, G) =
Judge's note: On the page 3 image, the sentence reads V(G,D) and Eq. 1 reads V(D,G). On the page 5 image, Eq. 3 and 4 use V(G,D) and the proof of Theorem 1 uses V(D*_G, G). The notation is inconsistent, but the meaning can be recovered from context.
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Typo Related work, p.3: "Generative adversarial networks has been sometimes confused" — plural subject with singular verb; should be 'have sometimes been'.
- p. 3 Section 2, last paragraph
Generative adversarial networks has been sometimes confused
Judge's note: Visible on the page 3 image, at the start of the last paragraph of Section 2.
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Typo Eq. 4, last line: the denominator is printed "Pdata(x) + pg(x)" with a capital P, while pdata is used everywhere else, including the numerator of the same fraction.
- p. 5 Eq. 4, last line
Pdata(x) + pg(x)
Judge's note: The page 5 image shows a capital P in the first fraction's denominator and a lowercase p in the second fraction. This is a typesetting slip.
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Typo Proof of Proposition 1: "(a, b) ∈ R2 \ {0, 0}" — the excluded origin should be written {(0, 0)}.
- p. 5 Proof of Proposition 1
(a, b) ∈R2 \ {0, 0}
Judge's note: The page 5 image shows {0, 0}. The meaning is obvious, so this is cosmetic set notation.
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Typo Proof of Proposition 2: "with a unique global optima as proven in Thm 1" — should be 'optimum'.
- p. 5 Proof of Proposition 2
with a unique global optima as proven in Thm 1
Judge's note: Visible on the page 5 image. Grammatical only.
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Typo Eq. 3, first line: "pz(z) log(1 − D(g(z)))dz" uses a lowercase g for the generator, which is G everywhere else.
- p. 5 Eq. 3, first line
pz(z) log(1 −D(g(z)))dz
Judge's note: The page 5 image shows a lowercase g(z) in the typeset Eq. 3; Eq. 1, Eq. 4 and Algorithm 1 use G(z). This also covers the lowercase-g notes raised under C011.
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Typo Table 1 caption: "On TFD, σ was cross validated on each fold and mean log-likelihood on each fold were computed." repeats the preceding sentence ("with a different σ chosen using the validation set of each fold"), and 'mean log-likelihood ... were' does not agree in number.
- p. 6 Table 1 caption
On TFD, σ was cross validated on each fold and mean log-likelihood on each fold were computed.
- p. 6 Table 1 caption
On TFD, σ was cross validated on each fold and mean log-
Judge's note: I checked the caption on the page 6 image. The σ-per-fold point is made twice in consecutive sentences, and 'mean log-likelihood ... were computed' has a number mismatch. Both are copy-edit issues and the meaning is unchanged. The reviewer's claim that the MNIST comparison models are binary-input cannot be checked from this paper, so I did not adopt it.
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Typo Section 5 reads "We trained adversarial nets an a range of datasets"; 'an' should be 'on'.
- p. 6
We trained adversarial nets an a range of datasets
Judge's note: The page 6 image shows 'an a range' as printed.
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