Neural Message Passing for Quantum Chemistry
2017 · paper · AI and machine learning
Reformulates existing neural network models for molecules into one framework, Message Passing Neural Networks, and explores new variations. The authors report state-of-the-art results on a molecular property prediction benchmark.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
8 findings
Substance In Table 2 the "Average" row for all seven baseline columns is lower than the mean of the 13 printed target rows: "Average 2.17 2.08 3.37 53.97 1.35 2.59 1.36" against column means of 2.22 (BAML), 2.13 (BOB), 3.44 (CM), 57.57 (ECFP4), 1.38 (HDAD), 2.74 (GC) and 1.40 (GG-NN); the enn-s2s (0.68) and enn-s2s-ens5 (0.52) averages do equal their column means.
- p. 8 Table 2, Average row (BAML, BOB, CM, ECFP4, HDAD, GC, GG-NN)
Average 2.17 2.08 3.37 53.97 1.35 2.59 1.36
- p. 8 Table 2, Average row, GG-NN column
1.36
- p. 8 Table 2, Average row, GC column
2.59
- p. 8 Table 2, Average row, ECFP4 column
53.97
Only the authors can say what is right here.
Judge's note: Read every cell of Table 2 on the page 8 image and checked them against the aligned text layer; then summed each column myself. All seven baseline columns give a mean above the printed average, by 0.03 to 0.15 (3.6 for ECFP4), far beyond what rounding of two-decimal entries allows (at most 0.005). The two columns for the paper's own models reproduce, as do the averages in Tables 7 and 8, so the row is a plain mean of the 13 targets. Nothing in the article says the baseline averages were taken from another source, computed on unrounded or differently normalised values, or over a different set of targets. The DTNN column has no average. Whether individual cells or the averages are the stale ones cannot be told from the paper, hence author_query; the ordering of methods by average is not changed.
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Wording The introduction says "We develop several different MPNNs which predict DFT to within chemical accuracy on 5 out of 13 targets while operating on the topology of the molecule alone", but in Table 7 only the set2set model reaches 5 targets; the virtual-edge and master-node models reach 4 each and plain GG-NN none.
- p. 2 Introduction, second contribution bullet
We develop several different MPNNs which predict DFT to within chemical accuracy on 5 out of 13 tar-
- p. 7 Section 8, Training Without Spatial Information
the Set2Set output achieves chemical accuracy on 5 out of 13 targets
- p. 13 Table 7, columns ve / mn / s2s
1.05
Only the authors can say what is right here.
Judge's note: Read page 2, Section 8 on page 7 and Table 7 on page 13. Error ratios below 1 in Table 7: s2s has U0 0.72, U 0.79, H 0.80, G 0.74, Omega 0.78 (5); ve has U0 0.89, U 0.93, H 0.86, G 0.85 with Omega 1.05 (4); mn has U0 0.90, U 0.99, H 0.95, Omega 0.78 with G 1.02 (4); GG-NN has none. Section 8 itself attributes the figure only to set2set: "the Set2Set output achieves chemical accuracy on 5 out of 13 targets". The 'no distance' column of Table 10 is the same s2s model. No other model without spatial input is reported, so 'several different MPNNs' overstates the tables.
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Wording The paper predicts 13 targets and says "We can group the different properties we try to predict into four broad categories", but Section 4 and appendix 10.2 describe only 12; the heat capacity Cv, a row in every results table (e.g. Table 2 "Cv 1.64 1.83 2.36 30.29 0.88"), is never defined or placed in a category. Separately, appendix 10.2 has a missing verb: "First there the four atomization energies."
- p. 5 Section 4, description of the four property categories
We can group the different properties we try to predict into
- p. 8 Table 2, row Cv
Cv 1.64 1.83 2.36 30.29 0.88
- p. 11 Section 10.2
First there the four atomization energies.
- p. 2 Introduction
molecules with 13 properties for each molecule
Only the authors can say what is right here.
Judge's note: Read page 5, Section 10.2 on pages 11-12 and the tables on pages 8, 12, 13 and 14. Described: U0, U, H, G (4); ω1 and ZPVE (2); HOMO, LUMO, gap (3); R2, μ, α (3), which is 12. The tables list 13 rows, with 'Omega' for ω1 and an extra row 'Cv'. Searched the text for 'Cv' and 'heat capacity': 'Cv' occurs only as a table row label and 'heat capacity' does not occur. The appendix headed 'A More Detailed Description of the Quantum Properties' stops at the same 12. The missing 'are' in 'First there the four atomization energies' is printed as quoted on page 11 (S4 on its own).
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Wording Section 4 defines the gap with the terms reversed: "The electron energy gap is simply the difference ε_HOMO − ε_LUMO", whereas the appendix describes it as "the difference in energy between LUMO and HOMO. It is the lowest energy transition" (i.e. ε_LUMO − ε_HOMO, a positive quantity).
- p. 5 Section 4, third paragraph
The electron energy gap is simply the difference εHOMO − εLUMO.
- p. 12 Section 10.2, Electron energy gap bullet
This is the difference in energy between LUMO and HOMO. It is the lowest energy transition
- p. 5 Section 4, electronic properties
simply the difference εHOMO − εLUMO
- p. 12 Appendix 10.2, Electron energy gap
This is the difference in energy between LUMO and HOMO
Judge's note: Read page 5 and Section 10.2 on page 12. The main text prints an explicit signed expression, HOMO minus LUMO. The appendix says the gap is the lowest-energy transition from an occupied to an unoccupied state, which is LUMO minus HOMO and positive, since LUMO is by the paper's own description the lowest unoccupied state above the highest occupied one. As printed, the Section 4 expression has the opposite sign. It is a slip in a prose definition and affects no reported number, hence S3.
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Wording Section 5.4 says the propagation step produces "temporary embeddings {h̃^{t+1,k}_v, v ∈ G}", but equation 5 mixes h̃^{t,1}_v, ..., h̃^{t,k}_v and writes the result as (h^{t,1}_v, ..., h^{t,k}_v), the same symbol as the step's input; both sides should carry t+1.
- p. 6 Section 5.4, text before equation 5
temporary embeddings {h̃t+1,k v , v ∈ G}
- p. 6 Equation 5
= g ( h̃t,1 v , h̃t,2 v , . . . , h̃t,k v )
Judge's note: Read Section 5.4 and equation 5 on page 6 (no crop file exists for this cluster; used the full page and the text layer, which agree). The sentence before the equation has superscript t+1,k on the temporary embeddings; equation 5 has superscript t on both sides, so the output of the step is written with the input's time index. Also k serves both as the number of copies and as the running index of a copy. The stated complexity and results are unaffected.
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Wording Section 8 says "Overall, these three modifications help on all 13 targets", but in Table 7 the master node is worse than plain GG-NN on mu (4.02 vs 3.94) and virtual edges are worse on R2 (17.11 vs 14.74); only the set2set column is below GG-NN on all 13 targets.
- p. 7 Section 8, Training Without Spatial Information
Overall, these three modifications help on all 13 targets
- p. 13 Table 7, rows mu and R2
mu 3.94 3.76 4.02 3.81
- p. 13 Table 7, row R2
R2 14.74 17.11 13.16 13.67
- p. 13 Table 7, row mu
3.94
Only the authors can say what is right here.
Judge's note: Read Table 7 on the page 13 image, column by column. ve is lower than GG-NN on 12 of 13 targets (not R2), mn on 12 of 13 (not mu), s2s on all 13. The Table 7 averages (3.47, 2.90, 2.62, 2.57) equal Table 3, so it is the same experiment that the sentence describes and the text points to the supplementary material for details. The sentence holds only if read as 'for each target at least one modification helps' or as a statement about the averages; no such qualification is printed. Rated S3 because the per-target numbers themselves are available and the average ordering is as stated.
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Wording Section 10.4 says "on both R2 and Omega our models are equal or better with 11k samples than the best baseline is with 110k samples", but Table 6 gives Omega 0.28 at N=11k while Table 2 gives BAML 0.27 on Omega; the statement holds for R2 (0.28 against 0.80 for BOB) but not for Omega as printed.
- p. 12 Section 10.4, first paragraph
on both R2 and Omega our models are equal or better with 11k samples than the best baseline is with 110k samples
- p. 13 Table 6, row Omega, N=11k
Omega 0.28 0.25 0.24 0.15 0.19
- p. 8 Table 2, row Omega, BAML
Omega 0.27 0.35 1.32 1.47 0.34 0.32 0.53
- p. 13 Table 6, row Omega, N=11k
0.28
Judge's note: Read Table 6 on page 13 (Omega row: 0.28, 0.25, 0.24, 0.15, 0.19; R2 row: 0.28 at 11k) and Table 2 on page 8 (Omega: BAML 0.27, BOB 0.35, CM 1.32, ECFP4 1.47, HDAD 0.34, GC 0.32, GG-NN 0.53; R2 best baseline BOB 0.80). Error ratios, lower is better, so 0.28 is slightly worse than 0.27. The text does not restrict "best baseline" to the MPNN baselines, and Table 2 is the only baseline table. The gap is 0.01, so the overstatement is slight; the unrounded values could be closer, but as printed the claim fails for Omega.
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Wording Section 10.1.1 says "Relabelling the row vector H^{l+1}_{(v)} as an N dimensional column vector h^{t+1}_v", but a row of H is D dimensional (H^l is defined as an N × D matrix "indicating the D dimensional node states for the N nodes"); it should read "D dimensional".
- p. 11 Section 10.1.1, before equation 8
as an N dimensional col- umn vector
- p. 11 Section 10.1.1, definition of H
dimensional matrix indicating the D dimen- sional node states for the N nodes
- p. 11 10.1.1, after the H^{l+1}_{(v)} equation
as an N dimensional col-
Judge's note: Read page 11. H^l is stated to be R^{N×D} and M_(v) denotes the row of M indexed by node v, so H_(v) has D entries. W^l is D×D and (W^l)^T multiplies h_w in equation 8, which also requires h to be D dimensional. N is the number of nodes throughout the appendix. Wrong symbol with an evident fix.
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25 minor (typos and the like; most checked by the judge only)
Wording The size of QM9 is given three ways without explanation: "QM9 consists of 130k molecules" and "all 134k molecules" (both p.2), "about 134k drug-like organic molecules" (Section 4), and "The QM-9 dataset has 130462 molecules in it" (Section 7, which also writes 'QM-9' where the rest of the paper writes 'QM9').
- p. 2 Introduction, second paragraph
QM9 consists of 130k molecules
- p. 2 Introduction, right column
all 134k molecules
- p. 4 Section 4
this results in about 134k drug-
- p. 7 Section 7
The QM-9 dataset has 130462 molecules in it.
Only the authors can say what is right here.
Judge's note: Read pages 2, 4 and 7. All four statements are printed as quoted. Searched the text for any statement that a subset of the ~134k molecules was used or that molecules were removed; there is none. 130462 minus the 10000 validation and 10000 test samples gives 110462, which agrees with the '110k' training size in Table 6, so 130462 is the number actually used; the paper just never reconciles it with 134k. Either number may be legitimate for a different set, so this is an unexplained ambiguity rather than a wrong value. The 'QM-9' hyphenation is a cosmetic side point.
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Wording The text says "Estimates of DFT error and chemical accuracy are provided for each of the 13 targets in Faber et al. (2017)" and "For all 13 targets, achieving chemical accuracy is at least as hard as achieving DFT error", but Table 5 prints "-" for the DFT error of R2, so the paper gives the estimate for only 12 targets.
- p. 2 Introduction
Esti- mates of DFT error and chemical accuracy are provided for each of the 13 targets in Faber et al. (2017)
- p. 2 Introduction, right column
For all 13 targets, achieving chemical accuracy is at least as hard as achieving DFT error.
- p. 12 Table 5, row R2
R2 - 1.2
- p. 2 Introduction, paragraph on benchmark error levels
mates of DFT error and chemical accuracy are provided for each of the 13 targets in Faber et al. (2017)
Only the authors can say what is right here.
Judge's note: Read page 2 and Table 5 on page 12. The R2 row reads 'R2 - 1.2'; every other row has a DFT error. Section 10.3 says both sets of estimates come from Faber et al. and gives no reason for the missing value. For the other 12 rows chemical accuracy is less than or equal to the DFT error (mu is equal, .1 and .1), so the 'for all 13' comparison holds for 12 and cannot be checked for R2 from this paper. Whether Faber et al. gives an R2 value cannot be settled from the files.
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Wording The introduction claims chemical accuracy on 5 of 13 targets "while operating on the topology of the molecule alone (with no spatial information as input)", but Section 8 says "The experiments shown tables 3 and 4 were run with a partial charge feature as a node input. This feature is an output of the DFT calculation and thus could not be used in an applied setting"; the partial charge feature is also absent from Table 1, which Section 6 calls "a list of all of the features".
- p. 7 Section 8, Training Without Spatial Information
experiments shown tables 3 and 4 were run
- p. 2 Introduction, second contribution bullet
gets while operating on the topology of the molecule alone (with no spatial information as input)
- p. 7 Section 8, Training Without Spatial Information
experiments shown tables 3 and 4 were run with a partial charge feature as a node input. This feature is an output of the DFT calculation and thus could not be used in an ap-
- p. 7 Section 8
were run with a partial charge feature as a node input
Only the authors can say what is right here.
Judge's note: Read the contribution bullet on page 2, Section 8 on page 7, Table 1 on page 6 and Table 7 on page 13. The 5-of-13 result is the s2s column of Table 7 (U0 0.72, U 0.79, H 0.80, G 0.74, Omega 0.78 below 1), whose average 2.57 equals Table 3, so it is one of the experiments the paper says used the DFT-derived partial charge. The parenthesis 'no spatial information as input' is literally true, but 'topology of the molecule alone' is not, by the paper's own statement. Table 1 lists seven atom features and no partial charge. The paper discloses the caveat itself in Section 8 (and the acknowledgements mention an issue with partial charges in an earlier version), so this is a wording inconsistency between the introduction and the results. The missing word in 'shown tables 3 and 4' is the subject of C024.
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Wording Section 2 gives the Kipf & Welling coefficient as "c_vw = (deg(v)deg(w))^{-1/2} A_vw" with the plain adjacency matrix, while the appendix derivation gives "Ã_vw(deg(v)deg(w))^{-1/2} h^t_w" with à = A + I_N; Section 2 also sends the reader to the supplementary material for "the exact expressions for the C^t_vw", a symbol the appendix never uses.
- p. 4 Section 2, Laplacian Based Methods
(deg(v)deg(w))−1/2 Avw
- p. 4 Section 2, Laplacian Based Methods
= ReLU(W tmt+1 v )
- p. 11 Section 10.1.1, message and update functions
Ãvw(deg(v)deg(w))−1/2ht w
- p. 11 Section 10.1.1, update function
= σ((W t)T mt+1)
Only the authors can say what is right here.
Judge's note: Read page 4 and Section 10.1 on page 11. The appendix defines à = A + I_N (self loops) and degrees from Ã; the main text uses A_vw, which would drop a node's own state from its message. The appendix writes the Bruna/Defferrard matrices as L̃_{v,w}, not C^t_vw, so the pointer does not land on a named expression. The other differences raised are harmless: ReLU is one choice of σ, W versus its transpose is only a relabelling of a learned matrix, and the missing subscript v on m^{t+1} in the appendix update is cosmetic.
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Wording Section 7 says "Each model and target combination was trained using a uniform random hyper parameter search with 50 trials", while Section 10.4 reports 300 trials (100 + 200) for the jointly trained baseline, 100 for the individually trained baseline and 100 for the jointly trained towers model; only the individually trained towers model used 50.
- p. 7 Section 7
Each model and target combination was trained using a uni- form random hyper parameter search with 50 trials.
- p. 13 Section 10.4, Table 8 paragraph
we report the minimum test error across all 300 trials
- p. 13 Section 10.4, Table 8 paragraph
For individual training of the baseline we used 100 trials
- p. 7 Section 7, first sentence
Each model and target combination was trained using a uni-form random hyper parameter search with 50 trials
Judge's note: Read Section 7 on page 7 and the Table 8 paragraph on page 13. The appendix numbers are as quoted. Section 7 is worded without exception, so the two descriptions differ, but the appendix can reasonably be read as stating the exceptions for the Table 8 comparison, so this is a consistency point and not an error in any result. The reviewer's separate point that the paper writes both 'hyper parameter' (p. 7) and 'hyperparameters' (p. 5) is true and cosmetic.
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Wording In Section 5.3 the symbol T is both the final time step and the name of the set in one expression, "the set of projected tuples T = {(h^T_v, x_v)}"; the embedding is written q*_t with an undefined subscript t, after "M steps of computation", where M elsewhere denotes the message function.
- p. 6 Section 5.3
the set of projected tuples T = {(hT v , xv)}
Judge's note: Read Section 5.3 on page 6. The expression is printed as quoted: T names the set while h^T_v uses T as the last message passing step (equation 3 on page 3). q*_t appears twice with no definition of t in this context. M as the number of set2set computations is defined later in Section 7 ('The number of set2set computations M'), and M is the message function in Sections 2 and 5.1. Readable from context; a notation overload only.
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Wording Section 7 says "We use the validation set to do early stopping and model selection and we report scores on the test set", but Section 10.4 says of the jointly trained baseline "we report the minimum test error across all 300 trials".
- p. 7 Section 7, second paragraph
We use the vali- dation set to do early stopping and model selection and we report scores on the test set.
- p. 13 Section 10.4, Table 8 paragraph
we report the minimum test error across all 300 trials
- p. 7 Section 7, second paragraph
dation set to do early stopping and model selection and we report scores on the test set
Only the authors can say what is right here.
Judge's note: Read both passages on the page 7 and page 13 images; both are as quoted. Taken literally the appendix describes choosing the trial by test error, which differs from the stated protocol. It may be loose wording for the test error of the trial selected on validation error, and it concerns the GG-NN baseline in Table 8 / Table 4, not the paper's own best model. Only the authors can say which was done.
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Wording Section 8 says "training one model per target consistently outperformed jointly training on all 13 targets", but in Table 8 individual training is worse than joint training on gap for both models (GG-NN 1.78 vs 1.73; tow8 1.68 vs 1.55) and on HOMO for towers (1.20 vs 1.19).
- p. 7 Section 8, second paragraph
also found that training one model per target consistently outperformed jointly training on all 13 targets
- p. 13 Table 8, row gap
1.73
- p. 13 Table 8, row gap, GG-NN-i
1.78
- p. 13 Table 8, row HOMO, tow8-i
1.20
Judge's note: Read Table 8 on the page 13 image. GG-NN-i is lower than GG-NN-j on 12 of 13 targets (not gap); tow8-i is lower than tow8-j on 11 of 13 (not gap, not HOMO). Averages favour individual training (1.53 vs 1.92, 1.37 vs 1.75). Table 8 is the only like-for-like joint/individual comparison in the paper, and it covers the no-explicit-hydrogen GG-NN and towers models, so the sentence may also rest on unreported experiments with other variants. 'Consistently' is slightly stronger than the one table shown supports; minor.
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Wording Table 5 ("Target DFT Error Chemical Accuracy") gives no units, and the property list in Section 10.2 that supplies units for the other targets does not include Cv, so the unit of the Cv row (.34, .050) is not stated in the appendix.
- p. 12 Table 5 header
Target DFT Error Chemical Accuracy
Judge's note: Read page 12 (Table 5 and 10.2) and the end of 10.2 on page 11. Section 10.2 describes U0, U, H, G, ω1, ZPVE, HOMO, LUMO, gap, R2, mu and alpha with units: twelve of the thirteen targets. Cv appears in every table but is not described there, and a text search finds no definition of it elsewhere in the article. Missing units in the table alone would be a style point because 10.2 gives them; the omission of Cv is the real gap. Section 10.3 does say the Table 5 numbers are mean absolute errors, so that part of the finding is not a defect.
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Typo Stray comma in the Kearnes et al. edge update: "α(W4(α(W2, e^t_vw), α(W3(h^t_v, h^t_w))))" should read α(W2 e^t_vw), a weight matrix applied to the edge state.
- p. 3 Section 2, Molecular Graph Convolutions
α(W4(α(W2, et vw), α(W3(ht v, ht w))))
Judge's note: Read the crop and page 3. The comma after W2 is printed. In the line above, the vertex update writes α(W0 h^t_v) with the matrix applied directly, and the paper defines (.,.) as concatenation, so 'W2, e' would concatenate a weight matrix with a vector. W3(h_v, h_w) shows the intended form: a matrix applied to its argument.
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Typo Misspellings: "Flourine (F) atoms" (Section 4; Fluorine), "abscence" (Section 6; absence), "accruacy" (Section 10.3; accuracy), "Alexandre haand Müller" (Rupp et al. reference; stray 'ha') and "Mller, Klaus-Robert" (Hansen et al. reference; Müller).
- p. 4 Section 4
and Flourine (F) atoms
- p. 4 Section 4, QM9 Dataset
Flourine (F) atoms
- p. 6 Section 6, Chemical Graph
abscence
- p. 12 Section 10.3
accruacy
Judge's note: Checked each on the page image or crop: 'Flourine' on page 4, 'abscence' on page 6, 'chemical accruacy' on page 12, 'Alexandre haand Müller' in the Rupp entry on page 10 and 'Mller' in the Hansen entry on page 9. All are printed in the PDF, including 'Mller', which is rendered without the ü in the image and is not an extraction loss.
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Typo Duplicated word: "which can then be fed into into a standard classifier".
- p. 4 Section 3, last paragraph
can then be fed into into a stan-
- p. 4
which can then be fed into into a stan- dard classifier
- p. 4
ntation which can then be fed into into a stan- dard classi
Judge's note: Read page 4, Section 3, last paragraph. 'into into' is printed on one line before the line break at 'stan-dard', so it is not a wrap artefact.
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Typo Reference list, personal communication entry: "Bing, Huang, von Lillenfeld, O. Anatole, and Bakowies, Dirk" misspells 'von Lilienfeld' and inverts the first author's names, so the text cites it as "(Bing et al., 2017)"; other entries print "Huang, Bing" and "von Lilienfeld, O. Anatole".
- p. 9 References, personal communication
Bing, Huang, von Lillenfeld, O. Anatole, and Bakowies,
- p. 4 Section 3
(Bing et al., 2017)
- p. 9 References, Bing et al. entry
Bing, Huang, von Lillenfeld, O. Anatole
- p. 9 References
von Lillenfeld, O. Anatole, and Bakowies
Judge's note: Read the crop of page 9: 'Lillenfeld' with a double l is typeset. The Faber, Hansen, Huang & von Lilienfeld, Montavon, Ramakrishnan and Rupp entries all print 'Lilienfeld'. The same reference list has 'Huang, Bing' as an author of the Faber entry and as first author of 'Huang, Bing and von Lilienfeld, O. Anatole', so in this entry family and given name are swapped, which is why the in-text citation on page 4 reads 'Bing et al.'. Both points are settled from the paper's own reference list.
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Typo Section 10.1 writes the identity as "L = I_n − D^{−1/2}WD^{−1/2}" where the matrices are N × N and the next subsection writes I_N; the update function "U_t(h^t_v, m^{t+1}_v) = σ((W^t)^T m^{t+1})" drops the node subscript on m and writes W^t where equations 7-8 use W^l.
- p. 11 Section 10.1, definition of the graph Laplacian
L = In − D−1/2WD−1/2
- p. 11 Section 10.1.1
Let L = D̃−1/2 ÃD̃−1/2
- p. 4 Section 2, Kipf & Welling
(deg(v)deg(w))
- p. 11 10.1.1
Let L = ˜D−1/2 ˜A ˜D−1/2
Judge's note: Read pages 11 and 4. I_n versus I_N and the missing subscript v on m^{t+1} are visible on the page image and are small notational slips. The other parts of the cluster are not defects: the second L is introduced explicitly with "Let L = D̃^{−1/2}ÃD̃^{−1/2}", the adjacency matrix being W in 10.1 (following Bruna et al.) and A in 10.1.1 (following Kipf & Welling) is locally defined each time, and identifying layer l with step t is the point of the relabelling. The message function writes Ã_vw(deg(v)deg(w))^{−1/2} without saying the degrees are those of the graph with self loops (D̃), which is loose but not clearly wrong.
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Typo Duplicated words: "which is invariant to the order of the of the tuples T".
- p. 6 Section 5.3
invariant to the order of the of
Judge's note: Read Section 5.3 on page 6. The line ends 'the order of the of' and the next begins 'the tuples T', so 'of the' is repeated in the printed text.
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Typo Section 5.3 prints a duplicated 'of the': "which is invariant to the order of the of the tuples T".
- p. 6 Section 5.3, Readout Functions
order of the of the tuples T
Judge's note: Read the crop of page 6. The line ends 'the order of the of' and the next begins 'the tuples T', so the duplication is in the typeset text and is not a line-wrap artefact.
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Typo Section 8 abbreviates Extended Connectivity Fingerprints as "ECPF4" ("Extended Connectivity Fingerprints (ECPF4, Rogers & Hahn (2010))"); the Table 2 header prints "ECFP4".
- p. 7 Section 8, description of baselines
prints (ECPF4, Rogers & Hahn (2010))
- p. 8 Table 2 header
ECFP4
- p. 7 Section 8, description of baselines
ECPF4
- p. 7 Section 8, baseline list
Extended Connectivity Finger-prints (ECPF4, Rogers & Hahn (2010))
Judge's note: Read page 7 (bold 'ECPF4' in the right column) and the Table 2 header on page 8 ('ECFP4'). The initials of the spelled-out name in the same sentence give ECFP, so the text form is a transposition; no outside knowledge is needed.
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Typo Section 8 is missing a preposition: "The experiments shown tables 3 and 4 were run with a partial charge feature" (should read 'shown in tables 3 and 4').
- p. 7 Section 8, Training Without Spatial Information
The experiments shown tables 3 and 4
Judge's note: Read the right column of the page 7 image; the sentence is printed as quoted, with no 'in'.
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Typo Section 8 is missing an article: "The state of art numbers we report in table 2 do not use this feature" (elsewhere the paper writes 'state of the art').
- p. 7 Section 8, last sentences
The state of art numbers we report in table 2
Judge's note: Read the right column of the page 7 image; 'state of art' is printed. The abstract, introduction and the same page ('previous state of the art', 'state of the art on all 13 targets') use the full phrase.
Second check: none (judge only)
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Typo Reference list, Hansen et al. (2015): author printed as "Mller, Klaus-Robert" with the 'ü' missing; the Montavon and Rupp entries print "Müller, Klaus-Robert".
- p. 9 References, Hansen et al. 2015
Mller, Klaus-Robert, and Tkatchenko
- p. 9 References, Hansen et al. entry
Mller, Klaus-Robert
Judge's note: Read the crop of page 9: 'Mller, Klaus-Robert, and Tkatchenko, Alexandre' is what is typeset, so the missing letter is in the PDF and not a text-layer loss. The same author appears as 'Müller' in two other entries on page 10, which fixes the intended spelling from the paper itself.
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Typo Reference list, Rupp et al. (2012): author list printed as "Rupp, Matthias, Tkatchenko, Alexandre haand Müller, Klaus-Robert, and von Lilienfeld, O. Anatole" with a stray 'haand'.
- p. 10 References, Rupp et al. 2012
Tkatchenko, Alexandre haand M
- p. 10 References, Rupp et al. entry
Tkatchenko, Alexandre haand M¨uller
- p. 10
Rupp, Matthias, Tkatchenko, Alexandre haand M¨uller,
Judge's note: Read the crop of page 10: 'Alexandre haand Müller' is typeset, so the garbled token is in the PDF and is not an extraction artefact.
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Typo Missing words in the appendix: "the full model can defined as stacking these operations" (can be defined); "First there the four atomization energies." (there are); "generalize the notion of convolutions a general graph G with N nodes" (convolutions to a general graph).
- p. 11 Section 10.1
can defined as stacking these operations
- p. 11 Section 10.2
First there the four atomization energies.
- p. 10 Section 10.1
of convolutions a general graph G with N nodes
Judge's note: All three sentences read as quoted on the page images of pages 10 and 11.
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Typo Section 10.3: "Both the estimates of chemical accruacy and DFT error were provided in Faber et al. (2017)"; "accruacy" should be "accuracy".
- p. 12 Section 10.3
ical accruacy and DFT error
- p. 12 Section 10.3
chem-ical accruacy and DFT error
- p. 12 10.3
chem-ical accruacy
- p. 12
Both the estimates of chem- ical accruacy and DFT error were provided
Judge's note: Visible on the page 12 image ("chem-ical accruacy" across a line break).
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Typo Table 7, row "Omega 1.28 1.05 0.78 0.78": the mn and s2s entries are both 0.78 but only the s2s entry is bold.
- p. 13 Table 7, row Omega
Omega 1.28 1.05 0.78 0.78
- p. 13 Table 7, row Omega
0.78
Judge's note: Seen on the page 13 image; in every other row of Table 7 a single lowest value is bold. The unrounded s2s value may be lower, in which case the bolding is right, so either form could be legitimate.
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Typo Section 10.4: "In Table 9 right 2 columns compare the edge network (enn) with the pair message network (pm)"; Table 9 has only two data columns (pm-j, enn-j), and the sentence is ungrammatical. Likewise "The left 4 columns" of Table 7 are all of its data columns.
- p. 13 Section 10.4
In Table 9 right 2 columns compare the edge network (enn)
- p. 14 Table 9 header
Target pm-j enn-j
Judge's note: Read the text on pages 12-13 and Table 9 on page 14 (header: Target, pm-j, enn-j) and Table 7 on page 13 (GG-NN, ve, mn, s2s). The column qualifiers look like leftovers from a wider combined table; the meaning is unaffected. The reviewer's side remark on "consistently outperforms ... across most targets" is not a defect: Table 9 shows enn better on 11 of 13 targets, which is what the main text says.
Second check: none (judge only)