# 2D-TPE: Two-Dimensional Positional Encoding Enhances Table Understanding for Large Language Models

arXiv: https://arxiv.org/abs/2409.19700 · HTML: https://mlsanity.com/paper/2409.19700/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 69 references that are in the map.
- First posted on arXiv 29 Sep 2024.

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Compositional Semantic Parsing on Semi-Structured Tables](https://mlsanity.com/paper/1508.00305/) (2015)
- [TAPAS: Weakly Supervised Table Parsing via Pre-training](https://mlsanity.com/paper/2004.02349/) (2020)
- [Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation](https://mlsanity.com/paper/2010.16061/) (2020)
- [TaBERT: Pretraining for Joint Understanding of Textual and Tabular Data](https://mlsanity.com/paper/2005.08314/) (2020)
- [∞Bench: Extending Long Context Evaluation Beyond 100K Tokens](https://mlsanity.com/paper/2402.13718/) (2024)
- [MedAgents: Large Language Models as Collaborators for Zero-shot Medical Reasoning](https://mlsanity.com/paper/2311.10537/) (2023)
- [Unified-IO 2: Scaling Autoregressive Multimodal Models with Vision, Language, Audio, and Action](https://mlsanity.com/paper/2312.17172/) (2023)
- [ToTTo: A Controlled Table-To-Text Generation Dataset](https://mlsanity.com/paper/2004.14373/) (2020)
- [Binding Language Models in Symbolic Languages](https://mlsanity.com/paper/2210.02875/) (2022)
- [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)
- [FeTaQA: Free-form Table Question Answering](https://mlsanity.com/paper/2104.00369/) (2021)
- [TableLlama: Towards Open Large Generalist Models for Tables](https://mlsanity.com/paper/2311.09206/) (2023)
- [HiTab: A Hierarchical Table Dataset for Question Answering and Natural Language Generation](https://mlsanity.com/paper/2108.06712/) (2021)
- [Large Language Models are few(1)-shot Table Reasoners](https://mlsanity.com/paper/2210.06710/) (2022)
- [Table Meets LLM: Can Large Language Models Understand Structured Table Data? A Benchmark and Empirical Study](https://mlsanity.com/paper/2305.13062/) (2023)
- [TABBIE: Pretrained Representations of Tabular Data](https://mlsanity.com/paper/2105.02584/) (2021)
- [TUTA: Tree-based Transformers for Generally Structured Table Pre-training](https://mlsanity.com/paper/2010.12537/) (2020)
- [TableFormer: Robust Transformer Modeling for Table-Text Encoding](https://mlsanity.com/paper/2203.00274/) (2022)

## Built on by (most cited first, 3 of 3)

- [FormFactory: An Interactive Benchmarking Suite for Multimodal Form-Filling Agents](https://mlsanity.com/paper/2506.01520/) (2025)
- [How Do Language Models Understand Tables? A Mechanistic Analysis of Cell Location](https://mlsanity.com/paper/2602.08548/) (2026)
- [CRAFT: An Agentic Spreadsheet Form Filling System with Template Awareness](https://mlsanity.com/paper/2610.04437/) (2026)

## Abstract (arXiv)

Tables are ubiquitous across various domains for concisely representing structured information. Empowering large language models (LLMs) to reason over tabular data represents an actively explored direction. However, since typical LLMs only support one-dimensional~(1D) inputs, existing methods often flatten the two-dimensional~(2D) table structure into a sequence of tokens, which can severely disrupt the spatial relationships and result in an inevitable loss of vital contextual information. In this paper, we first empirically demonstrate the detrimental impact of such flattening operations on the performance of LLMs in capturing the spatial information of tables through two elaborate proxy tasks. Subsequently, we introduce a simple yet effective positional encoding method, termed ``2D-TPE'' (Two-Dimensional Table Positional Encoding), to address this challenge. 2D-TPE enables each attention head to dynamically select a permutation order of tokens within the context for attending to them, where each permutation represents a distinct traversal mode for the table, such as column-wise or row-wise traversal. 2D-TPE effectively mitigates the risk of losing essential spatial information while preserving computational efficiency, thus better preserving the table structure. Extensive experiments across five benchmarks demonstrate that 2D-TPE outperforms strong baselines, underscoring the importance of preserving the table structure for accurate table comprehension. Comprehensive analysis further reveals the substantially better scalability of 2D-TPE to large tables than baselines.