# Document-Level Tabular Numerical Cross-Checking: A Coarse-to-Fine Approach

arXiv: https://arxiv.org/abs/2506.13328 · HTML: https://mlsanity.com/paper/2506.13328/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 58 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 30 of 37)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [TabFact: A Large-scale Dataset for Table-based Fact Verification](https://mlsanity.com/paper/1909.02164/) (2019)
- [LLM2Vec: Large Language Models Are Secretly Powerful Text Encoders](https://mlsanity.com/paper/2404.05961/) (2024)
- [A Survey on Automated Fact-Checking](https://mlsanity.com/paper/2108.11896/) (2021)
- [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024)
- [StructGPT: A General Framework for Large Language Model to Reason over Structured Data](https://mlsanity.com/paper/2305.09645/) (2023)
- [Fake News Detection on Social Media: A Data Mining Perspective](https://mlsanity.com/paper/1708.01967/) (2017)
- [Fine-Tuning LLaMA for Multi-Stage Text Retrieval](https://mlsanity.com/paper/2310.08319/) (2023)
- [Generative Representational Instruction Tuning](https://mlsanity.com/paper/2402.09906/) (2024)
- [Chain-of-Table: Evolving Tables in the Reasoning Chain for Table Understanding](https://mlsanity.com/paper/2401.04398/) (2024)
- [Large Language Models are Versatile Decomposers: Decompose Evidence and Questions for Table-based Reasoning](https://mlsanity.com/paper/2301.13808/) (2023)
- [FEVEROUS: Fact Extraction and VERification Over Unstructured and Structured information](https://mlsanity.com/paper/2106.05707/) (2021)
- [TableLlama: Towards Open Large Generalist Models for Tables](https://mlsanity.com/paper/2311.09206/) (2023)
- [Table Meets LLM: Can Large Language Models Understand Structured Table Data? A Benchmark and Empirical Study](https://mlsanity.com/paper/2305.13062/) (2023)
- [In-context Pretraining: Language Modeling Beyond Document Boundaries](https://mlsanity.com/paper/2310.10638/) (2023)
- [Exploring the Numerical Reasoning Capabilities of Language Models: A Comprehensive Analysis on Tabular Data](https://mlsanity.com/paper/2311.02216/) (2023)
- [PromptReps: Prompting Large Language Models to Generate Dense and Sparse Representations for Zero-Shot Document Retrieval](https://mlsanity.com/paper/2404.18424/) (2024)

## Built on by (most cited first, 2 of 2)

- [Reasoning Pattern Matters: Learning to Reason without Human Rationales](https://mlsanity.com/paper/2510.12643/) (2025)
- [PaperFit: Vision-in-the-Loop Typesetting Optimization for Scientific Documents](https://mlsanity.com/paper/2605.10341/) (2026)

## Abstract (arXiv)

Numerical consistency across tables in disclosure documents is critical for ensuring accuracy, maintaining credibility, and avoiding reputational and economic risks. Automated tabular numerical cross-checking presents two significant challenges: (C1) managing the combinatorial explosion of candidate instances at the document level and (C2) comprehending multi-faceted numerical semantics. Previous research typically depends on heuristic-based filtering or simplified context extraction, often struggling to balance performance and efficiency. Recently, large language models (LLMs) have demonstrated remarkable contextual understanding capabilities that helps address C2 at the instance level, yet they remain hampered by computational inefficiency (C1) and limited domain expertise. This paper introduces CoFiTCheck, a novel LLM-based coarse-to-fine framework that addresses these challenges through two sequential stages: embedding-based filtering and discriminative classification. The embedding-based filtering stage introduces an instructional parallel encoding method to efficiently represent all numerical mentions in a table with LLMs, as well as a decoupled InfoNCE objective to mitigate the isolated mention problem. The discriminative classification stage employs a specialized LLM for fine-grained analysis of the remaining candidate pairs. This stage is further enhanced by our crosstable numerical alignment pretraining paradigm, which leverages weak supervision from cross-table numerical equality relationships to enrich task-specific priors without requiring manual annotation. Comprehensive evaluation across three types of real-world disclosure documents demonstrates that CoFiTCheck significantly outperforms previous methods while maintaining practical efficiency.