Mastering the Game of Go with Deep Neural Networks and Tree Search

• p. 8 Methods, Evaluation

  computed by the BayesElo program37 using the standard constant celo = 1/400

• p. 4 Figure 4 caption

  a 230 point gap corresponds to a 79% probability of winning

Only the authors can say what is right here.

Judge's note: Page 8 crop shows the formula with exp and celo = 1/400; page 4 crop shows 'a 230 point gap corresponds to a 79% probability of winning'. exp(−230/400) = exp(−0.575) ≈ 0.5627, giving 1/(1+0.5627) = 0.640. 10^(−0.575) ≈ 0.2661, giving 1/(1+0.2661) = 0.790. So the caption follows the base-10 Elo formula and the printed Methods formula does not reproduce it. Nothing elsewhere in the paper redefines celo. The denominator also appears to be missing a closing parenthesis. Either the base or the constant is misprinted; authors to say which.

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• p. 8 Methods, Neural network architecture

  Fig. 2b and Extended Data Table 3 additionally show the results of training with k = 128, 256 and 384 filters

• p. 2 Figure 2 caption

  a, Plot showing the playing strength of policy networks as a function of their training accuracy. Policy networks with 128, 192, 256 and 384 convolutional filters per layer

• p. 8

  Fig. 2b and Extended Data Table 3 additionally show the results

• p. 8 Methods, Neural network architecture

  Fig. 2b and Extended Data Data Table 3 additionally show the results of training with k = 128, 256 and 384 filters

Judge's note: Page 8 crop confirms the sentence as quoted (the 'Data Data' variant is a reviewer transcription slip). Page 2 image: panel a's legend lists 128, 192, 256 and 384 filters and the caption says so; panel b plots mean squared error of the value network versus rollout policies by move number and has no filter-count data. The main text on page 2 correctly cites Fig. 2a. The missing 384 row in Extended Data Table 3 is handled in C021.

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• p. 6 Reference list, entry 27

  27. Sutton, R. & Barto, A. Reinforcement Learning: an Introduction (MIT Press, 1998).

• p. 3 Reinforcement learning of value networks

  tion s of games played by using policy p for both players28–30

Only the authors can say what is right here.

Judge's note: Reference 27 is in the list on p6. Searched the whole extracted text for a citation of 27, alone or inside a range: the citation groups are 13–15, 21–24, 25,26, 28–30, 28,29,47, 24,28,29 and so on, and none covers 27; every other "27" in the text is a move number in a figure or a table value. Checked p2 (25,26) and p3 (28–30) on the images. A citation was probably lost; the authors must say where it belongs.

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• p. 6 Reference list, entry 16

  In 17th International Conference on Machine Learning, 273–280 (2007).

• p. 6 Reference list, entry 24

  In 32nd International Conference on Machine Learning, 1766–1774

• p. 9 Reference list, entry 51

  In 26th International

• p. 9 Reference 39

  In 11th International Conference on Machine Learning, 157–163

Judge's note: Read refs 16 and 24 on p6 and refs 39 and 51 on p9. All three other entries fit ordinal = year - 1983, so 2007 gives 24th, not 17th. The inference is internal to the reference list (it assumes one conference a year, which the three entries are consistent with). The image shows "17th", so it is not an extraction artefact.

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• p. 7 Methods, Search algorithm, Expansion (Fig. 3b)

  P(s′,a) = pσ(a|s′)}, using a tree policy pτ(a|s′)

• p. 7 Methods, Expansion, later sentence

  these replace the placeholder prior probabilities

Judge's note: Read the passage on the p7 image and the crop: the subscript in the initialisation is σ and the tree policy is pτ. The same paragraph says the tree policy supplies placeholder priors and that the SL policy network output replaces them after asynchronous GPU evaluation; the distributed-search paragraph and the Extended Data Table 7 legend ("placeholder probabilities from the tree policy pτ") say the same. So the initialisation as printed contradicts the surrounding description; the evident reading is P(s′,a) = pτ(a|s′). A symbol error; the described algorithm is clear from the text.

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• p. 12 Extended Data Table 3 caption

  20 input feature planes listed in Extended Data Table 1

• p. 10 Extended Data Table 1 title

  Details of match between AlphaGo and Fan Hui

• p. 11 Extended Data Table 2 title

  Input features for neural networks

• p. 12

  input feature planes listed in Extended Data Table 1.

Judge's note: Read the ED Table 3 caption on p12 in the image. ED Table 1 (p10) lists the Fan Hui match games: date, colours, category, result. ED Table 2 (p11) is titled 'Input features for neural networks'. The main text (text-layer lines 77 and 2563) cites ED Table 2 for the input features. The first 4, 12 and 20 planes match ED Table 2's rows (3+1=4, +8=12, +8=20). The caption pointer is wrong.

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• p. 15 Extended Data Table 6 caption

  CN4, ZN4 and PC4 were given 4 handicap stones

• p. 15 Extended Data Table 6, Short name column

  CS4

• p. 15

  CN4, ZN4 and PC4 were given 4 handicap stones;

• p. 18 Extended Data Table 9 footnote

  CN4, ZN4 and PC4 were given 4 handicap stones

Judge's note: Page 15 image: rows are CS4, ZN4, PC4 and the footnote reads CN4. Page 18 crop: row label CS4, footnote CN4 again. No program is abbreviated CN anywhere.

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• p. 16 Extended Data Table 7 caption

  either using the policy network pσ(αrvp, αvp, αrp), or no policy network (αrvp, αvp, αrp)

• p. 16 Extended Data Table 7, Policy network column

  [pτ]

• p. 16

  or no policy network (αrvp, αvp, αrp)

• p. 16 Extended Data Table 7 footnote

  or no policy network (αrvp, αvp, αrp), that is, instead using the placeholder probabilities from the tree policy pτ throughout

Judge's note: Read the subscripts in the caption image on p16: both lists clearly read αrvp, αvp, αrp. In the table, the rows αrv, αv and αr have [pτ] in the Policy network column, and αrvp, αvp and αrp have pσ. So the second list should be (αrv, αv, αr). This is a labelling error in the caption; the data are fine.

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• p. 18 Extended Data Table 9 caption

  CN4, ZN4 and PC4 were given 4 handicap stones

• p. 18 Extended Data Table 9, row labels

  CS4

• p. 18

  CN4, ZN4 and PC4 were given 4 handicap stones;

Judge's note: Viewed the crop and the full page 18 image. Row labels are CS, ZN, PC, FG, GG, CS4, ZN4, PC4; there is no CN row or program abbreviated CN anywhere in the table. The footnote clearly prints CN4 in italics with subscript 4. The text layer shows the same label mismatch in the Extended Data Table 6 caption (CS4 row, CN4 in caption), so this is a repeated caption typo, not an extraction artefact. Rated S2 as a wrong label in a caption; the data are unaffected and the intended meaning is evident.

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• p. 7 Methods, Expansion (Fig. 3b)

  {N(s′, a) = Nr(s′, a) = 0, W(s′, a) = Wr(s′, a) = 0

• p. 7 Methods, Search algorithm, edge statistics

  {P(s, a), Nv(s, a), Nr(s, a), Wv(s, a), Wr(s, a), Q(s, a)}

Judge's note: Read page 7 image. The search-algorithm paragraph defines only Nv, Nr, Wv, Wr; the backup paragraph updates Nv/Wv and Nr/Wr. The expansion line pairs un-subscripted N, W with Nr, Wr and never initialises Nv, Wv, so the subscript v was dropped. Notation slip; meaning recoverable.

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