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arxiv: 2512.09874 · v2 · submitted 2025-12-10 · 💻 cs.CV · cs.AI· cs.IR

Benchmarking Document Parsers on Mathematical Formula Extraction from PDFs

Pius Horn , Janis Keuper This is my paper

Pith reviewed 2026-05-16 23:05 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.IR
keywords PDF parsingmathematical formula extractionLLM evaluationdocument benchmarkingsemantic equivalencesynthetic datascientific literature processing
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The pith

A benchmarking framework with synthetic PDFs and LLM semantic judgment reveals large performance gaps among PDF parsers on mathematical formula extraction.

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

The paper develops a controlled test for how accurately document parsers extract mathematical formulas from PDFs. It generates synthetic PDFs from LaTeX sources that supply exact ground truth and then applies an LLM to decide whether each parsed formula conveys the same mathematical meaning as the original. A study with human raters confirms that this LLM judge tracks human semantic assessments at r=0.78, far above the r=0.34 obtained by simple character matching. When the method is run on twenty-plus parsers across one hundred documents containing more than two thousand formulas, clear differences in accuracy appear. The results give concrete guidance for choosing parsers when building scientific databases or training models on research papers.

Core claim

We introduce a benchmarking framework centered on synthetically generated PDFs with precise LaTeX ground truth, enabling systematic control over layout, formulas, and content characteristics. For evaluation, we apply LLM-as-a-judge to assess semantic equivalence of parsed formulas, capturing mathematical meaning beyond surface-level notation differences. We validate this approach through a human study (250 formula pairs, 750 ratings from 30 evaluators), showing a Pearson correlation of r=0.78 with human judgment, compared to r=0.34 for character-level matching. Evaluating 20+ contemporary PDF parsers across 100 synthetic documents with 2,000+ formulas reveals significant performance disparit

What carries the argument

LLM-as-a-judge semantic equivalence scoring paired with a two-stage fuzzy matching pipeline that aligns parser outputs to LaTeX ground truth despite notation and format differences.

If this is right

  • Practitioners can use the reported rankings to pick parsers that preserve mathematical content more reliably for downstream scientific applications.
  • Semantic evaluation allows fair comparison even when parsers emit formulas in different notations or with minor rendering variations.
  • Controlled synthetic documents make it possible to isolate how layout complexity or formula density affects extraction accuracy.
  • Higher-quality formula extraction improves the training data available for large language models that process scientific literature.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same synthetic-generation and LLM-judge approach could be extended to benchmark extraction of tables, figures, or citations under controlled conditions.
  • Running the benchmark on real scanned papers would reveal whether the observed parser gaps persist outside the synthetic setting.
  • Because the LLM judge correlates well with humans, it could scale evaluation for other document-parsing tasks where human labeling is expensive.

Load-bearing premise

Synthetically generated PDFs with controlled layouts and formulas adequately represent the parsing difficulties present in real-world academic PDFs.

What would settle it

Applying the same 20+ parsers and LLM judge to a set of real multi-column academic PDFs and checking whether the performance ordering and human correlation remain the same.

Figures

Figures reproduced from arXiv: 2512.09874 by Janis Keuper, Pius Horn.

Figure 1
Figure 1. Figure 1: Overview of the three main components of the benchmarking framework. The formula dataset component extracts and processes mathematical formulas from Wikipedia to create the wikipedia-latex-formulas-319k collection. The benchmark dataset component generates synthetic PDFs with precise ground truth by randomly combining sampled formulas from this dataset with text segments and inline formu￾las using randomly… view at source ↗
Figure 2
Figure 2. Figure 2: Correlation of Automated Metrics with Human Evaluations [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
read the original abstract

Correctly parsing mathematical formulas from PDFs is critical for training large language models and building scientific knowledge bases from academic literature, yet existing benchmarks either exclude formulas entirely or lack semantically-aware evaluation metrics. We introduce a benchmarking framework centered on synthetically generated PDFs with precise LaTeX ground truth, enabling systematic control over layout, formulas, and content characteristics. For evaluation, we apply LLM-as-a-judge to assess semantic equivalence of parsed formulas, capturing mathematical meaning beyond surface-level notation differences. We validate this approach through a human study (250 formula pairs, 750 ratings from 30 evaluators), showing a Pearson correlation of r=0.78 with human judgment, compared to r=0.34 for character-level matching (CDM) and r~0 for text similarity. Our robust two-stage matching pipeline combining LLM-based extraction with fuzzy validation reliably aligns parsed formulas with ground truth despite format inconsistencies across parsers. Evaluating 20+ contemporary PDF parsers across 100 synthetic documents with 2,000+ formulas reveals significant performance disparities, providing actionable guidance for practitioners selecting parsers for downstream applications. Code and benchmark data: https://github.com/phorn1/pdf-parse-bench and https://github.com/phorn1/formula-metric-study

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a benchmarking framework for PDF parsers focused on mathematical formula extraction. It generates 100 synthetic PDFs with controlled layouts and over 2,000 formulas using precise LaTeX ground truth, proposes an LLM-as-a-judge metric for semantic equivalence, validates this metric via a human study (250 formula pairs, 750 ratings yielding Pearson r=0.78 vs. r=0.34 for character-level matching), and evaluates 20+ parsers to reveal performance disparities. Code and data are released publicly.

Significance. If the synthetic benchmark generalizes, the work supplies practitioners with concrete guidance on parser selection for formula extraction tasks and introduces a semantically-aware evaluation method superior to string matching. Key strengths include the direct human validation study supporting the LLM judge and the public release of code, data, and the two-stage matching pipeline, which supports reproducibility.

major comments (2)
  1. [§3 (Synthetic PDF Generation)] The synthetic PDF generation process (described at high level in the abstract and §3) provides no concrete details on incorporation of multi-column layouts, font variations, or rendering artifacts typical of real academic PDFs. This assumption is load-bearing for the central claim of actionable performance disparities in the evaluation of 20+ parsers, as the reported gaps may not transfer if these complexities are underrepresented.
  2. [Evaluation section] Parser selection criteria are not specified (evaluation section), leaving unclear whether the 20+ tools form a representative sample or are biased toward particular architectures; this affects the reliability of the disparity findings.
minor comments (2)
  1. Figure captions for parser output examples could include explicit annotations of matched vs. mismatched formulas to improve readability.
  2. [Methods] The two-stage matching pipeline is described clearly but would benefit from a pseudocode listing or explicit parameter values for the fuzzy validation step.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We address each major comment point by point below, indicating the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [§3 (Synthetic PDF Generation)] The synthetic PDF generation process (described at high level in the abstract and §3) provides no concrete details on incorporation of multi-column layouts, font variations, or rendering artifacts typical of real academic PDFs. This assumption is load-bearing for the central claim of actionable performance disparities in the evaluation of 20+ parsers, as the reported gaps may not transfer if these complexities are underrepresented.

    Authors: We agree that the current description of the synthetic PDF generation in §3 is high-level and would benefit from additional concrete implementation details to better justify transferability. In the revised manuscript, we will expand §3 to specify the exact mechanisms used: multi-column layouts generated via the LaTeX multicol package with controlled column counts and widths; font variations implemented through selection of standard academic typefaces (e.g., Computer Modern, Times, and sans-serif variants) with randomized sizes and styles; and rendering artifacts simulated by applying controlled PDF compression, noise injection, and anti-aliasing effects during compilation. These additions will directly address the concern and support the reliability of the observed performance disparities. revision: yes

  2. Referee: [Evaluation section] Parser selection criteria are not specified (evaluation section), leaving unclear whether the 20+ tools form a representative sample or are biased toward particular architectures; this affects the reliability of the disparity findings.

    Authors: We acknowledge that the evaluation section does not explicitly state the parser selection criteria, which is necessary to evaluate potential bias. The 20+ parsers were selected to represent a broad cross-section of contemporary tools, prioritizing those with high community adoption (measured by GitHub stars and citations), support for mathematical content extraction, and architectural diversity (including rule-based, OCR-dependent, and neural network-based parsers). In the revised manuscript, we will add a new subsection in the evaluation section that explicitly lists the selection criteria, the full list of evaluated parsers with their categories, and a brief rationale for inclusion to demonstrate representativeness. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical benchmark grounded in independent human validation and public releases

full rationale

The paper's central results derive from direct evaluation of 20+ parsers on 100 synthetic documents containing 2000+ formulas, using an LLM-as-a-judge metric that is separately validated against 750 independent human ratings (Pearson r=0.78 vs. r=0.34 for character matching). No equations, parameter fits, or derivations are present that reduce by construction to the paper's own inputs. The synthetic generation process and two-stage matching pipeline are described as controllable and robust but are not claimed to be derived from the evaluation outcomes themselves. Public code and data releases further allow external reproduction. No self-citation chains, uniqueness theorems, or ansatzes are invoked as load-bearing for the performance disparity claims. This is a standard empirical benchmarking study whose claims rest on observable outputs rather than self-referential definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework depends on the assumption that synthetic PDFs capture representative parsing challenges and that LLM judgments align with human semantic understanding of formulas.

axioms (1)
  • domain assumption Synthetically generated PDFs with controlled layouts and formulas adequately represent the parsing difficulties present in real-world academic PDFs.
    Invoked to justify generalization of benchmark results beyond the synthetic test set.

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