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TableMaster: A Recipe to Advance Table Understanding with Language Models
Lang Cao, Hanbing Liu
TL;DR
Language models still have difficulty understanding and reasoning over tables, and prior approaches often target isolated aspects. TableMaster integrates targeted solutions, including adaptive textual or symbolic reasoning, and reports improved benchmark performance, including 78.13% accuracy on WikiTQ with GPT-4o-mini.
Problem
Language models have room to improve at table understanding because prior methods often address isolated aspects rather than systematically analyzing and improving table understanding.
Source: §1 · pp. 1–2Method
TableMaster integrates targeted solutions for table challenges, including table-of-focus construction, table verbalization, and adaptive selection between textual and symbolic reasoning.
Source: §1 · p. 2, §3.1 · p. 4Results
78.13% accuracy on WikiTQ with GPT-4o-mini surpasses existing baselines; TableMaster also consistently achieves the highest performance across WikiTQ and TabFact under three backbone models.
Source: §1 · p. 2, §5.2 · p. 8Takeaways & Limitations
The authors present TableMaster as a unified recipe for table understanding and plan to refine it for diverse practical applications.
Source: §6 · p. 10The authors acknowledge limitations but do not specify them here, noting that future work may refine the technology and its downstream applications.
Source: B LIMITATIONS, EXTENDABILITY, AND… · p. 18
Abstract
from arXiv · showhide
Tables serve as a fundamental format for representing structured relational data. While current language models (LMs) excel at many text-based tasks, they still face challenges in table understanding due to the complex characteristics of tabular data, such as their structured nature. In this paper, we aim to enhance LMs for improved table understanding. We identify four key challenges: 1) difficulty in locating target data, 2) deficiency in table semantics, 3) numerical inaccuracies in textual reasoning, and 4) semantic inflexibility in symbolic reasoning. To address these issues, we propose TableMaster, a recipe and comprehensive framework that integrates multiple solutions to overcome these obstacles. TableMaster first extracts relevant table content and verbalizes it with enriched semantic context. Additionally, we introduce adaptive reasoning, a flexible approach that dynamically adjusts between textual and symbolic reasoning, tailoring the reasoning process to each query. Extensive analyses and experiments demonstrate our findings and the effectiveness of TableMaster. On the WikiTQ dataset, TableMaster achieves an accuracy of 78.13% using GPT-4o-mini, surpassing existing baselines. We hope this work will serve as a practical step toward more robust and reliable table understanding.
1 INTRODUCTION
The introduction frames table understanding as an open challenge for language models and presents TableMaster as a unified recipe integrating targeted solutions. It reports evaluation across three datasets, including a WikiTQ result with GPT-4o-mini.
1 INTRODUCTION
- Prior work either focused on a single basic aspect of table understanding or used isolated strategies, leaving no systematic analysis and comprehensive improvement method.The introduction positions TableMaster as addressing this gap through extensive experiments and an integrated framework.Source: §1 · p. 2
- TableMaster combines targeted solutions for four challenges: locating data, sparse table semantics, numerical errors in textual reasoning, and semantic inflexibility in symbolic reasoning.Its adaptive reasoning approach dynamically adjusts between textual and symbolic reasoning for each query.Source: §1 · p. 2
- 78.13% accuracy on WikiTQ with GPT-4o-mini, surpassing existing baselines, is the reported headline result for TableMaster.The paper also reports evaluation across WikiTQ, TabFact, and FetaQA.Source: §1 · p. 2
2 RELATED WORK
Related work covers reasoning methods for language models and two strands of table-understanding research: fine-tuning and adaptation without fine-tuning.
2 RELATED WORK
- Reasoning work uses inference-time prompting and structured reasoning methods, while this paper focuses on inference-time improvements for table understanding.The cited approaches include chain-of-thought, few-shot, least-to-most, program-of-thought, self-consistency, and tree- or graph-structured reasoning.Source: §2 · p. 3
- Fine-tuning approaches include specialized table pretraining, SQL-executor pretraining, larger decoder-only models, and reinforcement learning for spreadsheet-formula reasoning.Examples include TaPas, Pasta, TUTA, TAPEX, TableLlama, TableGPT, StructLLM, and Formula Tuning.Source: §2 · p. 3
- Without fine-tuning, prior methods generate SQL or Python, construct or operate on sub-tables, normalize tables, or interpret spreadsheet environments.This paper likewise adapts advanced language models without fine-tuning and addresses multiple table-understanding challenges.Source: §2 · p. 3
3 CHALLENGES IN TABLE UNDERSTANDING
The section analyzes how table structure, density, concise cell text, and numerical content relate to table-understanding challenges, then describes targeted responses and experimental findings.
3 CHALLENGES IN TABLE UNDERSTANDING
- Tables are two-dimensional, data-intensive structures whose concise cell text often provides sparse semantic context.The section's challenge analysis is organized around these characteristics and related table-understanding problems.Source: §3 · p. 3
3.1 DIFFICULTY IN LOCATING TARGET DATA
- Table accuracy tends to decline as table size increases across row count, column count, area, and token count; weaker models show a larger drop.The proposed table-of-focus narrows input to a sub-table containing information relevant to the query.Source: §3.1 · p. 4, Figure 2 · p. 4
3.2 TABLE SEMANTIC DEFICIENCY
- Verbalized tables with descriptions improve performance on some tables, with a 1.5% accuracy increase for weaker models; description quality also matters.The proposed response is to provide a natural-language description alongside the original table to enrich semantic context.Source: Figure 2 · p. 4, §3.2 · p. 5
3.3 NUMERICAL INACCURACY IN TEXTUAL REASONING
- Textual reasoning reaches 72.4% on questions not requiring calculation, but calculation-required questions bring a 20.1% decline, versus 7.6% for enhanced symbolic reasoning.The section identifies arithmetic errors and difficulty with iterative numerical processes as limitations of textual reasoning.Source: Figure 2 · p. 4, §3.3 · p. 5
3.4 SEMANTIC INFLEXIBILITY IN SYMBOLIC REASONING
- On noisy tables, symbolic reasoning drops 31.8% compared with a 20.5% decline for textual reasoning, while basic symbolic reasoning performs worse overall.The proposed response normalizes tables and uses textual reasoning to guide program generation; it reaches 59.1% accuracy on calculation-required questions.Source: Figure 2 · p. 4, §3.4 · p. 5
4 TableMaster: A RECIPE FOR TABLE UNDERSTANDING
TableMaster unifies table structure understanding, content understanding, and question-answering reasoning in a framework that adapts to each table and query.
4.1 TASK FORMULATION
- Table-based QA predicts a natural-language answer, while fact verification predicts True or False from a table and its question or statement.The task is formalized as F(T, Q) = A.Source: §4.1 · p. 6
4.2 TABLE STRUCTURE UNDERSTANDING
- Structure processing can peek at top rows, normalize table orientation and numeric formats, then select relevant columns and rows to construct a compact Table-of-Focus.The resulting table contains only information filtered as necessary for the task.Source: §4.2 · pp. 6–7
4.3 TABLE CONTENT UNDERSTANDING
- Content understanding checks whether the Table-of-Focus is sufficient, adds ranked columns when needed, and verbalizes the result to enrich its semantic context.The verbalized table is concise natural-language text that retains rich semantic context.Source: §4.3 · p. 7
4.4 TABLE REASONING FOR QUESTION ANSWERING
- Adaptive reasoning uses textual reasoning for small or non-numeric tables and programmatic symbolic reasoning for larger or numeric tables.For symbolic reasoning, textual reasoning first provides guidance for the programmatic step.Source: §4.4 · p. 7, Table 1 · p. 8
5 EXPERIMENTS
Experiments compare TableMaster with prior methods across datasets and language models, and ablations examine the contributions of its components.
5.1 SETTINGS
- Evaluation covers WikiTQ and TabFact with exact match accuracy, and FetaQA with BLEU and ROUGE; the experiments also include HiTab and FinQA.The study uses OpenAI models and Llama-3.1-70B, with Binder, Dater, and Chain-of-Table among its baselines.Source: §5.1 · p. 8
5.2 MAIN RESULTS
- TableMaster achieves the highest performance on WikiTQ and TabFact across gpt-3.5-turbo, gpt-4o-mini, and Llama-3.1-70B.WikiTQ gains over the strongest baselines are +3.51, +13.40, and +12.39 points, respectively, for those backbones. TabFact gains in the same order are +1.73, +1.19, and +4.10 points.Source: §5.2 · p. 8
5.3 ABLATION STUDY
- Removing any TableMaster component decreases accuracy on WikiTQ and TabFact.Table 2 reports ablation results and marks performance drops from the full model.Source: §5.3 · p. 9, Table 2 · p. 9
- Removing reconstruction drops accuracy by 2.58% on WikiTQ and 0.40% on TabFact; removing verbalization drops WikiTQ accuracy 2.35% and TabFact 0.23%.The authors note that verbalization's impact on TabFact is minimal and suggest it is more beneficial for complex table understanding tasks.Source: §5.3 · p. 9
- Removing textual reasoning produces the largest accuracy decline; removing symbolic reasoning or textual guidance also lowers performance on both datasets.Textual reasoning removal drops accuracy by 4.28% on WikiTQ and 1.73% on TabFact; symbolic reasoning removal drops it by 2.03% and 0.79%, respectively. Textual guidance removal drops accuracy by 2.92% on WikiTQ and 0.44% on TabFact.Source: §5.3 · p. 9
6 CONCLUSION
The conclusion presents TableMaster as a framework for table understanding and outlines its potential applications, risks, limitations, and future refinements. The accompanying sections identify technical boundaries and describe downstream settings and evaluation datasets.
6 CONCLUSION
- TableMaster combines multiple solutions for table understanding, with adaptive reasoning selecting between textual and symbolic approaches for each query.The conclusion also describes future refinement to improve performance across practical applications.Source: §6 · p. 10
A ETHICS STATEMENT
- TableMaster may support decision systems and spreadsheet collaboration, but inaccurate reasoning, misuse, bias, and uneven performance pose deployment risks.The paper recommends deterministic checks for symbolic outputs, diverse table evaluation, human oversight in high-stakes settings, and interpretability tools.Source: A ETHICS STATEMENT · p. 18
B.1 TECHNICAL REFINEMENT
- The evaluation uses cleaned tables without explicit normalization, and the framework assumes tables are flat despite hierarchical tables in real-world settings.The paper suggests converting hierarchical tables to flat ones or using tree-based extraction.Source: §B.1 · p. 18
- Table-of-Focus extraction is intentionally simple, while LM-generated verbalizations are not optimal because open-ended generation is challenging.The paper suggests that more advanced extraction may improve key-information selection and that trained small LMs could improve verbalization quality and efficiency.Source: §B.1 · pp. 18–19
- Adaptive reasoning can be unstable when LMs fail to select the optimal strategy, and row lookup can still omit information despite reconstruction.The paper proposes training a dedicated model to guide strategy selection as a possible route to improved stability and performance.Source: §B.1 · p. 19
B.2 DOWNSTREAM APPLICATIONS
- Potential applications include interpreting web tables, automating spreadsheet analysis, and querying databases without requiring users to write SQL.The paper notes that application scenarios may use selected components rather than the entire framework.Source: §B.2 · p. 19
C DATASETS USED FOR EVALUATION
- Table 3 lists the evaluation datasets along with their licenses and sources.Source: C DATASETS USED FOR EVALUATION · p. 19
D DETAILED SETTINGS OF CHALLENGE ANALYSIS EXPERIMENTS
The appendix describes the setup for challenge analyses on WikiTQ and experiments on additional table-understanding benchmarks. It specifies how table size, verbalization, reasoning approach, and table noise are examined.
D DETAILED SETTINGS OF CHALLENGE ANALYSIS EXPERIMENTS
- Challenge analyses use 4,344 WikiTQ instances, exact match, OpenAI models hosted on Azure, and temperature 0 unless otherwise stated.The listed model versions are gpt-4o-0806, gpt-4o-mini-0718, gpt-3.5-turbo-0125, and o1-preview-0912.Source: D DETAILED SETTINGS OF CHALLENGE… · pp. 19–20
- Table size is divided into quartiles from small to extra-large using row count, column count, area, and token count.Performance is analyzed across those size categories.Source: D DETAILED SETTINGS OF CHALLENGE… · p. 20
- Verbalization is compared as raw-table input, LM-generated verbalization alongside the table, and verbalization generated by gpt-4o.The last approach is intended to further enrich semantic context.Source: D DETAILED SETTINGS OF CHALLENGE… · p. 20
- Reasoning approaches are compared on calculation and non-calculation questions, classified by o1 into 2,692 and 1,652 instances, respectively.The comparison includes textual, symbolic, and text-guided symbolic reasoning using gpt-3.5-turbo.Source: D DETAILED SETTINGS OF CHALLENGE… · p. 20
- For noisy-table analysis, 2,565 human- and model-checked tables are evaluated against original normalized tables using gpt-4o-mini.Noise generation preserves actual values, diversifies entries within columns, and randomly transposes half of tables.Source: D DETAILED SETTINGS OF CHALLENGE… · p. 20
E EXTENDED EXPERIMENTS ON ADDITIONAL TABLE UNDERSTANDING BENCHMARKS
- Additional experiments assess TableMaster's robustness across diverse table-understanding tasks.Source: E EXTENDED EXPERIMENTS ON ADDITIONAL… · p. 20
E.1 EVALUATION ON FREE-FORM QA WITH THE FETAQA DATASET
Across free-form QA, hierarchical-table, numerical-reasoning, and baseline evaluations, TableMaster is reported to improve on comparison methods, with evaluation metrics and table conversion imposing important qualifications.
E.1 EVALUATION ON FREE-FORM QA WITH THE FETAQA DATASET
- The FetaQA experiments use gpt-4o because PaLM 2 is no longer accessible, with 20 few-shot exemplars to match the dataset format.The evaluation uses BLEU and ROUGE for FetaQA, rather than exact match accuracy used for WikiTQ and TabFact.Source: §E.1 · pp. 20–21
- 16.2% BLEU and 6.5% ROUGE-1 improvements over the base end-to-end QA model are reported for TableMaster on FetaQA.The improvements surpass those of Chain-of-Table relative to its respective end-to-end QA baseline.Source: Table 4 · p. 21, §E.1 · p. 21
- On FetaQA, ROUGE-based evaluation can assign low scores to an answer judged manually as correct and superior to the ground truth.In the FetaQA-164 example, only two words matched, while the authors describe ROUGE as insensitive to stylistic and structural improvements from in-context learning.Source: §E.1 · p. 21, Figure 4 · p. 21
E.2 EVALUATION ON HIERARCHICAL TABLES WITH THE HITAB DATASET
- HiTab’s hierarchical tables are converted into relational subtables with contextual tags, and the authors identify conversion information loss as the main source of residual errors.The framework is designed for relational tables; future work is proposed to integrate hierarchical relations directly into reasoning.Source: §E.2 · p. 22
- TableMaster outperforms the strongest Chain-of-Table baseline on converted HiTab tables by 0.7 point, from 73.5 to 74.2.Residual errors are attributed mainly to information loss during conversion.Source: Table 5 · p. 22, §E.2 · p. 22
E.3 EVALUATION ON NUMERICAL REASONING WITH THE FINQA DATASET
- On FinQA, TableMaster consistently boosts numerical-reasoning accuracy over both backbones, though the cited passages do not name the backbones or provide exact accuracy scores.The passage links this result to the symbolic reasoning module's reliable handling of complex calculations in the financial domain.Source: Table 6 · p. 22, §E.3 · p. 22
F TABLE UNDERSTANDING BASELINES
- Across tested base models, TableMaster achieves the highest accuracy; with gpt-4o-mini it scores 78.13% on WikiTQ and 90.12% on TabFact.These results surpass chain of thought at 72.97% and 87.40%, respectively.Source: Table 7 · p. 23, F TABLE UNDERSTANDING BASELINES · p. 23
- With gpt-3.5-turbo, TableMaster scores 68.21% on WikiTQ and 83.65% on TabFact, exceeding chain of thought and Program of Thought on both datasets.The reported performance gap is larger for this backbone than for gpt-4o.Source: F TABLE UNDERSTANDING BASELINES · p. 23
G PERFORMANCE ANALYSIS UNDER DIFFERENT TABLE SIZES
TableMaster retains strong performance across table-size categories, although accuracy generally declines as tables grow; stronger backbones show a smaller medium-to-large-table drop.
G PERFORMANCE ANALYSIS UNDER DIFFERENT TABLE SIZES
- For gpt-3.5-turbo, TableMaster scores 69.01% on small, 58.00% on medium, and 56.73% on large tables, outperforming baseline methods in each category.The reported gap is more pronounced on medium and large tables.Source: Table 8 · p. 24, G PERFORMANCE ANALYSIS UNDER DIFFERENT… · p. 24
- For gpt-4o-mini, TableMaster scores 78.71% on small, 70.50% on medium, and 70.19% on large tables.Its medium-to-large-table decline is 0.31%.Source: G PERFORMANCE ANALYSIS UNDER DIFFERENT… · p. 24
- TableMaster with gpt-4o-mini maintains high accuracy as row count rises, while smaller models show sharper declines and gpt-3.5-turbo peaks at 11–15 rows before falling.The size analysis partitions tables into quartiles from smallest to largest.Source: G PERFORMANCE ANALYSIS UNDER DIFFERENT… · p. 25
- TableMaster with gpt-4o-mini peaks at around five columns before a slight decline, and the analysis suggests column-heavy tables pose greater reasoning challenges than row-heavy tables.The authors associate the challenge with increased dimensional complexity and interdependencies between attributes.Source: G PERFORMANCE ANALYSIS UNDER DIFFERENT… · p. 25
- Accuracy generally falls as area size increases, with TableMaster using gpt-4o-mini peaking in the 96–167 area-size range before a slight decline.Area size is calculated as row count multiplied by column count.Source: G PERFORMANCE ANALYSIS UNDER DIFFERENT… · p. 25
- Accuracy generally declines as token count increases, while TableMaster with gpt-4o-mini consistently achieves the highest accuracy in the token-count comparison.The gpt-3.5-turbo model shows the sharpest drop.Source: Figure 5 · p. 24, G PERFORMANCE ANALYSIS UNDER DIFFERENT… · p. 25
- Across the reported size analyses, TableMaster is described as outperforming previous methods, with gradual accuracy decline as table size increases.The comparison covers row count, column count, area size, and token count.Source: G PERFORMANCE ANALYSIS UNDER DIFFERENT… · pp. 24–25
H PERFORMANCE ANALYSIS UNDER DIFFERENT TABLE PEEK SIZES
Table peek reduces the table context processed at selected steps; accuracy rises with larger peeks toward full-table use, while a theoretical cost expression accounts for peek and focus-table processing.
H PERFORMANCE ANALYSIS UNDER DIFFERENT TABLE PEEK SIZES
- Table peek is proposed to improve efficiency by reducing the context language models process at certain steps.Figure 6 examines WikiTQ row counts and accuracy variation by peek size; 72 extreme row-count outliers are removed from the distribution plot, and most tables have fewer than 20 rows with a peak around 10.Source: H PERFORMANCE ANALYSIS UNDER DIFFERENT… · pp. 25–26, Figure 6 · p. 25
- Accuracy is relatively low at peek sizes of 2–4 rows and reaches its minimum at size 4.The authors hypothesize that the three example rows at size 4 may encourage overfitting to early rows and impair row-lookup SQL generation.Source: H PERFORMANCE ANALYSIS UNDER DIFFERENT… · p. 26
- Accuracy improves sharply as peek size increases up to 25 rows, then rises more slowly and peaks when the entire table is used.The authors suggest a moderate peek can balance efficiency and accuracy without processing the full table.Source: H PERFORMANCE ANALYSIS UNDER DIFFERENT… · p. 26
I.1 THEORETICAL ANALYSIS
- The cost analysis defines k as peek size and e as the number of table-of-focus reconstructions after information estimation; a and b are the focus table’s dimensions.The theoretical cost is independent of the number of rows m, while a × b reflects the smaller focus table.Source: §I.1 · p. 26
- The stated total computational cost is (2k + 1) × n + (e + 2.5) × (a × b).The analysis counts table-input length, excludes prompts, external information, and output length, and weights textual and symbolic processes as 1 and 2.Source: §I.1 · p. 26
I.2 EMPIRICAL ANALYSIS
The empirical analysis reports table condensation and theoretical cost bounds, while the reconstruction algorithm expands selected columns only until the focused table contains sufficient information or candidates run out.
I.2 EMPIRICAL ANALYSIS
- WikiTQ tables shrink approximately 1:3 after table-of-focus construction, compared with roughly 1:2 for TabFact.Figure 7 encodes original and condensed table sizes as blue and orange bars, respectively.Source: §I.2 · pp. 26–27, Figure 7 · p. 27
- The estimated computational cost ranges from 1.6 to approximately 6 times the original table size, depending on peek and table-content requirements.The ideal case is approximately 1.6 × (m × n); examining the whole table when all content is needed reaches approximately 6 × (m × n).Source: §I.2 · p. 27
- On the first 100 TabFact examples using GPT-4o, TableMaster uses substantially fewer tokens than Chain-of-Table while maintaining strong performance.The comparison omits self-consistency decoding and the framework can fall back to early-exit or full-table reasoning.Source: §I.2 · p. 27, Table 9 · p. 27
J DETAILED ALGORITHM OF TABLE-OF-FOCUS RE-CONSTRUCTION
- Reconstruction starts with initially selected columns, estimates whether the extracted focus table contains enough information for the question, and adds ranked candidate columns if needed.It stops when information is sufficient or no candidate columns remain, returning the refined table and updated selected columns.Source: J DETAILED ALGORITHM OF TABLE-OF-FOCUS… · p. 28
- The reconstruction algorithm repeatedly extracts a table-of-focus and estimates its information sufficiency before deciding whether to stop or add another column.This iterates until the sufficiency condition is met or the candidates are exhausted.Source: J DETAILED ALGORITHM OF TABLE-OF-FOCUS… · pp. 27–28
K ANALYSIS OF TABLE-OF-FOCUS RE-CONSTRUCTION
Table-of-Focus reconstruction expands selected columns in both datasets, with a larger expansion for WikiTQ than for TabFact.
K ANALYSIS OF TABLE-OF-FOCUS RE-CONSTRUCTION
- TabFact: reconstruction raises selected columns from 2.44 (40.74%) to 3.34 (54.64%), adding 0.90 (13.91%).The figures are averages and percentages of each dataset’s total columns.Source: Table 10 · p. 28, K ANALYSIS OF TABLE-OF-FOCUS… · p. 29
- WikiTQ: reconstruction raises selected columns from 2.87 (47.67%) to 4.72 (75.91%), adding 1.85 (28.23%).The figures are averages and percentages of each dataset’s total columns.Source: Table 10 · p. 28, K ANALYSIS OF TABLE-OF-FOCUS… · p. 29
- The mechanism is described as lightweight; its more pronounced expansion on WikiTQ suggests those tables need greater information coverage.TabFact undergoes a more moderate refinement.Source: K ANALYSIS OF TABLE-OF-FOCUS… · p. 29
L ANALYSIS OF ADAPTIVE REASONING
The adaptive-reasoning analysis compares textual, symbolic, and hybrid strategies, while the following sections examine missing table information, case studies, prompts, notation, and LLM use.
L ANALYSIS OF ADAPTIVE REASONING
- Textual reasoning generally leads; text-guided symbolic reasoning helps weaker models and complex calculations, while adaptive TPoT reaches 74.08% in one pass.Adaptive reasoning balances accuracy and efficiency against multi-inference self-consistency; its perfect-selection TPoT upper bound is 85.06%.Source: L ANALYSIS OF ADAPTIVE REASONING · pp. 29–30
M INFORMATION MISSING AND TABLE REASONING WITH FULL TABLE
- Replacing the focus table with the full table yields 78.13% on WikiTQ, versus 77.23% when the full table is added only for 265 unanswered questions.Focus selection may omit relevant information; the full table and verbalized focus are described as complementary.Source: M INFORMATION MISSING AND TABLE… · pp. 30–31, Table 13 · p. 31
N.1 CASE STUDY OF TABLE VERBALIZATION
- In the congressional-representatives example, verbalization corrects a mistaken row count, producing the ground-truth answer of 4 rather than 5.The question asks how many people stayed at least three years in office.Source: Figure 8 · p. 31, §N.1 · p. 32
N.2 CASE STUDY OF TableMaster
- The Belgian-riders case filters relevant rows, then uses symbolic reasoning to sum their wins and produce the correct total of 7.The workflow includes structure extraction, column lookup, row lookup, SQL execution, and Python-based summation.Source: §N.2 · pp. 32–33
O PROMPT DESIGN IN TableMaster
- The appendix provides stage-specific prompts for structure extraction, column ranking, row selection, verbalization, reasoning, and answer formatting.The prompts also cover information estimation and reasoning-strategy assessment.Source: Figure 10 · p. 34, Figure 11 · p. 35, Figure 13 · p. 36
P PROMPTS USED IN ANALYSIS EXPERIMENTS
- Analysis prompts cover direct, chain-of-thought, and program-of-thought answers, plus verbalization, strategy evaluation, and calculation-type classification.Additional prompts generate textual guidance and noised tables.Source: Figure 21 · p. 40, Figure 22 · p. 40, Figure 23 · p. 41
Q NOTATION TABLE
- Table 14 lists the paper’s notations and corresponding descriptions as a reader reference.The notation table is identified as a quick reference for concepts used in the work.Source: Q NOTATION TABLE · p. 45, Table 14 · p. 45
R THE USE OF LARGE LANGUAGE MODELS (LLMS)
- The authors report using LLMs only to polish manuscript writing; they state that research ideas, methods, analyses, and experiments were their own.They specify grammar correction, phrasing suggestions, and readability improvements as the LLM uses.Source: R THE USE OF LARGE LANGUAGE MODELS… · p. 46