Piece of Table: A Divide-and-Conquer Approach for Selecting Subtables in Table Question Answering

TL;DR

PieTa addresses the difficulty of applying language models to 2D tables under token-length constraints by iteratively partitioning tables into windows, selecting relevant cells per window, and uniting them to form subtables. This multi-resolution divide-and-conquer approach preserves cross-row/column dependencies while avoiding long-context inputs. The authors introduce a coordinate-based subtable representation, fine-tune a dedicated selector, and demonstrate substantial improvements on WikiTQ and WikiSQL across multiple readers, with subtables averaging about 13.9% of the original size. The work provides a flexible, robust subtable-based QA paradigm that can be integrated with various readers and extended to SQL-based retrieval, offering practical gains for large, real-world tables.

Abstract

Applying language models (LMs) to tables is challenging due to the inherent structural differences between two-dimensional tables and one-dimensional text for which the LMs were originally designed. Furthermore, when applying linearized tables to LMs, the maximum token lengths often imposed in self-attention calculations make it difficult to comprehensively understand the context spread across large tables. To address these challenges, we present PieTa (Piece of Table), a new framework for subtable-based question answering (QA). PieTa operates through an iterative process of dividing tables into smaller windows, using LMs to select relevant cells within each window, and merging these cells into a subtable. This multi-resolution approach captures dependencies across multiple rows and columns while avoiding the limitations caused by long context inputs. Instantiated as a simple iterative subtable union algorithm, PieTa demonstrates improved performance over previous subtable-based QA approaches.

Figures (8)

• Figure 1: An overview of the proposed PieTa (Piece of Table) framework. Starting with an input table and a question, our algorithm synthesizes a subtable by iteratively dividing the table into smaller windows, using language models to select relevant cells within these windows (forming intermediate subtables), and merging these until the final subtable is constructed. Code will be made publicly available upon acceptance.
• Figure 2: Examples of generated training data with an window size of $w=4$. The table and the question are sourced from the WikiSQL training dataset ZXS17. Three conditions and their corresponding cell values are color-coded in green. The three example input windows $\{W_i\}_{i=1}^3$, arranged in raster order, are highlighted with orange boxes, while the corresponding training targets $\{V_i\}_{i=1}^3$ are shown on the right.
• Figure 3: Examples of subtable representations ($w=3$). The information matching the condition Total is located in a cell rather than the column header. Both the index and table representations fail to select the cell Total because the column Description Losses is not selected. The proposed coordinate representation overcomes this limitation by preserving the input window structure and relevant cell contents.
• Figure 4: Examples of (sub)tables and the corresponding QA results. The original table has two condition columns (Fuel and Years produced) and one answer column Engine, which respectively match the conditions and expected outcomes presented in the question. Two conditions and the corresponding cell values are color-coded. The union table consists of rows satisfying at least one condition, while the underlying gold table consists of rows satisfying all conditions. Estimating the gold table is challenging as it requires a comprehensive understanding of the entire input table. The answers below the respective tables are the corresponding outputs of the TaPEx reader. Feeding the original complete table leads to incorrect results, while both the gold and union table produce correct answers.
• Figure 5: Table QA performance (EM; %) across varying table sizes (number of cells) on WikiTQ (top) and WikiSQL (bottom).