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Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context

Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, 2019 · paper · AI and machine learning

Introduces Transformer-XL, a language model architecture that reuses information across text segments and uses a new positional encoding to capture dependencies beyond a fixed length. It reports improved results on several language modeling benchmarks and much faster evaluation than vanilla Transformers.

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

2 findings

Reference or label The reference entry "Bryon Knol. 2017. cmix v13." and the Table 2 citation "Knol (2017)" misspell the author's name; the entry's own URL is byronknoll.com.
  • p. 10 Reference list
    Bryon Knol. 2017. cmix v13.
  • p. 6 Table 2
    Knol (2017) - cmix v13
  • p. 10 References
    Bryon Knol. 2017.

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: the author of cmix is Byron Knoll. Within the file, the URL in the same entry (http://www.byronknoll.com/cmix.html) supports this. The page-10 and page-6 images show 'Bryon Knol' and 'Knol (2017)'.

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Wording Appendix B, explicit matrix B, last row: "q⊤_{L−1}W_{k,R}R_{M+L−1} ··· q⊤_{L−1}W_{k,R}R_{M+L−1} q⊤_{L−1}W_{k,R}R_{L−1} ··· q⊤_{L−1}W_{k,R}R_0". Columns M and M+1 should be R_{L−1} and R_{L−2}, as in the Q-form below.
  • p. 12 Appendix B, definition of B (first form, last row)
    q⊤L−1Wk,RRM+L−1 · · · q⊤L−1Wk,RRM+L−1

Only the authors can say what is right here.

Judge's note: Worked from the page-12 image. Q_k = W_{k,R}R_{M+L−1−k}. In the Q-form, row L−1 is Q_0..Q_M, Q_{M+1}..Q_{M+L−1}, so column M = W R_{L−1} and column M+1 = W R_{L−2}. Rows 0 and 1 of the R-form agree with this pattern (row 0 ends at R_0 in column M; row 1 has R_1 in column M and R_0 in column M+1). Row L−1 of the R-form instead prints R_{M+L−1} in column M and R_{L−1} in column M+1. The two printed forms of B therefore disagree. The Q-form, B̃, and the shift procedure are unaffected, so the method stands.

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19 minor (typos and the like; most checked by the judge only)
Wording The abstract, the Introduction and Section 4.4 say the model generates "coherent, novel text articles with thousands of tokens" (see Appendix E). Appendix E says it generates "a pre-defined number of tokens (500 or 1,000 in our case)".
  • p. 1 Abstract
    text articles with thousands of tokens
  • p. 2 Introduction
    cles with thousands of tokens (see Appendix E)
  • p. 8 Section 4.4
    relatively coherent articles with thousands of to-kens
  • p. 16 Appendix E
    tokens (500 or 1,000 in our case)

Only the authors can say what is right here.

Judge's note: The Appendix E text on page 16 limits generation to 500 or 1,000 tokens after a seed of at most 512 tokens. No sample cited as support reaches 'thousands' of generated tokens. The authors may have longer unreported samples, so the wording is put as a query.

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Wording "The RECL of Transformer-XL is 80% and 450% longer than recurrent networks and Transformer respectively" comes straight after the 900-word result. The 80% comes from the 151M group (900 vs QRNN 500); the 450% matches only the 128M group (700 vs 128). Neither the text nor the abstract says so.
  • p. 8 Section 4.3, text after Table 8
    The RECL of Transformer-XL is 80% and 450% longer than recurrent net-works and Transformer respectively
  • p. 8 Table 8
    Transformer-XL 128M
  • p. 1 Abstract
    80% longer than RNNs and 450% longer than vanilla Trans-formers
  • p. 8 Section 4.3 text and Table 8
    The RECL of Transformer- XL is 80% and 450% longer than recurrent net- works and Transformer respectively.

Only the authors can say what is right here.

Judge's note: Table 8 on page 8 gives Transformer-XL 151M = 900 and QRNN = 500 at r=0.1, and Transformer-XL 128M = 700 and Transformer = 128. The caption says RECL is computed per model group, so the within-group comparison is legitimate. The sentence does not say which Transformer-XL model each percentage uses, and its subject reads as the 900-word model.

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Wording Appendix D says of the WikiText-103 SoTA model "Recall that, this model has 16 10-head transformer layers and relies on a memory of length 640", but the paper never states these settings earlier, and Section 4.1 gives "the attention length to 384 during training and 1600 during evaluation" for WikiText-103.
  • p. 14 Appendix D, first paragraph
    Recall that, this model has 16 10-head transformer layers and relies on a memory of length 640.
  • p. 6 Section 4.1, WikiText-103 paragraph
    the attention length to 384 during training and 1600 during evaluation
  • p. 8 Table 6, Transformer-XL (151M) row
    640
  • p. 14 Appendix D
    this model has 16 10-head transformer layers and relies on a memory of length 640

Only the authors can say what is right here.

Judge's note: Checked p.14 (Appendix D, Fig. 5 caption 'previous 640 tokens'), p.6 (Sec. 4.1: 384/1600) and p.8 (Table 6: 640 appears only as the attention length for the 151M ablation model; text says attention length 'can be increased to 640 at test time' in the ablation). I searched the text and found no earlier statement of 16 layers, 10 heads or memory 640 for the SoTA (257M, 18.3 PPL) model. So 'Recall that' points back to something the paper does not say. The visualisation may have used a shorter memory than the main evaluation, but the paper does not say so. Which model and settings were visualised is a question for the authors.

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Wording Table 10 labels the loss "Partial" and the columns "pplx best / pplx init". Table 6 and Section 4.2 call the same setting "Half" and order the columns "PPL init / PPL best" (same values: 26.77/27.02/500, 28.33/28.69/460).
  • p. 12 Table 10, Loss column and header
    Partial
  • p. 8 Table 6, Loss column
    Half
  • p. 12 Table 10 header
    pplx best
  • p. 8 Table 6 header
    PPL init

Judge's note: The page-12 and page-8 images show identical numbers under different labels. Section 4.2 (page 7) defines only 'Full' and 'half' losses, so 'Partial' is undefined. The values sit in the correct columns, so only the terminology and column order differ.

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Wording RECL algorithm step 2: "set c = c′, c′ = c + ∆ and go to step 1." Step 1 is "Set initial short context length c", so returning to it would re-initialise c. The loop should return to step 2.
  • p. 14 Appendix C, RECL algorithm step 2
    set c = c′, c′ = c + ∆ and go to step 1.

Judge's note: Read on the page-14 image. Taken literally, step 1 resets c to its initial value and cancels the update made in step 2. The intended loop is clear: recompute g_i(c,c′), i.e. go to step 2.

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Wording Appendix D's head-158 bullet reads "the pattern is also different from the case of head 8, where a few locations are clearly attended more than others". Grammatically this gives head 8 a peaked pattern, but the first bullet describes head 8 as "almost uniform attention over the entire memory span".
  • p. 14 Appendix D, first bullet
    For the head 8 in the 1st layer, we see an almost uniform attention over the entire memory span
  • p. 15 Appendix D, third bullet
    different from the case of head 8, where a few locations are clearly attended more than others

Only the authors can say what is right here.

Judge's note: p.14 first bullet: head 8 is near-uniform. p.15 third bullet: the relative clause attaches to head 8. Fig. 6a (head 8) on p.15 looks diffuse, while Fig. 6c (head 158) shows scattered peaks. The clause probably means to describe head 158 in contrast to head 8, but as printed the two descriptions of head 8 contradict each other. The wording is ambiguous; I do not take this as evidence of a wrong head number.

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Wording The Table 11 commentary says XL "accurately uses the the phrase 'another back injury' in the 2013 season paragraph, since it has talked about one earlier injure in the 2012 season", but the only earlier injury to Kershaw in the 2012 generated text is "a shoulder injury" (the other is an injury to Javier Vázquez).
  • p. 17 Observations below Table 11, third bullet
    accurately uses the the phrase “another back injury” in the 2013 season paragraph
  • p. 17 Table 11, XL Generation, 2012 season
    expected to miss the season as a result of a shoulder injury
  • p. 17 Table 11 commentary, third bullet
    accurately uses the the phrase

Judge's note: On the p.17 image, the XL Generation 2012 section mentions 'After an injury to closer Javier Vázquez' and 'expected to miss the season as a result of a shoulder injury'. Neither is a back injury. 'Another' could be read loosely as 'another injury', so calling the use 'accurate' is an overstatement rather than a clear error. The typo parts are covered by C023.

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Typo Dataset name misspelled "en-wiki8" (abstract) and "enwiki8" (Section 3.2); elsewhere, e.g. the Table 2 caption, it is "enwik8".
  • p. 1 Abstract
    0.99 on en- wiki8
  • p. 4 Section 3.2, para 'Besides achieving extra long context'
    periments on enwiki8, Transformer-XL is up to
  • p. 4 Section 3.2
    In our ex-periments on enwiki8

Judge's note: In the page-1 abstract crop the text reads 'en-/wiki8', with the extra 'i'. The page-4 crop reads 'experiments on enwiki8'. The Table 2 caption on page 6 reads 'enwik8'.

Second check: none (judge only)

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Typo "Despite the wide adaption, RNNs..." and "since the ubiquitous adaption of LSTM": 'adoption' is meant.
  • p. 1 Introduction, col 2
    wide adaption, RNNs are difficult to optimize
  • p. 2 Section 2
    since the ubiquitous adaption of LSTM

Judge's note: Both instances are visible in the page images (p1 col 2, p2 Section 2). The sense is widespread use, so the word should be 'adoption'.

Second check: none (judge only)

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Typo In the N-layer computation summary, term (c) is printed "+ u⊤ k_{τ,j}" without the layer superscript n, while term (a) uses k^n_{τ,j}.
  • p. 5 Section 3.3, computational procedure, A^n_{τ,i,j}
    + u⊤kτ,j + v⊤Wn k,RRi−j

Judge's note: The page-5 crop shows A^n_{τ,i,j} = q^n⊤k^n + q^n⊤W^n_{k,R}R_{i−j} + u⊤k_{τ,j} + v⊤W^n_{k,R}R_{i−j}. The superscript n on k is missing only in term (c). This is a notational inconsistency, and the meaning is clear.

Second check: none (judge only)

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Typo The dataset name is written "WikiText-103" in the main text (e.g. Sec. 4.1) but "Wikitext-103" in Appendix E and the Table 11 caption.
  • p. 16 Appendix E
    Wikitext-103 dataset
  • p. 6 Section 4.1
    WikiText-103 (Merity et al.,

Judge's note: Both spellings are visible on p.6 and p.16/17. This is a cosmetic consistency point.

Second check: none (judge only)

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Typo Grammar slips: "our relative positional encodings is also superior" (Sec 4.2), "This example exhibit some additional interesting properties" (after Table 12), and "corresponds to a attention head ... There are totally 160 attention heads" (Fig. 5 caption).
  • p. 7 Section 4.2, last sentence
    relative positional encodings is also superior to
  • p. 18 Notes below Table 12
    This example exhibit some additional interesting properties
  • p. 14 Figure 5 caption
    There are totally 160 attention heads
  • p. 14 Figure 5 caption
    corresponds to a attention head

Judge's note: All phrases are visible in the page-7, page-18 and page-14 crops. They are subject-verb agreement and article errors.

Second check: none (judge only)

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Typo "See Appedix C for more details about RECL.": 'Appedix' should be 'Appendix'.
  • p. 8 Section 4.3
    See Appedix C for more details about RECL.
  • p. 8 Section 4.3
    See Appedix C for more details about RECL

Judge's note: Visible in the page-8 image. The pointer target (Appendix C, RECL details) is correct.

Second check: none (judge only)

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Typo "the gain of a long context is measure by the relative improvement": should be 'measured by'.
  • p. 8 Section 4.3
    measure by the relative improvement over the best

Judge's note: Visible in the page-8 image (Section 4.3).

Second check: none (judge only)

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Typo Appendix C: "we define the set T is the above equation as" should read "in the above equation".
  • p. 14 Appendix C
    we define the set T is the above equation as

Judge's note: Visible on the p.14 page image, first paragraph.

Second check: none (judge only)

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Typo Appendix E: "We seed the our Transformer-XL" has an extra determiner (should be "We seed our Transformer-XL").
  • p. 16 Appendix E, first paragraph
    We seed the our Transformer-XL
  • p. 16 Appendix E, first paragraph
    denote the Wikipedia page tile, section title and subsection title

Judge's note: Visible on the p.16 page image, Appendix E first paragraph. The 'page tile' typo is handled in C020 and the missing 'on' in C021.

Second check: none (judge only)

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Typo Appendix E: "denote the Wikipedia page tile, section title and subsection title"; "tile" should be "title".
  • p. 16 Appendix E, first paragraph
    denote the Wikipedia page tile, section title and subsection title

Judge's note: Visible on the p.16 page image.

Second check: none (judge only)

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Typo Appendix E: "our best model trained the Wikitext-103 dataset" is missing "on" ("trained on the").
  • p. 16 Appendix E
    trained the Wikitext-103 dataset
  • p. 16 Appendix E
    We seed the our Transformer-XL

Judge's note: Visible on the p.16 page image, first sentence of Appendix E. The 'the our' part of this cluster is covered by C019.

Second check: none (judge only)

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Typo The observations below Table 11 contain three typos: "accurately uses the the phrase" (duplicated 'the'), "one earlier injure in the 2012 season" ('injury'), and "to the finally 2013 season" ('final').
  • p. 17 Observations below Table 11
    accurately uses the the phrase
  • p. 17 Observations below Table 11
    one earlier injure in the 2012 season
  • p. 17 Table 11 commentary, third bullet
    accurately uses the the phrase “another back injury” in the 2013 season paragraph, since it has talked about one earlier injure in the 2012 season
  • p. 17 Table 11, XL Generation, 2012 season
    expected to miss the season as a result of a shoulder injury

Judge's note: All three are visible on the p.17 page image in the bullets after Table 11. The shoulder-vs-back injury point is judged in C024.

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