Domain Question Maps (DQMs)

• Domain Question Maps (DQMs) are formal structures that represent domain-specific questions and their hierarchical, pedagogically aligned relationships.
• They are generated using fine-tuned language models and a specificity classifier, with weighted edges pruned by a maximum spanning tree to ensure an acyclic, coherent structure.
• DQMs enable personalized learning and enhanced reasoning by decomposing complex problems into manageable sub-questions, as demonstrated in educational and quantitative domains.

A Domain Question Map (DQM) is a formal structure representing a network of domain-specific questions and their hierarchical relationships, directly aligned with learning or reasoning objectives. In contrast to traditional concept maps, which use abstract nodes to capture disciplinary concepts and their relations, DQMs make use of concrete, generated questions as nodes, each closely tied to an underlying segment of instructional or domain material. Recent advances leverage DQMs for systematic knowledge representation, adaptive learning, and improved domain-specific question answering, with demonstrated efficacy in educational and expert quantitative reasoning contexts (Noh et al., 11 Jan 2026, &&&1&&&).

1. Formal Definition and Conceptual Distinction

A DQM is a directed graph $G = (Q, E)$, where

• $Q = \{q_1, \dots, q_N\}$ is a set of auto-generated domain-relevant questions,
• $E \subseteq Q \times Q$ contains labeled, directed edges denoting hierarchical or logical relationships.

Each node $q_i$ corresponds to a question derived from a well-defined segment of source material (e.g., a textbook chunk, a problem statement) and is explicitly aligned with a pedagogical or task-driven objective. The edges $r_{ij}$ between nodes are typed as “general” or “specific” (i.e., $r_{ij} \in \{\text{general}, \text{specific}\}$), denoting their hierarchical placement, or omitted if no such relationship exists.

Key distinctions from concept maps include:

• Node granularity: DQM nodes are concrete educational or domain-specific questions rather than abstract concepts.
• Pedagogical alignment: Each node serves simultaneously as an assessment prompt and a learning target.
• Adaptive sequencing: The hierarchical, directed structure naturally supports sequencing for adaptive learning, quiz generation, or reasoning progression (Noh et al., 11 Jan 2026, Wang et al., 1 Oct 2025).

2. Mathematical Models and Algorithmic Frameworks

DQMs are constructed and operationalized through several formal components and algorithms:

Question Generation (QG)

Fine-tuned pre-trained LLMs (PLMs) such as BART-large, Pegasus-large, T5-Large-SQuAD-QG (encoder–decoder), and GPT-2/GPT-O4-mini (decoder-only), are used to generate question $q_i$ from each input chunk $c_i$. The generator is trained via cross-entropy loss on large QA datasets (KhanQ, SQuAD 2.0), optimizing $P(q_i | c_i)$.

Specificity-Relationship Classification

A classifier $\Phi$ predicts the edge label $r_{ij}$ given question pair $(q_i, q_j)$ and their source contexts:

$$\Phi(q_i, q_j, c_i, c_j) = r_{ij} \in \{\text{general}, \text{specific}, \text{other}\}$$

A confidence score $$\eta_{ij} = 1 - \text{softmax}(P(r_{ij} = \text{other})) \in [0, 1]$$ quantifies certainty in the hierarchical (“general/specific”) label (Noh et al., 11 Jan 2026).

Edge Weighting and MaxST Pruning

Semantic similarity $\xi_{ij}$ is computed using a sentence embedding model (Sentence-BERT), and edge weights are combined:

$$w_{ij} = \lambda \cdot \eta_{ij} + (1 - \lambda) \cdot \xi_{ij}$$

The edge weights $w_{ij}$ are then used in constructing a cycle-free Maximum Spanning Tree (MaxST), ensuring an acyclic, optimally cohesive hierarchy (Noh et al., 11 Jan 2026).

Decomposition Mapping for Domain QA

In expert quantitative domains, a DQM is viewed as a mapping $M: Q \rightarrow \{q_1, \ldots, q_n\}$, decomposing complex $Q$ into pivotal sub-questions whose answers resolve $Q$ when input together to a downstream QA model. This mapping $f_\theta$ is learned via fine-tuning and reward-driven policy optimization (Wang et al., 1 Oct 2025).

3. Construction Methodologies

For Educational Content (Noh et al., 11 Jan 2026)

1. Preprocessing: Source documents undergo OCR and format conversion, followed by semantically coherent text-chunking. Section IDs are hierarchically assigned to each chunk.
2. Question Generation: For each chunk $c_i$, a fine-tuned QG PLM generates $q_i$. The generative quality is assessed using BLEU, ROUGE-L, BLEURT, and BERTScore.
3. Relation Extraction: Question pairs are labeled using their section hierarchy (parent–child vs. non-hierarchical) and a GPT-2-Medium classifier is trained to predict $r_{ij}$.
4. Graph Assembly: A directed graph is built over all $q_i$, edges weighted and pruned using MaxST and node merging, producing a tree-structured, cycle-free DQM.

For Domain Quantitative Reasoning (Wang et al., 1 Oct 2025)

1. Step 1: Fine-tune a base PLM (Llama 3.1-8B-Instruct with LoRA) on expert-labeled question decompositions from specialized domains (e.g. ConvFinQA for finance).
2. Step 2: Reward-guided refinement: Use Proximal Policy Optimization (PPO) to maximize a reward function $r$ based on whether decomposed sub-questions boost downstream QA answer correctness, with reward values in $\{+2, +1, -1, -2\}$.
3. Inference: Given a test question $Q$, generate one or two sub-questions, merge with context and original $Q$, and apply to a QA model for final answer inference.

4. Hierarchy, Learning Objectives, and Structural Implications

DQMs encode scaffolding in learning or reasoning:

• Hierarchy: “General” questions target lower-order thinking (recall, comprehension), while “specific” questions focus on higher-order skills (analysis, application).
• Structural mapping: DQMs mirror the depth and progression of underlying curriculum structures or task decompositions, facilitating personalized progression and reinforcement.
• Learning Pathways: The MaxST-pruned DQM enables efficient, context-sensitive navigation from domain overviews to fine-grained details. Learners can be routed from specific failures back to general nodes, enabling adaptive remediation (Noh et al., 11 Jan 2026).

5. Evaluation Protocols and Quantitative Results

Educational DQMs (Noh et al., 11 Jan 2026)

• QG Performance: Encoder–decoder models (e.g., T5-Large-SQuAD-QG) achieve BLEU 0.263, ROUGE-L 0.534, BLEURT 0.538, BERTScore 0.937 on SQuAD.
• Specificity Classification: GPT-2 Medium classifier macro-averaged F1 = 0.899, with per-class (general/specific/other) F1s of 0.96, 0.90, 0.84, respectively.
• Map Construction: Initial graph (1,071 nodes) pruned to 300 nodes, yielding coherent, fully reachable, acyclic DQMs with clear learning paths.

Domain QA Decomposition (Wang et al., 1 Oct 2025)

• Benchmarks: Across FinQA, TAT-QA, ECTQA, EDTQA datasets, exact-match accuracy (EmAcc) gains for EQD-based DQM over direct QA ranged from +0.6% to +10.5%, with maximum gains in weaker QA models or more arithmetic-intensive tasks.

6. Illustrative Examples and Map Interpretability

Mini-DQM Path in Educational Context (Noh et al., 11 Jan 2026)

Level	Question Node	Type
Q1	What is the term for a query that is periodically executed on a collection to which new documents are incrementally added?	general
Q2	What is a common heuristic approach that web crawlers use to insert delays between successive fetch requests to the same host?	specific
Q3	What is the primary case of a statistical ranked retrieval model that supports structured query operators?	more specific
Q4	What was the relevance feedback mechanism introduced by Salton’s SMART system around 1970?	deeper specific
Q5	Which measures are best suited to compare the quality of the two clusterings?	lateral
Q6	What is the number of bits needed to transmit class memberships assuming cluster memberships are known?	detailed leaf

A path from Q1 to Q6 demonstrates ordered progression from general system-level inquiry to information-theoretic evaluation techniques.

Decomposition Example in Financial QA (Wang et al., 1 Oct 2025)

• Original Question: What is the growth rate in the balance of standby letters of credit from 2006 to 2007?
• EQD-generated Sub-question: What is the balance of standby letters of credit in 2006 and 2007?
• Resolution: Extract values, compute growth rate, and answer original Q.

7. Applications and Implications

DQMs enable:

• Personalized learning: Each learner’s mastery is modeled at the question node level, supporting adaptive sequence selection and remediation (e.g., via knowledge tracing).
• Efficient reasoning: Decomposition into sub-questions allows domain-specific QA models to focus on tractable sub-tasks, improving performance and transparency.
• Automated assessment design: All nodes are both learning objectives and assessment prompts, streamlining construction of quizzes aligned to curricular goals or reasoning steps.

A plausible implication is that DQMs, by enforcing both granularity and hierarchy in question representation, can systematize the development of scalable, adaptive instructional and reasoning systems across diverse domains (Noh et al., 11 Jan 2026, Wang et al., 1 Oct 2025).