Component-Correlation Tree (CCTree) in MoDora

• Component-Correlation Tree (CCTree) is a hierarchical model that organizes OCR-derived document components by capturing layout-specific distinctions and semantic correlations.
• It leverages local-alignment aggregation and MLLM-based hierarchical title detection to separate main content from supplementary elements like sidebars and footers.
• Empirical results demonstrate that CCTree significantly enhances question answering and retrieval accuracy by effectively summarizing and indexing document structures.

Component-Correlation Tree (CCTree) is the structural representation introduced in MoDora for semi-structured document analysis. In that formulation, CCTree hierarchically organizes layout-aware document components derived from OCR output, and explicitly models inter-component relations and layout distinctions across text, tables, charts, images, and supplementary material. The representation is motivated by the claim that prior methods are often too flat, too page-centric, or too text-centric to capture cross-block hierarchies, inter-section organization, and layout-specific distinctions such as separating main body content from sidebars or footers (Xu et al., 26 Feb 2026).

1. Definition and problem setting

In MoDora, CCTree is defined as a hierarchical tree in which each node corresponds to a semantically coherent document component, and the tree edges encode the correlations among components. It is introduced for semi-structured documents that contain diverse interleaved elements, including tables, charts, and hierarchical paragraphs, arranged in irregular layouts. The representation is intended to preserve both semantic organization and layout-aware relations after OCR parsing, rather than treating the document as a flat text sequence or as isolated pages (Xu et al., 26 Feb 2026).

The motivating problem has three parts. First, OCR output is described as fragmented and detached from semantic context. Second, existing representations are said not to capture hierarchical structures or layout distinctions. Third, question answering often requires evidence scattered across different regions, pages, and modalities. CCTree is designed especially to address the second and third issues by turning extracted components into a document-level hierarchy that can support retrieval and answer generation (Xu et al., 26 Feb 2026).

The exact term “Component-Correlation Tree” is specific to MoDora. Earlier literature contains related ideas about tree-structured dependence, tree-organized correlations, and tree comparison, but not the same formal object. This distinction is important because the MoDora CCTree is a document-structure representation rather than a generic name for all tree-based correlation models.

2. Construction from components

CCTree is built on top of local-alignment aggregation and type-specific extraction. The preprocessing stage first groups OCR-parsed elements into components. Textual aggregation assigns a title plus its following paragraphs until the next title to one component. Table, chart, and image aggregation groups a visual element with its title if the title is before or after it; if no title exists, a default title is assigned. Supplement aggregation treats headers, footers, page numbers, sidebars, and related elements as independent components per page (Xu et al., 26 Feb 2026).

Two enrichment steps are then applied before tree construction. Hierarchical title detection uses an MLLM, exemplified by GPT-5, prompted with title text plus cropped title images to infer the title level represented with # symbols. Template-based information enrichment for non-text components produces the triplet

$$\mathcal{T}(CO)=\big(title(CO), metadata(CO), data(CO)\big),$$

with prompts tailored to tables, charts, or images so that titles, metadata, and detailed content are extracted (Xu et al., 26 Feb 2026).

Each node $v \in \mathcal{V}$ stores the component itself, a unique node index $v_{index}$, and child pointers $v_{child}$. The tree therefore functions both as a hierarchy and as a structured index over semantically meaningful units.

CCTree uses three edge types.

Edge type	Definition	Role
Text-to-text	$$\mathcal{E}_1 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_1\}$$	Nested title hierarchy
Text-to-other	$$\mathcal{E}_2 = \{(CO_i,CO_j)\mid CO_i \subset A_1, CO_j\subset A_2\}$$	Attach adjacent tables, charts, or other non-text components
Independent supplementary	$$\mathcal{E}_3 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_3\}$$	Separate headers, footers, sidebars, and page numbers from main content

Construction proceeds in two stages. The main branch is built from main-content components using reading order, element type, and title hierarchy. The procedure initializes a root node with title level 0, pushes it on a stack, processes components in reading order, pops until the stack top has a higher title level than the current text component, then attaches the current node as a child and pushes it; non-text components are attached directly as children of the current top node. Supplementary components are then attached to a dedicated branch under a virtual root and grouped by type, including header, footer, sidebar, and number. The overall construction first separates components into $L_1$ for main content and $L_2$ for supplementary content, constructs the two branches, and attaches both under the virtual root (Xu et al., 26 Feb 2026).

A central design decision is that main-content reasoning is kept separate from peripheral page artifacts. This prevents headers, footers, and similar elements from interfering with the main semantic branch.

3. Bottom-up summarization and retrieval behavior

After construction, CCTree undergoes bottom-up metadata summarization. The stated purpose is to ensure that higher-level nodes reflect the content of their subtrees, rather than containing only their own local contents. Leaf nodes invoke an LLM to generate a few nominal phrases summarizing their content. For internal nodes, metadata generation incorporates metadata from all children, so the representation becomes progressively more abstract toward the root (Xu et al., 26 Feb 2026).

The number of summaries for node $v_i$ is defined as

$v \in \mathcal{V}$0

where $v \in \mathcal{V}$1 is the maximum depth of the tree containing $v \in \mathcal{V}$2, $v \in \mathcal{V}$3 is the depth of $v \in \mathcal{V}$4, $v \in \mathcal{V}$5 is the total number of summaries generated by the children of $v \in \mathcal{V}$6, and $v \in \mathcal{V}$7 controls the growth rate. The factor

$v \in \mathcal{V}$8

is called the information attenuation coefficient. The intended effect is to reduce summarized detail as information propagates upward, thereby avoiding redundancy while retaining key content. The paper gives the example that if a parent node aggregates 12 child summaries, it may generate 7 summaries after attenuation. For non-text leaf nodes, metadata produced during template-based enrichment is reused directly, avoiding redundant LLM calls (Xu et al., 26 Feb 2026).

CCTree is then used by question-type-aware retrieval. For location questions, each node carries spatial metadata, the page is divided into a $v \in \mathcal{V}$9 grid, and question cues are mapped to grid regions so that overlapping nodes can be selected. For semantic questions, retrieval proceeds in two phases. In forward search, the LLM receives the question plus child-node indices and metadata, selects candidate nodes, and unselected nodes are passed to fallback embedding retrieval. In backward verification, an MLLM checks actual node content and cropped regions to remove false positives. Retrieved evidence is returned as $v_{index}$0 and $v_{index}$1 pairs, which are then combined with the tree index schema for final answer generation (Xu et al., 26 Feb 2026).

This coupling of hierarchy, summarization, and retrieval is a defining feature of the MoDora CCTree. The tree is not merely a storage structure; it is the navigation backbone for both semantic and location-aware reasoning.

4. Empirical profile, implementation, and limitations

MoDora reports that it outperforms baselines by 5.97%-61.07% in accuracy, and the paper attributes a substantial part of this behavior to CCTree and the component-construction pipeline (Xu et al., 26 Feb 2026).

The most direct ablation removes tree structure. In Table 8, the full model scores 83.70 on DUDE and 73.33 on MMDA, whereas the variant without tree structure scores 68.37 on DUDE and 57.84 on MMDA. The paper also reports a stronger degradation for the variant without component construction, which scores 55.96 on DUDE and 36.24 on MMDA. A variant without forward search retains the tree but disables LLM-guided traversal, scoring 78.35 on DUDE and 70.89 on MMDA. These results are used to argue that explicit hierarchical modeling and meaningful component formation are both necessary (Xu et al., 26 Feb 2026).

On question types, MoDora reports 76.73 for hierarchy questions, 79.95 for text, 68.00 for hybrid, and 68.21 for location. The hierarchy result is specifically cited as evidence for the effectiveness of CCTree’s structural modeling. Tree statistics further motivate the representation: DUDE has an average tree of 17.2 nodes, 12.6 leaves, 3.36 levels, while MMDA has 49.2 nodes, 37.7 leaves, 4.23 levels. Manual inspection reports that selector plus embedding search recalls 91% of required evidence, the verifier filters 84% of irrelevant nodes, and the verifier excludes 12% of necessary evidence (Xu et al., 26 Feb 2026).

Implementation details are explicit. The system uses PaddleOCR for OCR parsing, Qwen3-Embedding-8B for embeddings, Qwen2.5-VL-7B-Instruct for simpler local steps, and GPT-5 for harder tasks such as hierarchy detection, question parsing, and final answer generation. Summarization uses $v_{index}$2 and $v_{index}$3, retrieval uses 3 chunks/pages, and the system runs on a workstation with CPUs and 8 NVIDIA RTX 4090 GPUs (Xu et al., 26 Feb 2026).

The paper also identifies several limitations. Tree construction can suffer from OCR errors or hierarchy-detection mistakes; imperfect tree construction accounts for about 20% of observed analysis errors. Visual enrichment can produce hallucinations in about 3% of outputs. The verifier may exclude some necessary evidence. Future directions named in the paper include native PDF structure, typographic cues, multi-document forests, and more dynamic traversal such as backtracking or query-driven skipping (Xu et al., 26 Feb 2026).

5. Probabilistic and statistical precursors

A broader mathematical lineage for the phrase’s components appears in earlier work on tree-structured dependence. In “Tree-dependent Component Analysis,” the observed vector $v_{index}$4 is assumed to satisfy

$v_{index}$5

and the objective is no longer to make the latent components independent, but to make them well modeled by a tree-structured graphical model $v_{index}$6. The semiparametric contrast is

$v_{index}$7

which generalizes the ICA objective based on multivariate mutual information. In this formulation, ICA is recovered as the special case where the tree has no edges, while Chow–Liu is recovered when the transform is fixed and only the tree varies (Bach et al., 2012).

That framework has a “component-correlation tree” flavor in the sense that transformed coordinates are sought whose remaining dependencies are simple and pairwise-tree-like. The paper further proposes a KDE approximation,

$v_{index}$8

and a kernel generalized variance approximation,

$v_{index}$9

together with alternating optimization over $v_{child}$0 and $v_{child}$1 (Bach et al., 2012).

Another precursor appears in the construction of tree-based dependence structures on the discrete hypercube $v_{child}$2. There, nodes $v_{child}$3 form a binary tree, independent variables $v_{child}$4 are placed on tree nodes, and the vector $v_{child}$5 is defined by

$v_{child}$6

The covariance structure obeys

$v_{child}$7

and Möbius inversion is used to recover node variances from the covariance matrix. The paper states that, in this framework, the analogue of a Component-Correlation Tree is a binary tree on $v_{child}$8 whose nodes represent shared dependence blocks (Kızıldemir et al., 2015).

These works do not define the MoDora CCTree, but they show that tree-structured organization of components and pairwise dependence has an established statistical background.

6. Related but distinct uses of tree correlation

Several later works use tree structure together with correlation, but in senses different from MoDora’s document-level CCTree. RETCO, for example, is a correlation-aware tree methodology for correlated data. Its predictor has the form

$v_{child}$9

and tree fitting is modified so that split criteria, stopping rules, and leaf estimates account for the correlation structure. RETCO uses correlation-aware objectives such as

$$\mathcal{E}_1 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_1\}$$0

a generalized AIC, and

$$\mathcal{E}_1 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_1\}$$1

This is a “tree for correlated data,” but not a document component hierarchy (Rabinowicz et al., 2021).

In recursive partition analysis, trees have also been compared and combined through distances and correlations in a vector subspace of recursive partition functions. There, a tree is treated as a function on a domain, affine combinations are defined by aligning partitions recursively, and tree correlation is written as

$$\mathcal{E}_1 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_1\}$$2

The same paper defines norms, distances, and forest distances after constructing a common partition refinement. This usage concerns functional comparison of trees rather than organization of document components (Skwerer et al., 2015).

A further distinct line studies tree-shaped datasets directly. The statistic TD $$\mathcal{E}_1 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_1\}$$3 measures correlation between two tree-shaped datasets by the included angle $$\mathcal{E}_1 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_1\}$$4 between tangent lines to a quantile ellipse. In the Gaussian setting, $$\mathcal{E}_1 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_1\}$$5 is a decreasing function of the correlation parameter, so smaller $$\mathcal{E}_1 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_1\}$$6 indicates stronger tree correlation. The method is explicitly not called CCTree in that paper (Mao et al., 2023).

A common misconception is therefore to treat all “tree-correlation” methods as instances of the same framework. The literature instead contains several different constructions: document-component hierarchies for question answering, latent tree dependence models for transformed variables, dependence trees on $$\mathcal{E}_1 = \{(CO_i,CO_j)\mid CO_i,CO_j \subset A_1\}$$7 for covariance and supermodular ordering, correlation-aware regression trees, recursive-partition comparison methods, and geometric statistics for tree-shaped data. The MoDora CCTree is specific to semi-structured document analysis and is best understood within that narrower, explicitly defined setting (Xu et al., 26 Feb 2026).