SemiHMER: Semi-supervised Handwritten Mathematical Expression Recognition using pseudo-labels

Haoyang Shen; Kehua Chen

REVIEW 5 major objections 5 minor 42 references

SemiHMER: Semi-supervised Handwritten Mathematical Expression Recognition using pseudo-labels

T0 review · 5 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that semi-supervised learning—two decoder branches pseudo-supervising each other on weakly and strongly augmented images—raises handwritten mathematical expression recognition accuracy by about five percentage points on…

desk verdict Plausible SSL adaptation for HMER, but the headline gains are measured against an unreproduced baseline and the controlled SSL effect is small, unreplicated evidence. read the letter →

arxiv 2502.07172 v3 pith:TOKZAPUQ submitted 2025-02-11 cs.CV cs.AI

Kehua Chen , Haoyang Shen This is my paper · ORCID

classification cs.CVcs.AI

keywords handwrittenmathematicalexpressionrecognitionsemi-supervisedlearningpseudo-labelingconsistencyregularizationweak-to-strongaugmentationGlobalDynamicCountingModuleCROHMEbenchmarkencoder-decoderarchitecture

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Handwritten mathematical expression recognition normally requires large labeled datasets, and manually transcribing formulas into LaTeX is slow and expensive. The paper claims that semi-supervised learning can ease that bottleneck: two decoder branches share an encoder, the weakly augmented branch generates pseudo-labels for the strongly augmented branch, and unlabeled formula images join the training pool. The framework, SemiHMER, adds a Global Dynamic Counting Module (GDCM) that refreshes a per-symbol count vector at each decoding step to reduce long-distance and repeated-character errors. On the CROHME 2014, 2016, and 2019 benchmarks, the authors report expression recognition rates of 60.95%, 58.23%, and 58.63%, which they state are gains of 5.47, 4.87, and 5.25 points over their reproduced baseline. They further claim this is the first pseudo-supervised semi-supervised framework for handwritten formula recognition, making unlabeled handwriting a usable training resource.

What carries the argument

The load-bearing mechanism is the cross-head weak-to-strong pseudo-supervision loop: a shared DenseNet encoder feeds two identical CAN-style decoder heads, one branch sees minimally augmented images while the other sees strongly augmented versions (random distortion, 50% stretch, 30% perspective), and the roles swap every epoch. For every image the weak branch's prediction is converted into a hard pseudo-label that supervises the strong branch's prediction via cross-entropy, for both labeled and unlabeled data, and the total loss is $\mathcal{L} = \mathcal{L}^{sup}_{cls} + \mathcal{L}^{unsup}_{cls} + \mathcal{L}'^{unsup}_{cls} + \mathcal{L}_{counting}$. The second mechanism is the Global Dynamic Counting Module (GDCM), which upgrades CAN's static counting vector: at each decoding step the count vector is refreshed using the previous step's prediction, and the output probability is computed with an update of the form $p(\hat{y}_t) = W_k (\hat{h}_t - \sum_{i=1}^{C} \mathrm{softmax}(p(y_t))) + b_k$, combining context, hidden state, and the dynamically updated count. This is what the paper credits with reducing long-distance misrecognition and repeated-character errors.

What would settle it

Retrain SemiHMER against a supervised baseline that matches the published CAN numbers (57.00, 56.06, 54.88 on CROHME 2014, 2016, 2019) with the same augmentation schedule, and measure whether the dual-branch semi-supervised loop plus GDCM still adds roughly five points; if the gain shrinks to about one to three points, the headline improvement largely reflects the gap in the reproduced baseline rather than the semi-supervised mechanism.

Watch

Extended reading notes

Core claim

The paper's central claim is that handwritten mathematical expression recognition can be improved by a dual-branch consistency framework in which each branch's prediction supervises the other. For labeled images, the weakly augmented view of an image passes through one decoder; its prediction is checked against the ground truth and simultaneously converted into a hard pseudo-label that supervises the other decoder's prediction on a strongly augmented view of the same image. For unlabeled images, the weakly augmented branch's prediction acts directly as the training target for the strongly augmented branch, and the two branches alternate weak and strong augmentation each epoch. On top of this, the Global Dynamic Counting Module (GDCM) replaces the static counting vector of the CAN decoder with one that is refreshed at each decoding step using the previous step's prediction, which the authors state alleviates long-distance misrecognition and repeated-character errors. The reported outcome is an expression recognition rate of 60.95%, 58.23%, and 58.63% on CROHME 2014, 2016, and 2019, exceeding the authors' CAN baseline by 5.47, 4.87, and 5.25 points respectively.

Load-bearing premise

The load-bearing premise is that the authors' reproduced CAN baseline is a fair comparison point: the paper itself states that this baseline scores below the published CAN results (55.48% versus 57.00% on CROHME 2014) and that they could not close the gap after extensive tuning, so if the baseline is unfairly weak, part of the reported five-point gain is recovery of lost baseline performance rather than an effect of semi-supervised learning.

Editorial extensions

If this is right

If the reported gains hold, unlabeled handwritten formula images become a directly usable training resource: the authors report CROHME 2014/2016/2019 expression recognition rates of 60.95%, 58.23%, and 58.63%, up 5.47, 4.87, and 5.25 points over their reproduced CAN baseline.
In the CROHME 2014 ablation, the gain from cross-pseudo supervision grows as augmentation strengthens: +1.92 points with distortion alone, +2.13 with distortion plus stretch, and +2.63 with all three transforms, showing that the weak-to-strong gap is what makes mutual supervision effective.
The GDCM ablation attributes gains of 0.82, 2.78, and 0.16 points on CROHME 2014, 2016, and 2019 to dynamic counting, so the module's contribution is positive but uneven across benchmarks.
With the consistency weight at $\lambda = 10^{-3}$ the framework reaches 60.95% on CROHME 2014, while $\lambda = 10^{-2}$ collapses it to 33.6%, meaning the unsupervised signal must stay weak relative to the supervised loss.
Both decoder branches reach near-equal accuracy with weak-to-strong augmentation (60.95 and 60.34 on CROHME 2014), so the gain does not depend on which branch happens to see the stronger augmentation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the headline +5.47/+4.87/+5.25 point gains are computed against the authors' own CAN reproduction, which they explicitly state underperforms the published CAN results (55.48 vs 57.00 on CROHME 2014). Measured against their augmentation-only baseline, the semi-supervised component contributes +2.63/+1.03/+1.00 points, so the fair magnitude of the semi-supervised effect is likel
Editorial inference: the 1,000 unlabeled images are drawn from CROHME 2023, which shares the test sets' symbol vocabulary and writing style distribution, so the demonstrated value of unlabeled data is in-distribution. A test with out-of-domain unlabeled handwriting would clarify how far the mechanism generalizes.
Testable extension: the same dual-branch weak-to-strong consistency loss transfers directly to other image-to-sequence transcription tasks with cheap unlabeled data, such as printed formula recognition or table-structure recognition, where the pseudo-supervision loop needs no architectural change.
Testable extension: because GDCM's gains are uneven (0.82, 2.78, 0.16 points across the three benchmarks), isolating the module on formulas with many repeated symbols and long-distance dependencies would show whether dynamic counting itself, rather than the semi-supervised loop, drives the improvement.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing here is applying known semi-supervised recipes (CPS, FixMatch-style weak-to-strong consistency) to handwritten formula recognition and pairing that with a counting module that updates the count vector dynamically during decoding. The idea is sensible, the writing is clear, and the paper cites the relevant SSL and HMER literature. I buy that the framework is a legitimate new application rather than a trivial copy-paste.

What the paper does well: the ablation structure is mostly right. Table 3 shows a step-by-step progression from the no-augmentation baseline to the full method, and the weak-to-strong configuration does beat all-weak and all-strong variants. That is real, useful evidence for the central architectural choice. The GDCM ablation also shows a consistent positive effect on two of three benchmarks, though it is a modest extension of CAN's counting vector.

Now the soft spots, in proportion. The headline numbers (5.47/4.87/5.25) are misleading because they are computed against the authors' own unreproduced CAN baseline, which they explicitly admit falls short of the published CAN numbers. The controlled comparison against their augmented baseline (baseline-aug) shows gains of 2.63/0.95/1.00 points. That is the honest effect size for the SSL+augmentation package, and on CROHME16 and CROHME19 it is small enough that run-to-run variation is a real worry. There are no seeds, no error bars, and lambda is tuned on the test sets, which inflates the reported numbers. Table 3's delta columns are also inconsistent: some deltas are from the no-augmentation row, others from the previous row, so the printed increments do not have a single reference point. That needs fixing.

A minor but real issue: Equation (3), the GDCM update rule, is under-specified. It is not clear what the sum is over or how the count vector is updated from the softmaxed predictions; as written, the dimensions do not obviously work out. A referee should ask for a proper derivation or a clearer formulation.

Overall: the core claim, that semi-supervised pseudo-labeling helps HMER, is plausible and weakly supported, but the evidence as presented is not strong enough to back the magnitude claimed in the abstract. The paper deserves a serious referee, but it should be sent back for: code and seeds, a fairly reproduced or clearly disclosed CAN baseline, error bars, a validation split for lambda, and clarification of the GDCM equation.

For you: this is a reasonable paper to skim if you work on HMER or structured sequence SSL, but I would not cite the headline numbers without checking the controlled comparison. I would send it to review, with a request for major revision.

Referee Report

5 major / 5 minor

Summary. The paper proposes SemiHMER, a semi-supervised handwritten mathematical expression recognition (HMER) framework that combines a dual-branch cross-pseudo-supervision strategy with weak-to-strong augmentation and a new Global Dynamic Counting Module (GDCM). The two decoder heads are trained with alternating weak/strong augmentations; pseudo-labels from one branch supervise the other branch. The authors report expression-recognition-rate gains over a CAN baseline on CROHME 2014, 2016, and 2019, and provide ablation studies for GDCM, augmentation strategies, and the trade-off weight lambda.

Significance. If the controlled comparison were as strong as the abstract claims, the paper would be a useful early demonstration that semi-supervised learning can improve HMER, a task that has not yet received much SSL attention. The dual-branch weak-to-strong consistency idea is simple and plausible, and the explicit disclosure of a baseline reproduction problem is commendable. However, as presented, the evidence is insufficient: the headline gains are computed against a baseline the authors themselves could not reproduce, the controlled SSL gains are small and unreplicated, and the ablation tables are internally inconsistent. The strengths of the paper are the clear problem statement and the reasonable algorithmic components; the weaknesses are in experimental validation and statistical rigor.

major comments (5)

[Sec. 4.4, Table 1] The abstract and Table 1 report gains of +5.47/+4.87/+5.25 'compared to our baselines,' but Section 4.4 states that the reproduced CAN baseline is 55.48/53.36/53.38, below the published CAN numbers despite hyperparameter tuning. Because SemiHMER adds GDCM, augmentation, and cross-pseudo supervision simultaneously, these headline gains conflate recovery of the baseline gap with the SSL effect. The controlled comparison to 'baseline-aug' is only +2.63/+0.95/+1.00, and no seeds or error bars are given, so on CROHME16 and CROHME19 the SSL contribution may be within run-to-run variation. Please report multiple seeds with mean and standard deviation and use the strongest reproducible baseline as the reference for all claimed gains.
[Table 3] The delta columns in the last row of Table 3 do not use a common reference row: +2.63 for CROHME14 is the difference from the previous row (58.32), while +2.01 for CROHME16 and +5.09 for CROHME19 are differences from the first row (56.14 and 53.54). In addition, the SemiHMER CROHME16 ExpRate is 58.23 in Table 1 but 58.15 in Table 3, and Section 4.4 says the improvement is 1.03% while the tables indicate 0.95%. Please recompute all deltas with a single, clearly stated reference row and reconcile the numbers across tables.
[Sec. 4.8, Table 5] The trade-off weight lambda is selected using the test-set ExpRate, with Table 5 reporting only CROHME14 and no validation split. Since lambda controls the strength of the semi-supervised signal, tuning it on the test set can inflate the reported gains. Please describe the model-selection procedure and, if possible, use a held-out validation set for hyperparameter selection.
[Sec. 4.1] The 1,000 unlabeled images are sampled from CROHME 2023, but the paper does not verify that these images are disjoint from the CROHME 2014/2016/2019 test sets. Because CROHME competitions often reuse and evolve data, overlap between the unlabeled set and the test sets would directly inflate the semi-supervised gains. Please add an explicit overlap check and report its result.
[Sec. 3.3, Eq. (3), Table 2] The GDCM update subtracts a sum of softmax probabilities from the hidden state, but the paper provides no analysis showing that this mechanism specifically reduces repeated-character or long-distance errors. Table 2 shows a gain of only 0.16 on CROHME19, and Table 3 has no error-type breakdown. Please add an error-type analysis or an explicit experiment on repeated-character cases to support the claimed mechanism.

minor comments (5)

[Sec. 3.1 vs. Sec. 3.2] The alternating strategy is described as epoch-level switching in Section 3.1 ('During the i-th epoch, we apply weak augmentation to Decoder1...'), while Section 3.2 says transformations are chosen per sample in each mini-batch randomly. Please clarify which mechanism is actually used.
[Sec. 3.4] The symbol L_unsup_cls is defined in Eq. (4) for labeled data and then reused in Eq. (6) for unlabeled data, and the total loss in Eq. (8) includes both L_unsup_cls and L'_unsup_cls. This notation is confusing; please rename the labeled-data consistency term.
[Sec. 4.5, Table 3] The text refers to '4, shows' in the ablation discussion; it should reference Table 4. Also, Table 3 uses an uninterpretable checkmark glyph ('/enc-33') that should be replaced with standard symbols such as checkmarks or crosses.
[Sec. 4.1] The dataset section says example images are shown in Fig. 2, but the figure is labeled Fig. 3; please fix the cross-reference.
[Table 1] The parenthetical deltas in the SemiHMER row should state their reference baseline explicitly, because they are relative to CAN(baseline) while the text in Section 4.4 uses baseline-aug as the reference. This inconsistency makes the headline numbers difficult to interpret.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: SemiHMER's claims are empirical benchmark comparisons; the reported gains rest on baseline fairness and test-set tuning, not on a derivation that reduces to its inputs.

full rationale

SemiHMER does not derive a result from first principles; its central claim is an empirical accuracy improvement on CROHME test sets. The pseudo-labeling loop is self-referential in the ordinary self-training sense, but the final evaluation is against ground-truth labels on held-out test sets, so Eq. (8)'s loss is not definitionally equivalent to the reported ExpRate. No fitted parameter is renamed as a prediction: the only tuned scalar, lambda in Sec. 4.8, is a loss weight selected on the test sets, which is a test-set-tuning/statistical concern rather than a circular reduction. The paper's own Sec. 4.4 admits the CAN baseline was not reproduced (55.48/53.36/53.38 vs published 57.00/56.06/54.88), weakening attribution of the headline +5.47/+4.87/+5.25 gains; against baseline-aug the gains are only 2.63/0.95/1.00. This is an experimental fairness problem, not circularity. Table 3's delta columns are internally inconsistent, but inconsistent arithmetic is not circularity. There is no load-bearing self-citation: [25] is cited only as related object-detection work, and the FixMatch inspiration [20] is external. Verdict: no significant circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 1 invented entities

The central claim rests on several hand-chosen hyperparameters, the reliability of pseudo-labels, and an under-specified counting module. These items carry much of the modeling burden that the paper does not independently justify.

free parameters (4)

Trade-off weight lambda = 1e-3
Selected as best in Table 5 by ExpRate; not shown in the total loss Eq. (8); no validation split is described.
Number of unlabeled images = 1000
Randomly selected from CROHME 2023 in Section 4.1; no sweep, no seed, and no analysis of sensitivity.
Strong augmentation probabilities = stretch 50%, perspective 30%
Chosen by hand in Section 3.2; no ablation on the probabilities themselves.
Semi-supervised start epoch = 240
Cross-training begins only after 240 epochs; chosen by hand in Section 4.2 with no sensitivity study.

assumptions (4)

standard math Softmax cross-entropy sequence prediction with attention is a valid HMER decoder (CAN/WAP baseline).
Adopted from CAN [12] and DenseNet [9] as backbone; not re-derived in this paper.
domain assumption Pseudo-labels from the weakly augmented branch are reliable enough to supervise the strongly augmented branch.
Core of the weak-to-strong consistency loss in Section 3.4, Eqs. (4)-(6); if pseudo-labels are noisy, the unlabeled loss injects errors.
domain assumption Unlabeled CROHME 2023 images match the labeled CROHME distribution and contain no out-of-vocabulary symbols.
Authors state all characters in the unlabeled set are included in CROHME, but distribution shift is not analyzed; Section 4.1.
ad hoc to paper The GDCM update rule in Eq. (3) is a valid way to reduce repeated-character errors.
Introduced without derivation; hhat_t and the count-vector update mechanism are not defined in the text.

invented entities (1)

Global Dynamic Counting Module (GDCM)
purpose: Dynamically updates a global symbol-count vector during decoding to reduce repeated-character and long-distance recognition errors.
New architectural component; the only evidence is in-paper ablations on CROHME, with no external falsifiable prediction or formal specification.

how reviews work

0 comments

Cite this review

Pith. "Pith review of SemiHMER: Semi-supervised Handwritten Mathematical Expression Recognition using pseudo-labels." pith.science (2026). https://pith.science/paper/TOKZAPUQ

@misc{pith2026250207172,
  author       = {Pith},
  title        = {Pith review of: SemiHMER: Semi-supervised Handwritten Mathematical Expression Recognition using pseudo-labels},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TOKZAPUQ}},
  note         = {Machine review of arXiv:2502.07172}
}

read the original abstract

In this paper, we study semi-supervised Handwritten Mathematical Expression Recognition (HMER) via exploring both labeled data and extra unlabeled data. We propose a novel consistency regularization framework, termed SemiHMER, which introduces dual-branch semi-supervised learning. Specifically, we enforce consistency between the two networks for the same input image. The pseudo-label, generated by one perturbed recognition network, is utilized to supervise the other network using the standard cross-entropy loss. The SemiHMER consistency encourages high similarity between the predictions of the two perturbed networks for the same input image and expands the training data by leveraging unlabeled data with pseudo-labels. We further introduce a weak-to-strong strategy by applying different levels of augmentation to each branch, effectively expanding the training data and enhancing the quality of network training. Additionally, we propose a novel module, the Global Dynamic Counting Module (GDCM), to enhance the performance of the HMER decoder by alleviating recognition inaccuracies in long-distance formula recognition and reducing the occurrence of repeated characters. The experimental results demonstrate that our work achieves significant performance improvements, with an average accuracy increase of 5.47% on CROHME14, 4.87% on CROHME16, and 5.25% on CROHME19, compared to our baselines.

Figures

Figures reproduced from arXiv: 2502.07172 by the authors.

**Figure 1.** Overview of our Semi-supervised Handwritten Mathematical Expression Recognition using pseudo-labels. In this scheme, we use Decoder1 as an example. Weakly augmented (non-augmented) labeled data flows through the encoder module and the corresponding prediction Decoder1 to produce the prediction Classif ication V ectorsuper,weak, which is then supervised by the ground truth. At the same time, the prediction Classif i… view at source ↗

**Figure 2.** Structure of the proposed decoder based on the Global Dynamic Counting Module (GDCM) 3.3 Global Dynamic Counting Module CAN [12] calculates the global counting vector from the global image features by the encoder using an additional multi-scale counting module. This global counting vector is then fed into the decoder to inform the decoding process. By providing the decoder with this additional weak supervision inf… view at source ↗

**Figure 3.** Some example images from the CROHME dataset. We conduct experiments on CROHME benchmark datasets and compare the performance with the state-of-the-art methods. CROHME Dataset [17] is from the competition on recognition of online handwritten mathematical expression, which is the most widely used public dataset. It is derived from the competition focused on recognizing online handwritten mathematical expressions. The… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 37 canonical work pages

[1]

Pattern Recogni- tion Letters 35, 68–77 (2014)

Awal, A.M., Mouchere, H., Viard-Gaudin, C.: A global lear ning approach for an online handwritten mathematical expression recognition s ystem. Pattern Recogni- tion Letters 35, 68–77 (2014)

work page 2014
[2]

, Oliver, A., Raﬀel, C.A.: Mixmatch: A holistic approach to semi-supervised learning

Berthelot, D., Carlini, N., Goodfellow, I., Papernot, N. , Oliver, A., Raﬀel, C.A.: Mixmatch: A holistic approach to semi-supervised learning . Advances in neural information processing systems 32 (2019)

work page 2019
[3]

In: Proceedings of the AAAI conference on artiﬁcial int elligence

Bian, X., Qin, B., Xin, X., Li, J., Su, X., Wang, Y.: Handwri tten mathematical expression recognition via attention aggregation based bi -directional mutual learn- ing. In: Proceedings of the AAAI conference on artiﬁcial int elligence. vol. 36, pp. 113–121 (2022)

work page 2022
[4]

In: Proceedings

Chan, K.F., Yeung, D.Y.: Elastic structural matching for online handwritten al- phanumeric character recognition. In: Proceedings. Fourt eenth International Con- ference on Pattern Recognition (Cat. No. 98EX170). vol. 2, p p. 1508–1511. IEEE (1998)

work page 1998
[5]

In: Proceedings of the IEEE/ CVF conference on computer vision and pattern recognition

Chen, X., Yuan, Y., Zeng, G., Wang, J.: Semi-supervised se mantic segmentation with cross pseudo supervision. In: Proceedings of the IEEE/ CVF conference on computer vision and pattern recognition. pp. 2613–2622 (20 21)

work page
[6]

In: European Conference on Computer Vision

Guan, T., Lin, C., Shen, W., Yang, X.: Posformer: recogniz ing complex handwritten mathematical expression with position forest transformer . In: European Conference on Computer Vision. pp. 130–147. Springer (2025) Semi-supervised HMER using pseudo-labels 15

work page 2025
[7]

: Primitive con- trastive learning for handwritten mathematical expressio n recognition

Guo, H.Y., Wang, C., Yin, F., Liu, H.Y., Wu, J.W., Liu, C.L. : Primitive con- trastive learning for handwritten mathematical expressio n recognition. In: 2022 26th International Conference on Pattern Recognition (ICP R). pp. 847–854. IEEE (2022)

work page 2022
[8]

In: 2011 International conference on Document analys is and Recognition

Hu, L., Zanibbi, R.: Hmm-based recognition of online hand written mathematical symbols using segmental k-means initialization and a modiﬁ ed pen-up/down fea- ture. In: 2011 International conference on Document analys is and Recognition. pp. 457–462. IEEE (2011)

work page 2011

Show all 42 references

[9]

In: Proceedings of the IEEE confer ence on computer vision and pattern recognition

Huang, G., Liu, Z., Van Der Maaten, L., Weinberger, K.Q.: D ensely connected convolutional networks. In: Proceedings of the IEEE confer ence on computer vision and pattern recognition. pp. 4700–4708 (2017)

2017
[10]

In: Ninth International Conference on Doc ument Analysis and Recognition (ICDAR 2007)

Keshari, B., Watt, S.: Hybrid mathematical symbol recog nition using support vector machines. In: Ninth International Conference on Doc ument Analysis and Recognition (ICDAR 2007). vol. 2, pp. 859–863. IEEE (2007)

2007
[11]

In: Proceedings of the Fifth International Conference on Do cument Analysis and Recognition

Kosmala, A., Rigoll, G., Lavirotte, S., Pottier, L.: On- line handwritten formula recognition using hidden markov models and context depende nt graph grammars. In: Proceedings of the Fifth International Conference on Do cument Analysis and Recognition. ICDAR’99 (Cat. No. PR003...

1999
[12]

In: European conference on computer vision

Li, B., Yuan, Y., Liang, D., Liu, X., Ji, Z., Bai, J., Liu, W ., Bai, X.: When count- ing meets hmer: counting-aware network for handwritten mat hematical expression recognition. In: European conference on computer vision. p p. 197–214. Springer (2022)

2022
[13]

In: 2020 17th International Conference on Frontiers in Handwriting Recognition (ICFHR)

Li, Z., Jin, L., Lai, S., Zhu, Y.: Improving attention-ba sed handwritten mathemat- ical expression recognition with scale augmentation and dr op attention. In: 2020 17th International Conference on Frontiers in Handwriting Recognition (ICFHR). pp. 175–180. IEEE (2020)

2020
[14]

In: Proceedings of the Asian Conference on Computer Vi sion

Lin, Q., Huang, X., Bi, N., Suen, C.Y., Tan, J.: Cclsl: Com bination of contrastive learning and supervised learning for handwritten mathemat ical expression recogni- tion. In: Proceedings of the Asian Conference on Computer Vi sion. pp. 3724–3739 (2022)

2022
[15]

In: Pro- ceedings of the IEEE/CVF conference on computer vision and p attern recognition

Liu, C., Zhang, W., Lin, X., Zhang, W., Tan, X., Han, J., Li , X., Ding, E., Wang, J.: Ambiguity-resistant semi-supervised learning for dense o bject detection. In: Pro- ceedings of the IEEE/CVF conference on computer vision and p attern recognition. pp. 15579–15588 (2023)

2023
[16]

In: International conference on document analysis and recognition

Liu, Z., Yuan, Y., Ji, Z., Bai, J., Bai, X.: Semantic graph representation learning for handwritten mathematical expression recognition. In: International conference on document analysis and recognition. pp. 152–166. Springe r (2023)

2023
[17]

: Icfhr 2014 competition on recognition of on-line handwritten mathematical expres sions (crohme 2014)

Mouchere, H., Viard-Gaudin, C., Zanibbi, R., Garain, U. : Icfhr 2014 competition on recognition of on-line handwritten mathematical expres sions (crohme 2014). In: 2014 14th International Conference on Frontiers in Handwri ting Recognition. pp. 791–796. IEEE (2014)

2014
[18]

arXiv preprint arXiv:2302.09899 (2023)

Peláez-Vegas, A., Mesejo, P., Luengo, J.: A survey on sem i-supervised semantic segmentation. arXiv preprint arXiv:2302.09899 (2023)

2023 arXiv
[19]

arXiv preprint arXiv:1506.01497 (2015)

Ren, S.: Faster r-cnn: Towards real-time object detecti on with region proposal networks. arXiv preprint arXiv:1506.01497 (2015)

2015 arXiv
[20]

Advances in neural information processing systems 33, 596–608 (2020) 16 K

Sohn, K., Berthelot, D., Carlini, N., Zhang, Z., Zhang, H ., Raﬀel, C.A., Cubuk, E.D., Kurakin, A., Li, C.L.: Fixmatch: Simplifying semi-su pervised learning with consistency and conﬁdence. Advances in neural information processing systems 33, 596–608 (2020) 16 K. Chen et al

2020
[21]

arXiv preprint arXiv:2005.04757 (2020)

Sohn, K., Zhang, Z., Li, C.L., Zhang, H., Lee, C.Y., Pﬁste r, T.: A sim- ple semi-supervised learning framework for object detecti on. arXiv preprint arXiv:2005.04757 (2020)

2020 arXiv
[22]

In: 2020 17th International Conference on F rontiers in Handwriting Recognition (ICFHR)

Truong, T.N., Nguyen, C.T., Phan, K.M., Nakagawa, M.: Im provement of end- to-end oﬄine handwritten mathematical expression recogni tion by weakly super- vised learning. In: 2020 17th International Conference on F rontiers in Handwriting Recognition (ICFHR). pp. 181–186. IEEE (2020)

2020
[23]

arXiv preprint ar Xiv:2410.06671 (2024)

Tu, G., Li, D., Lin, B., Zheng, Z., Ng, S.K.: Gla-da: Globa l-local alignment domain adaptation for multivariate time series. arXiv preprint ar Xiv:2410.06671 (2024)

2024 arXiv
[24]

Expert Systems with Applications 37(1), 886–893 (2010)

Vuong, B.Q., He, Y., Hui, S.C.: Towards a web-based progr essive handwriting recognition environment for mathematical problem solving . Expert Systems with Applications 37(1), 886–893 (2010)

2010
[25]

in 2023 ieee

Wang, X., Yang, X., Zhang, S., Li, Y., Feng, L., Fang, S., L yu, C., Chen, K., Zhang, W.: Consistent-teacher: Towards reducing inconsis tent pseudo-targets in semi-supervised object detection. in 2023 ieee. In: CVF Con ference on Computer Vision and Pattern Recognition (CVPR)....

2023
[26]

In: 1996 IEEE International Conference on Ac oustics, Speech, and Signal Processing Conference Proceedings

Winkler, H.J.: Hmm-based handwritten symbol recogniti on using on-line and oﬀ- line features. In: 1996 IEEE International Conference on Ac oustics, Speech, and Signal Processing Conference Proceedings. vol. 6, pp. 3438 –3441. IEEE (1996)

1996
[27]

In: Proceedings of the AAAI Conference on Artiﬁcial Intelligence

Wu, C., Du, J., Li, Y., Zhang, J., Yang, C., Ren, B., Hu, Y.: Tdv2: A novel tree- structured decoder for oﬄine mathematical expression reco gnition. In: Proceedings of the AAAI Conference on Artiﬁcial Intelligence. vol. 36, p p. 2694–2702 (2022)

2022
[28]

In: Machine learning and knowledge discovery in databases: European conference, ECML PKDD 2018, Dublin, Ireland, Septem- ber 10–14, 2018, Proceedings, Part I 18

Wu, J.W., Yin, F., Zhang, Y.M., Zhang, X.Y., Liu, C.L.: Im age-to-markup genera- tion via paired adversarial learning. In: Machine learning and knowledge discovery in databases: European conference, ECML PKDD 2018, Dublin, Ireland, Septem- ber 10–14, 2018, Proceedings, Part I ...

2019
[29]

International Journal of Computer Vision 128, 2386–2401 (2020)

Wu, J.W., Yin, F., Zhang, Y.M., Zhang, X.Y., Liu, C.L.: Ha ndwritten mathemati- cal expression recognition via paired adversarial learnin g. International Journal of Computer Vision 128, 2386–2401 (2020)

2020
[30]

Advances in neural information p rocessing systems 33, 6256–6268 (2020)

Xie, Q., Dai, Z., Hovy, E., Luong, T., Le, Q.: Unsupervise d data augmentation for consistency training. Advances in neural information p rocessing systems 33, 6256–6268 (2020)

2020
[31]

, Saini, R., Nakagawa, M., Nguyen, C.T., Truong, T.N.: Icdar 2023 crohme: Competition on recognition of handwritten mathematical expressions

Xie, Y., Mouchère, H., Simistira Liwicki, F., Rakesh, S. , Saini, R., Nakagawa, M., Nguyen, C.T., Truong, T.N.: Icdar 2023 crohme: Competition on recognition of handwritten mathematical expressions. In: International Conference on Document Analysis and Recognition. pp. 553–565...

2023
[32]

arXiv prepri nt arXiv:1905.00546 (2019)

Yalniz, I.Z., Jégou, H., Chen, K., Paluri, M., Mahajan, D .: Billion-scale semi- supervised learning for image classiﬁcation. arXiv prepri nt arXiv:1905.00546 (2019)

2019 arXiv
[33]

In: Procee dings of the IEEE/CVF conference on computer vision and pattern recognition

Yang, L., Zhuo, W., Qi, L., Shi, Y., Gao, Y.: St++: Make sel f-training work bet- ter for semi-supervised semantic segmentation. In: Procee dings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 4268–4277 (2022)

2022
[34]

I n: Proceedings of the IEEE/CVF conference on computer vision and pattern recogni tion

Yang, Q., Wei, X., Wang, B., Hua, X.S., Zhang, L.: Interac tive self-training with mean teachers for semi-supervised object detection. I n: Proceedings of the IEEE/CVF conference on computer vision and pattern recogni tion. pp. 5941–5950 (2021)

2021
[35]

In: Proceedings of the IEEE/CVF conference on computer vision and pattern reco gnition

Yuan, Y., Liu, X., Dikubab, W., Liu, H., Ji, Z., Wu, Z., Bai , X.: Syntax-aware network for handwritten mathematical expression recognit ion. In: Proceedings of the IEEE/CVF conference on computer vision and pattern reco gnition. pp. 4553– 4562 (2022)

2022
[36]

arXiv preprint arXiv:1212.5701 (2012) Semi-supervised HMER using pseudo-labels 17

Zeiler, M.D.: Adadelta: an adaptive learning rate metho d. arXiv preprint arXiv:1212.5701 (2012) Semi-supervised HMER using pseudo-labels 17

2012 arXiv
[37]

In: 2017 14th IAPR international conference on document analysis and recogni tion (ICDAR)

Zhang, J., Du, J., Dai, L.: A gru-based encoder-decoder a pproach with attention for online handwritten mathematical expression recogniti on. In: 2017 14th IAPR international conference on document analysis and recogni tion (ICDAR). vol. 1, pp. 902–907. IEEE (2017)

2017
[38]

In: 2018 24th intern ational conference on pattern recognition (ICPR)

Zhang, J., Du, J., Dai, L.: Multi-scale attention with de nse encoder for handwritten mathematical expression recognition. In: 2018 24th intern ational conference on pattern recognition (ICPR). pp. 2245–2250. IEEE (2018)

2018
[39]

IEEE Transactions on Multimedia 21(1), 221–233 (2018)

Zhang, J., Du, J., Dai, L.: Track, attend, and parse (tap) : An end-to-end framework for online handwritten mathematical expression recogniti on. IEEE Transactions on Multimedia 21(1), 221–233 (2018)

2018
[40]

In: International C onference on Machine Learning

Zhang, J., Du, J., Yang, Y., Song, Y.Z., Wei, S., Dai, L.: A tree-structured de- coder for image-to-markup generation. In: International C onference on Machine Learning. pp. 11076–11085. PMLR (2020)

2020
[41]

Pattern Recognitio n 71, 196–206 (2017)

Zhang, J., Du, J., Zhang, S., Liu, D., Hu, Y., Hu, J., Wei, S ., Dai, L.: Watch, attend and parse: An end-to-end neural network based approa ch to handwritten mathematical expression recognition. Pattern Recognitio n 71, 196–206 (2017)

2017
[42]

arXiv p reprint arXiv:2408.08578 (2024)

Zhu, J., Zhao, W., Li, Y., Hu, X., Gao, L.: Tamer: Tree-awa re transformer for handwritten mathematical expression recognition. arXiv p reprint arXiv:2408.08578 (2024)

2024 arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

Pattern Recogni- tion Letters 35, 68–77 (2014)

Awal, A.M., Mouchere, H., Viard-Gaudin, C.: A global lear ning approach for an online handwritten mathematical expression recognition s ystem. Pattern Recogni- tion Letters 35, 68–77 (2014)

work page 2014

[2] [2]

, Oliver, A., Raﬀel, C.A.: Mixmatch: A holistic approach to semi-supervised learning

Berthelot, D., Carlini, N., Goodfellow, I., Papernot, N. , Oliver, A., Raﬀel, C.A.: Mixmatch: A holistic approach to semi-supervised learning . Advances in neural information processing systems 32 (2019)

work page 2019

[3] [3]

In: Proceedings of the AAAI conference on artiﬁcial int elligence

Bian, X., Qin, B., Xin, X., Li, J., Su, X., Wang, Y.: Handwri tten mathematical expression recognition via attention aggregation based bi -directional mutual learn- ing. In: Proceedings of the AAAI conference on artiﬁcial int elligence. vol. 36, pp. 113–121 (2022)

work page 2022

[4] [4]

In: Proceedings

Chan, K.F., Yeung, D.Y.: Elastic structural matching for online handwritten al- phanumeric character recognition. In: Proceedings. Fourt eenth International Con- ference on Pattern Recognition (Cat. No. 98EX170). vol. 2, p p. 1508–1511. IEEE (1998)

work page 1998

[5] [5]

In: Proceedings of the IEEE/ CVF conference on computer vision and pattern recognition

Chen, X., Yuan, Y., Zeng, G., Wang, J.: Semi-supervised se mantic segmentation with cross pseudo supervision. In: Proceedings of the IEEE/ CVF conference on computer vision and pattern recognition. pp. 2613–2622 (20 21)

work page

[6] [6]

In: European Conference on Computer Vision

Guan, T., Lin, C., Shen, W., Yang, X.: Posformer: recogniz ing complex handwritten mathematical expression with position forest transformer . In: European Conference on Computer Vision. pp. 130–147. Springer (2025) Semi-supervised HMER using pseudo-labels 15

work page 2025

[7] [7]

: Primitive con- trastive learning for handwritten mathematical expressio n recognition

Guo, H.Y., Wang, C., Yin, F., Liu, H.Y., Wu, J.W., Liu, C.L. : Primitive con- trastive learning for handwritten mathematical expressio n recognition. In: 2022 26th International Conference on Pattern Recognition (ICP R). pp. 847–854. IEEE (2022)

work page 2022

[8] [8]

In: 2011 International conference on Document analys is and Recognition

Hu, L., Zanibbi, R.: Hmm-based recognition of online hand written mathematical symbols using segmental k-means initialization and a modiﬁ ed pen-up/down fea- ture. In: 2011 International conference on Document analys is and Recognition. pp. 457–462. IEEE (2011)

work page 2011