Gradient-Based Learning Applied to Document Recognition
Proceedings of the IEEE, 1998 · paper · AI and machine learning
Reviews methods for handwritten character recognition and introduces Graph Transformer Networks for training multi-module document systems globally. Convolutional networks outperform other techniques on digit recognition, and a check-reading system built on them is deployed commercially.
Checked: PDF from vision.stanford.edu, fetched 4 Oct 2026. Page numbers are those of that PDF.
10 findings
Substance Sec. III-C.6 (p13) names the two-hidden-layer net '28x28-1000-150-10' (2.95%, and 2.45% with distortions), while Figs. 9, 11 and 12 give the same 2.95 and 2.45 results for '28x28-500-150-10'.
- p. 13 Section III-C.6
Increasing the network size to 28x28-1000-150-10 yielded
- p. 12 Fig. 9 labels
28x28−500−150−10
- p. 14 Fig. 11 labels
28x28−500−150−10
- p. 13 Sec. III-C.6, distorted-training sentence
2.45% for the 28x28-1000-150-10 network
Judge's note: p13 text: 'Increasing the network size to 28x28-1000-150-10 yielded only marginally improved error rates: 2.95%' and '2.45% for the 28x28-1000-150-10 network'. Fig. 9 (p12) shows 2.95 and 2.45 only for 28x28-500-150-10, and its 28x28-1000-10 rows (4.5/3.8) are the one-hidden-layer net. Fig. 11 gives 469 (thousand) multiply-adds and Fig. 12 gives 469 (thousand) variables for 500-150-10. Both values match 500 first-layer units, not 1000. The text label is the one that is inconsistent.
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Substance Sec. III-C.11 (p14): RS-SVM 'attained 1.1% on the regular test set', but in Fig. 9 the 'RS-SVM poly 5' bar is labelled '1' and is visibly shorter than the 1.1 bars for Tangent Distance and SVM poly 4.
- p. 14 Section III-C.11
which attained 1.1% on the regular test set
- p. 12 Fig. 9 bar for RS-SVM poly 5
RS−SVM poly 5
- p. 14 Sec. III-C.11, RS-SVM
which attained ! on the regular test set
- p. 14 C.11
(RS-SVM), which attained 1.1% on the regular test set
Only the authors can say what is right here.
Judge's note: The Fig. 9 crop shows the RS-SVM label '1', with neighbouring bars labelled '1.1'. The p14 text gives 1.1%. The two values for the same result cannot both be right as printed, and only the authors can say which is correct. The Fig. 9 caption's 'uncertainty about 0.1%' does not explain printing two different values.
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Substance p.39 Section X-C: "confidence = exp(E_dforw)" lacks the minus sign; Section VI-E says the posterior estimate is the exponential of minus E_dforw.
- p. 39 Section X-C
confidence = exp (Edforw)
- p. 26 Section VI-E
the exponential of minus Edforw can be interpreted as an estimate of the posterior probability
- p. 39 Sec. X-C
confidence = exp(E_dforw)
Judge's note: The p.39 image shows 'confidence = exp(E_dforw)' with no minus, and the text layer has 'expE dforw', also with no minus. Section VI-E (p.26) says 'the exponential of minus E_dforw can be interpreted as an estimate of the posterior probability'. P.26 also states that the constrained forward penalty is always at least the unconstrained one, so E_dforw is non-negative and exp(E_dforw) is at least 1, which cannot be a probability. The surrounding p.39 text calls the loss an estimate of the log of this probability.
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Reference or label 'the set of centers of the receptive fields of the last convolutional layer (C3, see below) form a 20x20 area': the last convolutional layer of LeNet-5 is C5, not C3.
- p. 7 Section II-B
the last convolutional layer (C3, see below)
Only the authors can say what is right here.
Judge's note: Page 7 lists the convolutional layers as C1, C3 and C5. Either the word 'last' or the label 'C3' is wrong, and only the authors can say which.
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Reference or label Fig. 12 (p15) labels the distortion-trained virtual SVM '[dist] V−SVM poly 5', whereas Figs. 9 and 11 label the same entry '[dist] V−SVM poly 9'.
- p. 15 Fig. 12 label
[dist] V−SVM poly 5
- p. 14 Fig. 11 label
[dist] V−SVM poly 9
- p. 12 Fig. 9 row label
[dist] V−SVM poly 9
- p. 15 Fig. 12 label
V−SVM poly 5
Judge's note: The crops confirm 'poly 9' in Fig. 9 (p12) and Fig. 11 (p14), and 'poly 5' in Fig. 12 (p15). It is the same row in the same position with the same 28,000 off-scale marker as Fig. 11. The paper describes only one V-SVM, and RS-SVM is the poly 5 entry.
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Reference or label 'the second-derivative back-propagation Equation 22 given in the Appendix' points to Eq. 22, which is the exact h_kk double-sum formula. The Gauss-Newton second-derivative back-propagation that bbprop implements is Eq. 27 (Eq. 26 is the exact recursion).
- p. 18 Section IV-B
second-derivative back-propagation Equation 22 given in the Appendix
- p. 18 Sec. IV-B, bbprop paragraph
Equation given in the Appendix
- p. 42 Appendix C, Eq. (22) vs Eqs. (26)-(27)
The exact formula
Judge's note: Checked page 18 and the Appendix C numbering on page 42.
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Reference or label p.31: "Another example of transduction was mentioned in Section V: the path selector used in the heuristic over-segmentation training GTN"; the path selector is introduced in Section VI-A, not Section V.
- p. 31 Sec. VIII-B
Another example of transduction was mentioned in Section V: the path selector used in the heuristic over-segmentation training GTN
Judge's note: The text layer has no occurrence of 'selector' before p.21. On p.21 (Section VI-A, Viterbi Training, Fig. 19) the path selector is introduced as 'an extra graph transformer called a path selector', and on p.22 back-propagation through it is described. Section V (recognition with HOS) does not mention it.
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Reference or label p.38: "The segmentation transformer T_seg, similar to the one described in Section VIII"; Section VIII (pp.31-34) describes no segmentation transformer.
- p. 38 Section X-A
similar to the one described in Section VIII
- p. 38 Sec. X-A
similar to the one described in Section VIII examines each zone
Only the authors can say what is right here.
Judge's note: Section VIII (pp.31-34) covers transducers, generalized composition, notes on graph structures and GTN/HMMs; it does not describe a segmenter, apart from the remark on p.32-33 that segmenters can be formulated as generalized transduction. Segmenters are described in Section V-A (HOS) and in Section IX-C (the on-line system's Segmentation Transformer, p.36). Only the authors can say whether V or IX was intended.
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Wording Sec. II-C (p9): the MSE criterion 'lacks three important properties', but only two are described ('First, ... collapse' and 'The second problem is that there is no competition between the classes').
- p. 9 Section II-C
it lacks three important properties
- p. 9 Section II-C Loss Function
it lacks three important properties. First, if we allow the
Judge's note: Read the full Loss Function subsection on the p9 image. After 'First' and 'The second problem', no third property is stated before the text moves on to the MAP criterion.
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Wording Sec. VI intro (p21): 'The following section describes three different gradient-based methods ...: Viterbi training, discriminative Viterbi training, forward training, and discriminative forward training' lists four methods.
- p. 21 Section VI intro
describes three different gradient-based methods
- p. 21 Sec. VI, intro
describes three di erent gradient
- p. 21 Sec. VI, same sentence
Viterbi training, discriminative Viterbi training, forward training, and discriminative for ward training
- p. 21 Section VI intro
The following section describes three different gradient-based methods for training GTN-based handwriting recognizers at the string level: Viterbi training, discriminative Viterbi training, forward training, and discriminative forward training.
Judge's note: The p21 image shows the sentence with four items, and Sections VI-A to VI-D treat four methods. 'The last one' refers to the fourth item.
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50 minor (typos and the like; most checked by the judge only)
Reference or label Sec. I-D (p4): 'Section V explores various ways to ensure that the loss function is differentiable', but the loss functions and their differentiability (Viterbi, discriminative and forward training) are in Section VI, as the p2 roadmap also says.
- p. 4 Section I-D
The first solution, described in Section V consists in training the system at the level of whole strings
- p. 4 Section I-D
The first solution, described in Section V consists in training the system at the level of whole strings of characters
- p. 4 Section I-D
explores various ways to ensure that the loss function is differentiable
- p. 4 Sec. I-D, paragraph on the first solution
Section V explores various ways to ensure that the loss function is dif
Only the authors can say what is right here.
Judge's note: p4 attributes both the string-level training solution and the loss-function discussion to Section V. Section V (Heuristic Over-Segmentation) covers the segmentation graph and the recognition/Viterbi transformers. Its own opening says 'This section and the next describe in detail a simple example of GTN', so pointing the first solution at Section V is defensible. The specific claim about making the loss differentiable belongs to Section VI. The p2 roadmap places GTN in Section IV and the training methods in Section VI. Rated minor because Sections V and VI form one exposition.
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Wording The Introduction (p2) says 'It is reading millions of checks per month in several banks across the United States', while the Abstract ('reads several million checks per day'), Sec. X-D ('has been reading millions of checks per day since then') and the Conclusions (p40, 'reads millions of business and personal checks per day') give a daily rate.
- p. 2 Introduction
It is reading millions of checks per month
- p. 40 Section X-D
has been reading millions of checks per day since then
- p. 1 Abstract
reads several million checks per day
- p. 2 Introduction, last paragraph before I-A
It is reading millions of checks per month in several banks across the United States
Only the authors can say what is right here.
Judge's note: Checked p2 (crop), p1 and p40. All four statements describe the same NCR deployment, and nothing in the text says they cover different periods. 'Millions per day' does not strictly contradict 'millions per month', but the stated volumes differ by about 30x, and only the authors can say which rate is meant.
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Wording Section I-D says Section V 'introduces the idea of GTN', while the roadmap says GTNs are 'also introduced in Section IV'.
- p. 4 Section I-D
and introduces the idea of GTN
- p. 2 Introduction roadmap
also introduced in Section IV
Judge's note: GTNs are defined in Section IV-C, and Section V presents a simple GTN example. The wording is loose rather than clearly wrong.
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Wording Sec. III-D (p14): 'Figure 10 shows the number of patterns in the test set that must be rejected', while the Fig. 10 caption reads 'percentage of test patterns that must be rejected to achieve 0.5% error'.
- p. 14 D. Discussion
Figure 10 shows the number of patterns in the test set
- p. 14 Fig. 10 caption
percentage of test patterns that must be rejected to achieve 0.5% error
Judge's note: On the p14 image, the Fig. 10 axis runs 0–9 with values such as 8.1 and 0.5, which are percentages. The text's 'number of patterns' misdescribes the unit. Minor, because the caption makes the unit clear.
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Wording 'The reduced-set SVM requirements are within a factor of two of the Convolutional Networks' holds for multiply-accumulates (Fig. 11: 650 vs 401) but not for memory (Fig. 12: 650 vs 60).
- p. 15 Section III-D Discussion
The reduced-set SVM requirements are within a factor of two of the Convolutional Networks
- p. 15 Fig. 12
650
Only the authors can say what is right here.
Judge's note: The preceding sentence refers to both memory and computational requirements, so the factor-of-two claim reads as covering both. It holds only for computation.
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Typo Wrong verb forms in several places: 'to provides record accuracy' (Abstract, p1), 'forces the recognizer to increases' (p24), 'is often use in HMM-based' (p22), 'an produce the forward penalty' (p25), 'any final user would chose the latter' (p15).
- p. 1 Abstract
to provides record accuracy
- p. 24 Section VI-B
forces the recognizer to increases
- p. 22 Section VI-A
is often use in HMM-based
- p. 25 Section VI-C
an produce the forward penalty
Judge's note: All five slips appear in the page images: the Abstract on p1; the crop of p24 left column ('to in-creases'); the crop of p22 ('is often use'); p25 left column ('an produce the forward penalty of that graph on output'); p15 left column ('would chose the latter'). They are plain copy-editing errors.
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Typo Sec. I-E (p4): 'each path represent a alternative interpretation of the input string' should read 'each path represents an alternative interpretation'.
- p. 4 Section I-E
each path represent a alternative interpretation of the input string
Judge's note: The phrase appears as quoted in the p4 right column.
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Typo Sec. I-E (p5): 'In By analogy with ordinary multi-layer neural networks, all but the last module are called hidden layers ... outside. more complex situations than the simple cascade of modules' — the hidden-layers sentence is spliced into the sentence 'In more complex situations...'.
- p. 5 Sec. I-E, after the Jacobian discussion
In By analogy with ordinary multi-layer neural networks, all but the last module are called hidden layers
- p. 5 Right after Eq. 4 discussion, left column
In By analogy with ordinary multi-layer neural
- p. 5 Sec. I-E, after Eq. 4
In By analogy with ordinary multi-layer neural networks, all but the last module are called hidden layers because their outputs are not observable from the outside. more complex situations than
Judge's note: The p5 crop shows the splice as printed. A stray 'In' precedes 'By analogy', and the paragraph continues with a lowercase 'more complex situations'. It is a typesetting/editing error, not an extraction artefact.
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Typo 'half the number of rows and column as feature maps in C1' should read 'rows and columns'.
- p. 7 Layer S2 description
have half the number of rows and column as
Judge's note: The phrase is visible on page 7.
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Typo Sec. II-B (p8): 'is described in the section Section VII' repeats 'section'.
- p. 8 Section II-B, C5 paragraph
is described in the section Section VII
- p. 8 Layer C5 paragraph
described in the section Section VII
Judge's note: The phrase is visible in the p8 left column, in the Layer C5 paragraph.
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Typo 'many existing method combine' should read 'many existing methods combine'.
- p. 9 Section III intro
Though many existing method com
Judge's note: The phrase is visible on page 9.
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Typo 'The reason for this can be found on the fact that' uses the wrong preposition; it should read 'found in the fact'.
- p. 9 Section III-A
The reason for this can be found on the fact that SD-3
Judge's note: The crop confirms the wording.
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Typo The Fig. 6 caption 'The hollow square show the test error' should read 'shows'.
- p. 11 Fig. 6 caption
The hollow square show the test error
Judge's note: The caption is visible on page 11.
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Typo 'recent theoretical analysis seem to confirm this' has a subject-verb disagreement; it should read 'seems' (or 'analyses seem').
- p. 13 C.5
recent theoretical analysis seem to conrm
Judge's note: Wording checked on page 13, Section C.5.
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Typo 'any final user would chose the latter' should read 'would choose'.
- p. 15 Section III-D Discussion
any final user would chose the latter
- p. 15 Discussion, training time paragraph
any nal user would chose the latter
Judge's note: Wording checked on page 15.
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Typo 'The Overall performance depends on many factors' has a wrongly capitalised 'Overall'.
- p. 15 Discussion
The Overall performance depends on many factors
Judge's note: Checked on page 15.
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Typo The Fig. 15 caption 'communicate fixed-size vectors between layer' should read 'between layers'.
- p. 18 Fig. 15 caption
communicate xedsize vectors between layer
Judge's note: Checked on page 18.
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Typo 'viewing the system as a networks of modules' should read 'a network of modules'.
- p. 18 Section IV-C
viewing the system as a networks of modules
Judge's note: The crop confirms the wording.
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Typo The same module is spelled 'segmentor' (Section V, Fig. 18) and 'segmenter' (Fig. 20, Section X).
- p. 19 V-A
if the segmentor decided that
- p. 23 Fig. 20
Segmenter
Judge's note: Both spellings are acceptable; the point is only consistency.
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Typo The Fig. 18 caption 'refines each arc of the segmentation arc into a set of arcs' should read 'segmentation graph'.
- p. 20 Fig. 18 caption
each arc of the segmen
Judge's note: Checked on page 20.
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Typo Sec. VI intro (p21): 'such as the the Baum-Welsh algorithm' has a duplicated 'the'; the algorithm's name is spelled 'Baum-Welsh' here and also on p25.
- p. 21 Section VI intro
Baum-Welsh algorithm
- p. 21 Section VI intro
such as the the BaumWelsh algorithm
Judge's note: p21 shows 'the the Baum-Welsh algorithm', and p25 also has 'Baum-Welsh'. The duplicated word is visible on the page. The 'Welch' spelling part rests on outside knowledge: the algorithm is named after Lloyd Welch, a fact not stated in the files.
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Typo p.21 reads 'such as the the Baum-Welsh algorithm', with 'the' duplicated.
- p. 21
MM learning metho ds suc h as the the BaumW elsh algorith
Judge's note: The duplicated word is visible in the crop.
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Typo Fig. 20 (p23) has the misspelled box label 'Viterbi Tansformer' (another label reads 'Transfomer' in the text layer).
- p. 23 Fig. 20
Viterbi Tansformer
Judge's note: The crop shows 'Viterbi Tansformer' on the left side of Fig. 20, beside a correctly spelled 'Viterbi Transformer' on the right. I did not separately check the 'Transfomer' label on the image.
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Typo Figure label on p.23 reads "Recognition Transfomer" (should be "Transformer").
- p. 23
Recognition Transfomer
Judge's note: Crop shows the figure label 'Recognition Transfomer' next to T_rec; misspelling is in the printed figure.
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Typo Duplicated word "the the": "cancels the the +1 contribution" (p.24), "left half of the the GTN" (p.26), "as a function the the information" (p.32), "applies the the convolutional network" (p.36).
- p. 24 Section VI-B
cancels the the +1 contribution
- p. 26 Section VI-D
left half of the the GTN
- p. 32 Section VIII-C
as a function the the information
- p. 36 Section IX-C
applies the the convolutional network
Judge's note: All four instances are visible in the crops. On p.32 the phrase also lacks 'of' ('as a function of the information').
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Typo p.24: "it forces the recognizer to increases the penalty of wrongly recognized objects" should read "to increase".
- p. 24 VI-B
forces the recognizer to in
- p. 24 Sec. VI-B
forces the recognizer to in cr e ases the p enalt y of wrongly recognized ob jects
- p. 24
forces the recognizer to in cr e ases the p enalt y
Judge's note: The crop shows 'to in-creases' with 'increases' in italics; the italics is emphasis, but the verb form is ungrammatical.
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Typo p.24 reads 'Several rules can be used compute the penalty'; 'to' is missing.
- p. 24 VI-C
Several rules can be used
Judge's note: Checked on the p.24 page image, Sec. VI-C.
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Typo p.25 reads 'take an interpretation graph as input an produce the forward penalty'; 'an' should be 'and'.
- p. 25 VI-C
an interpretation graph as input
Judge's note: Checked on the p.25 page image.
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Typo p.26 reads 'Another approach would consists of directly minimizing'; it should be 'consist'.
- p. 26 VI-E
Another approach would consists of directly minimizing
Judge's note: The wording is visible in the crop.
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Typo p.28 reads 'recognized characters.The transducer', with no space after the full stop.
- p. 28 VII-A
recognized char acters.The transducer is a weighted
Judge's note: The text layer runs the two words together as 'actersThe', which matches the page; elsewhere the text layer keeps word breaks.
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Typo p.29 reads 'the string image were artificially generated from individual character'; it should be 'images' and 'characters'.
- p. 29 VII-C
the string image were arti
Judge's note: The wording is visible in the crop.
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Typo Missing article: "The transducer graph is linear graph which contains the correct label sequence" should read "is a linear graph".
- p. 31 VIII-B
The transducer graph is linear graph which con
Judge's note: Crop of p31 right column shows the text exactly as quoted.
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Typo Duplicated word and missing "of": "as a function the the information attached to the input arcs" should read "as a function of the information".
- p. 32 VIII-C bullet
as a function the the information attached to the input
Judge's note: Crop of p32 left column shows the text exactly as quoted.
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Typo Stray duplicated article: "In this case the, the generalized transduction does not take two input graphs" should read "In this case, the generalized transduction".
- p. 33 VIII-C
In this case the the generalized transduction
- p. 33
zed transduction In this case the the generalized transdu
Judge's note: The page image shows "case the, the" with a comma; the extra "the" is still a typo.
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Typo Wrong capitalisation: "In addition, It can be shown that" should read "it".
- p. 33 VIII-C
In addition It can be sho
Judge's note: Crop of p33 right column confirms the capital It.
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Typo Number agreement in the Fig. 29 caption: "The two main component of the composition appear clearly here" should read "components".
- p. 33 Fig. 29 caption
The two main
Judge's note: Seen in the Fig. 29 caption on p33.
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Typo p.34: "than the purely optical input from in image" should read "from an image".
- p. 34 Section IX
purely optical input from in image
Judge's note: Crop shows 'from in image' in Section IX intro.
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Typo Doubled article: "given the an input value" should read "given an input value".
- p. 34 VIII-E IOHMM
given the an input value
Judge's note: Seen in the IOHMM paragraph on p34.
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Typo Doubled article: "replicates the convolutional network over the a whole word image" should read "over a whole word image".
- p. 36 IX-C SDNN list
over the a whole word image
Judge's note: Seen in the SDNN Transformer list item on p36.
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Typo Duplicated word: "applies the the convolutional network character recognizer".
- p. 36 IX-C item 2
applies the the convolutional network
Judge's note: Crop of p36 item 2 confirms the text.
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Typo Duplicated word: "applies the the convolutional network character recognizer" (Section IX-C, item 2).
- p. 36
ognition T ransformer applies the the con v olutional net
Judge's note: The crop shows "the the" in the Character Recognition Transformer item.
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Typo "uses a variety of heuristics to find candidate cut" should read "candidate cuts".
- p. 38 X-A
to nd candi date cut
Judge's note: Seen on page 38, Section X-A.
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Typo p.38: "therefore its parameter are globally tunable" should read "its parameters are".
- p. 38 X-A
therefore its parameter are glob
- p. 38
therefore its parameter are globally tunable
Judge's note: Crop shows the text as quoted.
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Typo p.39: "although it only practical to do it down to the segmenter" is missing 'is' ("it is only practical").
- p. 39 X-B
although it only practical to do it
- p. 39
although it only practical to do it down to the segmenter
Judge's note: Crop shows the text as quoted.
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Typo "recognition systems will rely more and more of learning" should read "on learning".
- p. 40 Conclusions, first paragraph
rely more and more of learning
- p. 40 Conclusions
will rely more and
Judge's note: The crops confirm the wording; both reviewer notes report the same defect.
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Typo Misspelling "ill-conditionning of the error surface" (Appendix C) should be "ill-conditioning".
- p. 42 Appendix C
illconditionning of the error surface
Judge's note: Seen on page 42. The paper spells it "ill-conditioning" elsewhere.
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Typo "Some of the systems described in this paper is the work" should read "are the work".
- p. 43 Acknowledgments
Some of the systems described in this paper is the work
Judge's note: The crop confirms the wording.
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Typo References [84] and [108] are the same paper: M. Rahim, Y. Bengio, Y. LeCun, "Discriminative feature and model design for automatic speech recognition," Eurospeech 1997, Rhodes.
- p. 45 References [84],[108]
Discriminative feature and model design for automatic speech recognition
Judge's note: Both entries appear on page 45.
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Typo Reference [100] reads "Finite-State Devices for Natural Langue Processing"; "Langue" should be "Language".
- p. 45 Reference [100]
Natural Langue Processing
Judge's note: The entry on page 45 shows the misspelling, which is evident from the English title.
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Typo LeCun biography: "where he worked among other thing on neural networks" should read "other things".
- p. 46 Yann LeCun biography
among other thing on neural networks
Judge's note: The crop confirms the wording.
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