Technical Summary: Orthogonal Hierarchical Decomposition for Structure-Aware Table Understanding with Large Language Models

1. Problem Statement

Complex tables found in scientific reports, financial statements, and business intelligence often deviate from the canonical $N \times M$ grid. These structures present two primary challenges for Large Language Models (LLMs):

1. Structural Hierarchy: Multi-level nested headers require data cells to be semantically traced back through chains of ancestral labels. Without this context, isolated entries (e.g., "other cities") are ambiguous.
2. Spatial-Logical Discontinuity: Irregularly merged cells and offset headers break standard grid indexing. Spatial proximity no longer guarantees logical association, causing traditional coordinate-based scanning to fail (e.g., misinterpreting a "details" row as a child of a "year" column due to vertical alignment).

Existing approaches typically rely on flat linearization (losing hierarchical dependencies), programmatic modeling (struggling with non-canonical layouts), or logical topology reconstruction (often relying on geometry-based heuristics that ignore semantic nuances). These methods frequently result in structural collapse or misalignment between structural semantics and textual representations.

2. Methodology: Orthogonal Hierarchical Decomposition (OHD)

The authors propose the Orthogonal Hierarchical Decomposition (OHD) framework, which shifts the paradigm from global grid modeling to decomposing tables into independent, semantically synchronized hierarchical structures. The pipeline consists of three core stages:

A. Orthogonal Tree Induction (OTI)

The core algorithm factorizes a table into two independent trees: a Column Tree ($T_{col}$) and a Row Tree ($T_{row}$). This decoupling isolates structural noise and handles irregular layouts by reconstructing the logical hierarchy of each dimension separately. The induction is guided by Semantic-Spatial Synergy:

• Semantic Agency: In $T_{col}$, only column headers act as internal branching nodes; row headers and data cells are treated as atomic leaf nodes. The roles are reversed for $T_{row}$.
• Semantic-Spatial Subsumption: An edge between a parent and child is established only if the child is spatially contained within the parent's bounding box and a Large Language Model (LLM) confirms a logical subsumption (e.g., category inheritance). This acts as a neural-symbolic bridge to correct geometric ambiguities.
• Structural Unidirectionality: Data cells are terminal nodes with no downward branching, preventing spurious nesting of footnotes or remarks under numerical values.
• Adaptive Data Anchoring: To resolve conflicts where data cells lie on overlapping boundaries of conflicting headers, the framework uses row-boundary constraints to adaptively assign the correct parent header.

B. Dual-Pathway Association

Once $T_{col}$ and $T_{row}$ are induced, the framework reconstructs the semantic lineage of each cell using a dual-pathway protocol. For any data cell $d$:

1. Premise Context: A depth-first search (DFS) on the primary tree (e.g., $T_{col}$) generates the path of headers leading to $d$.
2. Attribute Context: A bottom-up traversal of the orthogonal tree (e.g., $T_{row}$) captures the structural attributes. The framework queries the primary tree to find corresponding headers in the opposite dimension, interleaving these paths to recover multi-dimensional coordinates.
3. Synthesis: The final representation follows a "Premise Context $\to$ Attribute Context $\to$ Value" structure, symmetrically reconstructing the lineage from both perspectives.

C. Semantic Arbitration

Recognizing that $T_{col}$ and $T_{row}$ offer complementary views, an LLM acts as a semantic arbitrator. It evaluates the synthesized candidate sequences based on logical cohesion, information completeness, and syntactic readability. Using a zero-shot prompt, the LLM selects the clearest perspective or blends them to produce a high-fidelity, structure-aware textual surrogate ready for downstream reasoning.

3. Key Contributions

• OHD Framework: A novel paradigm that decomposes complex tables into orthogonal hierarchical trees, effectively mitigating structural collapse in non-standard layouts.
• Orthogonal Tree Induction (OTI): An algorithm incorporating spatial-semantic co-constraints to determine logical relationships, significantly improving robustness against flexible headers and merged cells.
• Dual-Pathway Association: A protocol that reconstructs multi-layered semantic lineages, enabling LLMs to perform faithful reasoning on heterogeneous structures by preserving both vertical and horizontal dependencies.

4. Experimental Results

The framework was evaluated on two complex table QA benchmarks: AITQA (financial/statistical tables) and HiTab (hierarchical tables requiring multi-hop reasoning).

• Performance: OHD consistently outperformed state-of-the-art baselines (including Chain-of-Table, E5, and ST-RAPTOR) across multiple LLM backbones (Qwen2-72B, TableLLaMA-7B, DeepSeek-V3).
  • On AITQA with Qwen2-72B, OHD achieved an Exact Match (EM) of 69.34, surpassing the strongest baseline (ST-RAPTOR) by 8.76 points.
  • On the HiTab Subset, OHD achieved an EM of 64.74, a 9.01 point improvement over the baseline.
  • The LLM Eval Avg. (semantic accuracy) showed even more significant gains, with OHD reaching 89.12 on AITQA (+18.09 over ST-RAPTOR).
• Ablation Studies:
  • Removing semantic constraints ($w/o\ C_{semantic}$) caused a performance drop of ~6%, confirming the necessity of LLM-driven semantic validation.
  • Removing one of the orthogonal pathways ($w/o\ TP$) led to drastic drops (up to 20% on AITQA), validating the need for dual-axis reconstruction.
  • Replacing the dual-pathway representation with standard Markdown/HTML linearization resulted in losses of over 10% in EM, proving the superiority of hierarchical path representation.
• Robustness: OHD demonstrated superior resilience as table scale increased. While baselines like Chain-of-Table saw performance drop by 19 points when moving from small to large tables, OHD's decline was marginal (7 points).

5. Significance and Claims

The paper claims that OHD successfully bridges the gap between complex two-dimensional table topologies and the linear reasoning capabilities of LLMs. By transforming fragile physical layouts into robust, structure-aware semantic lineages, the framework addresses the persistent challenge of understanding tables with multi-level headers and merged cells.

The authors emphasize that the dual-path lineage representation is the key driver of performance, effectively preventing the structural collapse common in traditional representations. They position OHD not as a replacement for LLMs, but as a "plug-and-play" architecture that complements and amplifies the reasoning capabilities of modern models. The work suggests that orthogonal decomposition provides a promising direction for achieving granular and reliable table understanding in diverse real-world applications, with future work planned to extend the framework to ultra-large-scale financial reports and integrate multimodal signals.