TableMoE: Neuro-Symbolic Routing for Structured Expert Reasoning in Multimodal Table Understanding

Junwen Zhang; Pu Chen; Yin Zhang

REVIEW 5 major objections 5 minor 59 references

TableMoE: Neuro-Symbolic Routing for Structured Expert Reasoning in Multimodal Table Understanding

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read TableMoE claims that predicting each visual token's semantic role before routing it to HTML, JSON, or code connector experts yields state-of-the-art accuracy on degraded and real-world table images.

desk verdict Genuinely new routing idea and promising out-of-domain numbers, but the headline WildStruct claim is compromised by training/eval overlap and inconsistent ablations. read the letter →

arxiv 2506.21393 v1 pith:YQ2DWLP7 submitted 2025-06-26 cs.AI

Junwen Zhang , Pu Chen , Yin Zhang This is my paper

classification cs.AI

keywords mixture-of-expertsmultimodaltableunderstandingneuro-symbolicroutingtokenrolepredictionWildStructbenchmarkMoE-Alignprogram-of-thoughtreasoningvisualdegradationrobustness

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

The paper claims that a vision-language model can reason over real-world table images much more reliably if, before feeding visual tokens to the language model, it predicts what each token is (header, data cell, axis, formula, and five other roles) and routes tokens to specialist connectors pretrained on HTML, JSON, and code views of tables. On the authors' WildStruct suite of degraded tables (blur, skew, watermarks, missing fonts, nested or incomplete layouts), TableMoE with Program-of-Thought reaches 80.31 average accuracy, 5.2 points above GPT-4o, and on the public MMMU-Table split it reaches 54.53%, 10.55 points above GPT-4o. The paper also releases a 1.2M-sample alignment corpus and four WildStruct benchmarks. If the reported gains hold, role-aware routing plus structured expert pretraining is a concrete alternative to simply scaling up monolithic multimodal models for table reasoning.

What carries the argument

The load-bearing mechanism is Neuro-Symbolic Routing (called NeuroSym-MoE in the paper), a two-stage gating procedure. First, a role classifier produces a soft distribution over nine table-centric token roles, and a learned compatibility matrix converts role probabilities into affinity scores for the connector experts; second, the normalized Shannon entropy of the role distribution is used as a confidence coefficient that scales the routing logits before a softmax. Each connector expert is pretrained on a different table-to-X alignment task (table to HTML for layout, table to JSON for spatial relations and visual attributes, table to code for executable rendering), and the fused representation is passed to an LLM decoder. The paper also uses a curriculum-guided annealing objective that gradually increases structural degradation and shifts weight from task loss to role and structure supervision.

What would settle it

Render fresh WMMFinQA-style test images from FinQA using an independent degradation generator (different blur, skew, and watermark routines), and compare TableMoE+PoT against GPT-4o on that set; if the +5.2-point margin shrinks or reverses, the claimed advantage is tied to the authors' own rendering pipeline rather than to role-aware routing.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that neuro-symbolic routing is what makes multimodal table understanding robust. Instead of treating a table image as a bag of visual tokens, TableMoE assigns each token a semantic role with a lightweight classifier, maps those roles through a learned compatibility matrix to four connector experts (General, HTML, JSON, Code), uses normalized entropy of the role distribution to suppress low-confidence routing, and fuses the expert-transformed tokens before LLM decoding. The authors report that this architecture beats strong monolithic baselines: 80.31 WildStruct-Bench average with Program-of-Thought versus 63.10 for GPT-4o and 36.94 for Qwen2.5-VL-72B, and 54.53% on MMMU-Table versus 43.98% for GPT-4o. Ablations attribute the margin to symbolic role prediction, the compatibility graph, entropy-based confidence fusion, and the code expert, with the largest drop when the expert module is removed entirely.

Load-bearing premise

The load-bearing premise, which the paper's limitations section (Section G) concedes is unproven, is that the automatically generated, human-verified token-role labels and reasoning traces are correct and representative enough for the router to learn genuine table structure rather than patterns in the benchmark pipeline itself.

Editorial extensions

If this is right

Degraded and incomplete table images can be handled by routing structure, not just by scaling up the LLM, since TableMoE's WildStruct gain over GPT-4o (+5.2 points) is achieved with an 8B-class backbone.
The router's role distribution doubles as an interpretability signal: low-confidence, high-entropy predictions trigger abstention under blur, which the paper contrasts with hallucinated answers from a 72B baseline.
Expert specialization is complementary, because removing the code expert costs 6.97 points, the HTML expert 4.67, and the JSON expert 2.97 on WMMFinQA, while removing all experts costs 18.47 points.
The gains transfer outside the authors' own benchmarks: TableMoE outperforms GPT-4o by 10.55 points on the MMMU-Table split and improves ChartQA and FinanceMath when mounted on Qwen2.5-VL-7B with only 10% of the alignment data.
Program-of-Thought supervision is the better reasoning mode for this router, raising WMMFinQA from 78.73 (CoT) to 81.98 (PoT).

Reading between the lines

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

Not claimed by the paper: the same role-routing design could be lifted out and used as an image-quality or trust estimator for table QA, since the router's per-token role entropy already predicts when the model should decline to answer.
If the gains hold, a natural next test is applying the role taxonomy to other structured visual domains, such as forms, invoices, or charts, where stable semantic roles exist but current MLLMs are not explicitly decomposed.
A possible source of bias the paper acknowledges is synthetic alignment data; an editorial test would be to train on handwritten or camera-captured tables and check whether the HTML, JSON, and code experts still carry the benchmark margin.
The reported MMMU-Table margin suggests that role-aware routing may matter more for heterogeneous tables than for generic image-text alignment; that claim could be probed by holding model size constant and varying only the router.

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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

Two things to know. First, the architectural idea is real: routing table tokens to HTML/JSON/Code connector experts via a role classifier is a new combination, and the WildStruct degradation typology is useful. Second, the headline number — +5.2 over GPT-4o on WildStruct-Bench — is not trustworthy as reported, because TableMoE is fine-tuned on WMMFinQA/WMMTatQA training splits built from FinQA/TAT-QA and then tested on test splits from those same sources, while GPT-4o is zero-shot. The ablations in the text also don't match Table 3: the text says the role predictor is worth 2.8 points, the table says 4.47; code expert is 5.3, the table says 6.97; graph-only is 3.0 vs 5.37; confidence fusion is 4.6 vs 6.27. That is sloppy enough to undermine the causal attribution.

Where the paper earns credit: the MMMU-Table gain (+10.55 over GPT-4o) is on a public, out-of-domain benchmark, and the FinanceMath improvements in Table 7 are also on public data. Those results are the best evidence that the neuro-symbolic routing does something beyond memorizing the WildStruct rendering pipeline. The alignment dataset is a serious resource; the qualitative examples are genuinely illustrative.

Soft spots beyond the ablation inconsistency: RQ9 says matched fine-tuned baselines were run, but no such results appear in any table — that is exactly the control the headline needs. The GPT-4-generated CoT/PoT and role annotations used for training come from the same pipeline used to build the WildStruct test sets, so there is a real risk of benchmark self-similarity. Table 8 reports 2.5M generated alignments while the abstract says 1.2M quadruples; the selection is explained but should be stated in the main text. Minor: GPT-4o version varies across tables, which can shift comparisons.

The paper is worth a serious referee. The architecture is new, the independent numbers are promising, and the benchmarks, once cleaned up, could be useful. I would not cite the headline results yet, but I would send it to review with a request for code/data release, corrected ablations, and a matched fine-tuning baseline.

Referee Report

5 major / 5 minor

Summary. This paper proposes TableMoE, a Mixture-of-Connector-Experts (MoCE) architecture for multimodal table understanding. The model routes visual tokens to HTML, JSON, Code, and General connector experts using a “neuro-symbolic” router that predicts nine semantic token roles, builds a compatibility graph, and applies entropy-based confidence weighting. The authors introduce a 1.2M-sample TableMoE-Align corpus for alignment pretraining, a curriculum-guided Neuro-Symbolic Annealing fine-tuning protocol, and four new WildStruct benchmarks. The central claims are state-of-the-art results on WildStruct-Bench (80.31 average with PoT, +5.2 over GPT-4o), on MMMU-Table (54.53, +10.55), and on FinanceMath, with ablations attributing the gains to role prediction, symbolic graph routing, confidence fusion, and the code expert.

Significance. If the empirical claims were fully supported, TableMoE would be a valuable contribution: the separation of routing from expert computation is intuitive, the alignment-driven expert pretraining is a sensible way to inject structural priors, and the four released benchmarks plus the alignment corpus would be useful resources. The qualitative analysis is unusually detailed, and the uncertainty-abstention behavior is a nice demonstration of the routing mechanism. However, the current evidence is not sufficient to establish the headline SOTA or the causal attribution: the ablation table and prose disagree on nearly every number, the WildStruct benchmarks are built from the same source corpora and rendering pipeline used for training, the promised matched fine-tuned WildStruct baselines are absent, and the annealing objective is defined inconsistently. The independent MMMU-Table result is the strongest evidence against pure benchmark self-similarity, but it does not by itself support the WildStruct-specific and component-level claims. With corrected numbers, matched baselines, and a genuinely held-out evaluation, the paper's central idea could be credible.

major comments (5)

[Section 5.3, Table 3] The ablation text and the ablation table disagree on nearly every reported delta. The table lists −5.37 for “w/o symbolic graph”, −4.47 for “w/o token role prediction”, −6.27 for “w/o confidence fusion”, and −6.97 for “w/o code expert”, while the prose states 3.0, 2.8, 4.6, and 5.3 points respectively. Similar mismatches occur for HTML (−4.67 vs. 3.0), JSON (−2.97 vs. 1.3), and full expert removal (−18.47 vs. 16.8). Because the causal attribution of TableMoE's gains rests on these deltas, the discrepancy must be resolved and all numbers reconciled before the ablation claims can be evaluated.
[Sections 4.2 and 5.2, Tables 9–10] The WildStruct headline result in Table 1 compares TableMoE after Neuro-Symbolic Annealing on WMMFinQA (6,251 training samples) and WMMTatQA (2,201) against zero-shot GPT-4o on test splits from the same FinQA/TAT-QA sources, rendered by the same pipeline described in Appendix F.3. Since Table 9 labels these benchmarks “Held-In”, the +5.2 average over GPT-4o cannot be attributed solely to neuro-symbolic routing; it may largely reflect in-domain fine-tuning. RQ9 states that matched fine-tuned baselines were run, but no such WildStruct results appear in any table. The authors should report matched fine-tuned controls using the same training data, curricula, and decoding settings for at least Qwen2.5-VL-7B and ideally for the strong API baselines as well.
[Appendices F.2–F.3 and G] The WildStruct benchmarks are constructed with the same GPT-4-generated CoT/PoT rationales, human verification, role annotations, and degradation transformations used to build the training data. This creates a risk that TableMoE learns the benchmark construction pipeline rather than generalizable structural understanding. The authors' own RQ7 acknowledges GPT-generated program bias, and Appendix G concedes the limitations of synthetic alignment data. The independent MMMU-Table result in Table 2 is the best evidence against pure self-similarity, but it does not rescue the WildStruct claim by itself. The paper should add a truly held-out evaluation, for example by applying the WildStruct degradation family to an unrelated public table benchmark and reporting zero-shot transfer without any training on that benchmark or its source corpus.
[Appendix A.2, Eq. (7); Table 5] The training objective is defined with task weight (1−λ(t)) and symbolic weight λ(t) in Eq. (7), matching Figure 5, but Table 5 reports LNSA = λ(t)·Lneural + (1−λ(t))·Lsymbolic. The two formulas describe opposite annealing schedules. Because the curriculum schedule is a core component of the method, this inconsistency must be corrected and the actual schedule used in the experiments stated explicitly.
[Section 1, Appendix C, Tables 6–7] The claimed state-of-the-art result on FinanceMath is not backed by a consistent comparison. Table 6 is titled “Performance comparison on FinanceMath and WMMFinanceMath benchmarks” but contains only TabPedia and Table-LLaVA rows; TableMoE's FinanceMath numbers appear only in Table 7 as a Qwen2.5-VL-7B variant, with no GPT-4o or domain-specific SOTA baseline in the same table. The paper should present a single, consistent FinanceMath leaderboard that includes the proposed model and the relevant strong baselines.

minor comments (5)

[Section 4.1, Table 8] The abstract and Section 4.1 describe TableMoE-Align as a 1.2M-sample corpus, while Table 8 reports 2.5M generated quadruples and then a selected 1.2M subset; please clarify in the main text that 1.2M is a selected subset and state the selection criteria.
[Section D.1, RQ8] RQ8 says the backbone scale ablation used LLaMA-2-7B and LLaMA-2-13B, while Section 5.1 says the backbone is LLaMA 3.1-8B-Instruct; these statements should be reconciled.
[Figures 10–11] The figures use the misspelling “WildStrcut” in their captions; the intended term is “WildStruct”.
[Section 3.2] The token-role classifier is a core component, but no role-classification accuracy or F1 is reported on a held-out role-label set; adding such a metric would support the interpretability claim.
[Section 5.1] The description of the manual audit of 10% of predictions should state whether the audit was blind and how disagreements were adjudicated, since manual resolution can affect the reported numbers.

Circularity Check

1 steps flagged · score 4.0 of 10

WildStruct headline compares a model fine-tuned on the same benchmark family against zero-shot GPT-4o; independent MMMU/ChartQA/FinanceMath results keep the central claim partially grounded.

fitted input called prediction [Section 4.2 / Section 5.2 / Tables 9-10 / Appendix F.2]
"Our held-in benchmarks, WMMFinQA and WMMTatQA, support model adaptation through supervised fine-tuning on in-domain financial QA and hybrid text-table reasoning tasks. ... TableMoE+PoT achieves an average accuracy of 80.31 ... surpassing GPT-4o by +5.2 points."

Table 9 labels WMMFinQA and WMMTatQA 'Held-In'; Table 10 lists WMMFinQA (6,251 samples) and WMMTatQA (2,201 samples / 13,215 turns) as 'Training Datasets for Neuro-Symbolic Annealing'; Section 4.2 states that all WildStruct sets use split and evaluation metrics similar to the original FinQA/TAT-QA. The headline +5.2 average is therefore computed on test splits of the same benchmark family, built with the same rendering/degradation pipeline, that supplied the fine-tuning corpus, while GPT-4o is a zero-shot API baseline. The gain partly reflects in-domain fine-tuning rather than the neuro-symbolic router, so the causal attribution is partially self-referential rather than independently demonstrated.

full rationale

At the level of equations and architecture, TableMoE's routing rules (Eqs. 1-6) and the NSA loss (Eq. 7) do not build in the reported accuracies, and no fitted constant is later renamed as a prediction. There are no load-bearing self-citations and no imported uniqueness theorem. The central architectural claim also has genuinely independent support: Table 2 shows +10.55 over GPT-4o on the public MMMU-Table split, and Table 7 reports a controlled comparison on ChartQA and FinanceMath where the same fine-tuning data is used with and without the TableMoE scaffold. The main circularity-adjacent issue is the WildStruct headlne: held-in training and evaluation are drawn from the same FinQA/TAT-QA family, with zero-shot API baselines, so the +5.2 point cannot cleanly be attributed to neuro-symbolic routing. This is more an evaluation-validity confound than a formal derivation-level equivalence, and the independent benchmarks prevent a higher score. The ablation prose/table discrepancy and the missing RQ9 matched-fine-tuning results are additional correctness concerns that should be weighed outside the circularity score.

Assumptions & free parameters 4 free parameters · 5 assumptions · 1 invented entities

The central claim depends mainly on the quality of synthetic data and benchmark construction rather than on a formal derivation. The routing equations in Section 3.2 are standard softmax operations; the only learned structures are the role classifier and compatibility matrix, both trained on author-generated labels. The ablation and main results therefore inherit all the uncertainty in the GPT-4o data pipeline.

free parameters (4)

Token role taxonomy (9 roles)
Roles HEADER, DATA, AXIS, UNIT, TOTAL, FORMULA, ANNOTATION, TEXT, EMPTY are chosen by hand; the compatibility matrix and routing depend on this set.
Compatibility matrix E = learned
Maps role probabilities to expert affinities in Eq. 3; trained on WildStruct corpora and role labels.
Annealing schedule lambda(t) and weights lambda1, lambda2 = sigmoid schedule; lambda1, lambda2 not reported
Controls how much symbolic loss is used during fine-tuning; values are selected, not derived.
Entropy suppression coefficient alpha = computed from role entropy
Scales routing logits in Eq. 4; the formula is defined, but the effective behavior is tuned implicitly through training.

assumptions (5)

domain assumption CLIP-ViT-Large-Patch14-336 and LLaMA-3.1-8B or Qwen2.5-VL-7B pretrained weights provide adequate visual and language priors.
Assumed for all experiments; stated in Section 5.1.
domain assumption GPT-4o-generated table-to-HTML/JSON/code alignments and CoT/PoT traces are correct and useful as supervision.
The alignment corpus and training rationales are produced by GPT-4o with human verification; Section F.1 and Table 12.
domain assumption The WildStruct rendering pipeline (CSS templates, cropping, watermark injection, noise) is representative of real-world table degradation.
Benchmarks WMMFinQA, WMMTatQA, and WMMTabDialog are built with this pipeline; Section F.3.
domain assumption Human verification and self-consistency filtering remove most annotation errors.
Used for data curation; no inter-annotator agreement or filtering statistics are reported.
domain assumption Exact match within 0.5% relative error and SBERT semantic similarity are valid proxies for table reasoning accuracy.
Section 5.1 defines metrics; no human agreement analysis beyond a 10% manual audit is reported.

invented entities (1)

Neuro-Symbolic Routing graph (semantic planner)
purpose: Predicts nine latent token roles and computes expert affinities via a learned compatibility matrix E to route tokens to HTML, JSON, Code, and General experts.
This is the paper's central architectural novelty, but no falsifiable prediction is attached to it beyond downstream accuracy; its existence is inferred from the model design itself.

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Cite this review

Pith. "Pith review of TableMoE: Neuro-Symbolic Routing for Structured Expert Reasoning in Multimodal Table Understanding." pith.science (2026). https://pith.science/paper/YQ2DWLP7

@misc{pith2026250621393,
  author       = {Pith},
  title        = {Pith review of: TableMoE: Neuro-Symbolic Routing for Structured Expert Reasoning in Multimodal Table Understanding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YQ2DWLP7}},
  note         = {Machine review of arXiv:2506.21393}
}

read the original abstract

Multimodal understanding of tables in real-world contexts is challenging due to the complexity of structure, symbolic density, and visual degradation (blur, skew, watermarking, incomplete structures or fonts, multi-span or hierarchically nested layouts). Existing multimodal large language models (MLLMs) struggle with such WildStruct conditions, resulting in limited performance and poor generalization. To address these challenges, we propose TableMoE, a neuro-symbolic Mixture-of-Connector-Experts (MoCE) architecture specifically designed for robust, structured reasoning over multimodal table data. TableMoE features an innovative Neuro-Symbolic Routing mechanism, which predicts latent semantic token roles (e.g., header, data cell, axis, formula) and dynamically routes table elements to specialized experts (Table-to-HTML, Table-to-JSON, Table-to-Code) using a confidence-aware gating strategy informed by symbolic reasoning graphs. To facilitate effective alignment-driven pretraining, we introduce the large-scale TableMoE-Align dataset, consisting of 1.2M table-HTML-JSON-code quadruples across finance, science, biomedicine and industry, utilized exclusively for model pretraining. For evaluation, we curate and release four challenging WildStruct benchmarks: WMMFinQA, WMMTatQA, WMMTabDialog, and WMMFinanceMath, designed specifically to stress-test models under real-world multimodal degradation and structural complexity. Experimental results demonstrate that TableMoE significantly surpasses existing state-of-the-art models. Extensive ablation studies validate each core component, emphasizing the critical role of Neuro-Symbolic Routing and structured expert alignment. Through qualitative analyses, we further showcase TableMoE's interpretability and enhanced robustness, underscoring the effectiveness of integrating neuro-symbolic reasoning for multimodal table understanding.

Figures

Figures reproduced from arXiv: 2506.21393 by the authors.

**Figure 2.** Overview and capabilities of TableMoE. We introduce a Neuro-Symbolic MoE architecture that routes [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Overview of the TableMoE architecture. The model encodes a table (image or structured) and text [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Token Role Taxonomy and Distribution in WMMFinQA (Training Set). Our semantic token-role system categorizes tokens into 9 interpretable types (e.g., HEADER, DATA, UNIT, etc.), facilitating role-aware expert routing. The accompanying table visually demonstrates each rol…

**Figure 5.** Figure 5: Neuro-Symbolic Annealing (NSA) loss scheduling visualization. During training, the annealing [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6: Two-stage Neuro-Symbolic Expert Training Flow. Stage 1 focuses on modal alignment; Stage 2 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]

**Figure 7.** Figure 7: Model Performance on WMMFinQA under WildStruct Perturbations. We compare TabPedia, Table-LLaVA, and TableMoE across Table-, Text-, and Table+Text-based QA. WMMFinQA features five challenging WildStruct styles: incomplete headers or fonts, skewed layouts, blurred conten…

**Figure 8.** Figure 8: Fine-grained Taxonomy of Table Image and Numerical Reasoning in [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]

**Figure 9.** Figure 9: Table Image Rendering Pipeline for WMMFinQA and WMMTatQA. [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]

**Figure 10.** Figure 10: WildStrcut images demonstration of WMMFinQA-bench. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_10.png]

**Figure 11.** Figure 11: WildStrcut images demonstration of WMMTabDialog-bench. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_11.png]

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B. Yang, Y . Zhang, D. Liu, A. Freitas, and C. Lin. Does table source matter? benchmarking and improving multimodal scientific table understanding and reasoning, 2025. URL https: //arxiv.org/abs/2501.13042

2025 arXiv
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F. Yang, L. Hu, X. Liu, S. Huang, and Z. Gu. A large-scale dataset for end-to-end table recognition in the wild. Scientific Data, 10(1), Feb. 2023. ISSN 2052-4463. doi: 10.1038/ s41597-023-01985-8. URL http://dx.doi.org/10.1038/s41597-023-01985-8

2023 doi
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X. Yue, Y . Ni, K. Zhang, T. Zheng, R. Liu, G. Zhang, S. Stevens, D. Jiang, W. Ren, Y . Sun, C. Wei, B. Yu, R. Yuan, R. Sun, M. Yin, B. Zheng, Z. Yang, Y . Liu, W. Huang, H. Sun, Y . Su, and W. Chen. Mmmu: A massive multi-discipline multimodal understanding and reasoning bench...

2024
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2024 arXiv
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Zheng, X

M. Zheng, X. Feng, Q. Si, Q. She, Z. Lin, W. Jiang, and W. Wang. Multimodal table under- standing, 2024. URL https://arxiv.org/abs/2406.08100. 11

2024 arXiv
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Zheng, D

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2020 arXiv
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Zhong, J

X. Zhong, J. Tang, and A. J. Yepes. Publaynet: largest dataset ever for document layout analysis,
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Zhong, E

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2020 arXiv
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2021 doi
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URL https://arxiv.org/abs/1908.07836

1908 arXiv
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Price with Tax Included

W. Zhuang, X. Huang, X. Zhang, and J. Zeng. Math-puma: Progressive upward multimodal alignment to enhance mathematical reasoning, 2024. URL https://arxiv.org/abs/2408. 08640. 12 Appendix A Design and Analysis of Neuro-Symbolic Routing in TableMoE Table 4: Token Role Taxonomy i...

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2024 arXiv
[44]

Generation steps include CSS-based HTML rendering, image post-processing, GPT-4-assisted rationale synthesis, human verification, role annotation, etc

into WMMFinQA and WMMTatQA by rendering incomplete, degraded or noisy table images and aligning CoT and PoT traces. Generation steps include CSS-based HTML rendering, image post-processing, GPT-4-assisted rationale synthesis, human verification, role annotation, etc
[45]

Designing CSS templates for realistic table rendering (e.g., zebra stripes, menus, check- boxes)
[46]

Generating incomplete and distorted images via coordinate-aware HTML cropping, water- mark injection, and synthetic noise (e.g., skew, blur), as illustrated in Figure 9
[47]

Converting HTML tables into rendered images using WebDriver and BeautifulSoup
[48]

Prompting GPT-4 to generate Program-of-Thought (PoT) and Multimodal Table Chain- of-Thought (MMTab-CoT) rationales using curated templates, as shown in Table 12 and Table 11
[49]

Applying self-consistency filtering [25] and expert validation to ensure program fidelity
[50]

True" or

Combining rendered images, CoT/PoT, domain knowledge, and original QA pairs to synthe- size training instances for Neuro-Symbolic Annealing. This procedure yields rich, visually noisy QA data with verified symbolic supervision, supporting robust and interpretable table reasoni...
[51]

**Calculate the growth for Citi in 2013:** Growth for Citi = Value at 31-Dec-2013−Value at 31-Dec-2012 Value at 31-Dec-2012 ×100 110.49−83.81 83.81 ×100 = 26.68 83.81 ×100 ≈ 31.84%

2013
[52]

**Calculate the growth for the S&P 500 in 2013:** Growth for S&P 500 = Value at 31-Dec-2013−Value at 31-Dec-2012 Value at 31-Dec-2012 × 100 148.65−118.45 118.45 × 100 = 30.2 118.45 × 100 ≈ 25.5%

2013
[53]

hum" in 2013 is $152, the value for

**Calculate the ratio:** Ratio of growth = Growth for Citi Growth for S&P 500 Substitute the values: Ratio of growth = 31.84 25.5 ≈ 1.25. Final Answer: The ratio of the growth of Citi to the S&P 500 in 2013 is approximately 1.25. TableMoE (Ours): Let’s think step by step: From...

2013
[54]

**Determine the number of shares repurchased in 2013:** Shares repurchased = -65516126 (as given in the table, which is "b") This means 65,516,126 shares were repurchased

2013
[55]

**Identify the average price paid per share in 2013:** Average price paid per share = 18.80 (as given in the table)

2013
[56]

TableMoE (Ours): Let’s think step by step: The table image provides the shares authorized for repurchase at december 31 of 2013 is 43,071,613

**Calculate the total cash outflow:** Total cash outflow = Shares repurchased × Average price paid per share Substituting the values: Total cash outflow = 65, 516, 126×18.80 = 1, 231, 705, 177 (in dollars, or 1,231.71 million dollars) Final Answer: The total cash outflow spent...

2013
[57]

**Extract the V AS revenues for 2019 and 2018:** - V AS revenue in 2019 = **199,391** (in RMB millions) - V AS revenue in 2018 = **176,646** (in RMB millions)

2019
[58]

**Calculate the change in revenue:** Change in revenue = Revenue in 2019 − Revenue in 2018 = 199,391 - 176,646 = 22,745(in RMB millions)

2019
[59]

**Calculate the year-on-year percentage change:** YoY percentage change = Change in revenue Revenue in 2018 × 100 YoY percentage change = 22,745 176,646 × 100 ≈ 12.88% Final Answer: The year-on-year change in V AS Business revenue is **RMB 22,745 million** (a growth of approxi...

2018
[2019]

URL https://arxiv.org/abs/1908.10084. 10

1908 arXiv
[2021]

URL https://aclanthology.org/2021

doi: 10.18653/v1/2021.emnlp-main.300. URL https://aclanthology.org/2021. emnlp-main.300

2021 doi

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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