Semantic-Level Internal Reasoning Graph

• Semantic-level internal reasoning graphs are explicit directed graphs that map LLM reasoning processes with semantically coherent nodes and causal edges.
• They employ advanced segmentation, edge inference, and annotation techniques to enhance model interpretability and verification in tasks like QA and fact-checking.
• Integrating these graphs into LLM pipelines improves explainability and robust reasoning, supporting applications in medical QA, autonomous planning, and fact verification.

A semantic-level internal reasoning graph is a structured, interpretable representation that formalizes the sequence and dependencies of reasoning steps—typically generated by a LLM—as an explicit directed (multi-)graph. Nodes correspond to semantically coherent steps, entities, or concepts, and edges model logical, causal, or structural relationships among them. These graphs provide a substrate for aligning, verifying, enhancing, or analyzing the internal cognitive processes of LLMs, as well as for integrating external knowledge into model-driven or retrieval-augmented reasoning. Across diverse architectures, tasks, and domains, semantic-level reasoning graphs have become a cornerstone for explainable, faithful, and robust complex reasoning in current LLM-centric AI systems.

1. Formal Definitions and Representational Schemes

Semantic-level internal reasoning graphs exhibit several structural variants depending on the target application. At the core, a reasoning graph is a directed, labeled graph $G = (V, E, \tau_V, \tau_E)$, where $V$ denotes a set of nodes (semantic units, concepts, reasoning steps), $E \subseteq V \times R \times V$ is a set of edges each carrying a relation $r$ from a fixed set $R$, and $\tau_V, \tau_E$ assign node and edge types, respectively. In QA and fact-checking, nodes may be argument phrases, predicates, or full sentences, enriched with types such as "Disease", "Gene", "Plan", or "Reasoning"; edges encode relations like "CAUSE", "Premise-Conclusion", or "parent-of" (Luo et al., 24 Jan 2025, Zheng et al., 2020, Xiong et al., 20 May 2025, Han et al., 14 Jan 2025). For complex trace analysis, graphs may also annotate nodes with semantic roles (e.g., Context, Planning, Fact, Reflection) and edges with fine-grained labels such as "Support", "Refute", "Plan-Step", enforcing acyclicity and temporal/logic orderings (Lee et al., 3 Jun 2025).

For knowledge-centric tasks (e.g., RAG, science QA, clinical reasoning), graphs may reference external or constructed knowledge graphs as subgraphs, filtered for causal strength or semantic relevance (Luo et al., 24 Jan 2025, Luo et al., 29 Sep 2025). In mathematical reasoning or logic tasks, graphs often encode operator structure and inference dependencies over variables and propositions, with nodes classified as "number", "operator", or "proposition", connected according to computation steps or deductive reference chains (Lin et al., 2024).

2. Construction Methodologies

Constructing a semantic-level reasoning graph involves several procedural stages:

• Segmentation and Node Creation: Raw reasoning traces or corpora (CoT, context, answer fragments) are segmented into spans by delimiters or LLM-guided clustering algorithms. Spans are aggregated into semantically coherent steps or entities, possibly using semantic affinity scores or role labeling (SRL, AMR, custom classifiers) (Xiong et al., 20 May 2025, Zheng et al., 2020, Xu et al., 2021).
• Edge Inference: Edges are inferred via explicit parsing—e.g., mapping an equation "a + b = c" to edges $(a, +), (b, +), (+, c)$—or via LLM-based adjudication, as in the adaptive semantic edge construction using rejection sampling and relationship prompts (Xiong et al., 20 May 2025). For causality, filtering by a learned or hand-crafted $f(r)$ yields subgraphs expressing only relationships above a threshold $\theta$ (Luo et al., 24 Jan 2025).
• Annotation and Weighting: Nodes and edges may be annotated with types (entity, event, logical role), attributes (CUI, semantic type, confidence), and computed weights (e.g., average attribution, frequency across reasoning paths, causal strength), which inform subsequent retrieval, scoring, or verification (Hu et al., 6 Jan 2026, Cao, 2023).
• Combining Automated and Iterative LLM Parsing: Some frameworks, notably "Reasoning with Graphs," utilize iterative prompt cycles: initial extraction of triples/entities, LLM critique and graph repair over multiple passes, ensuring all relations needed for question answering are discovered (Han et al., 14 Jan 2025).

The construction process may also involve semantic aggregation of token-level attributions (e.g., via LRP, AttnLRP) up to the fragment or sentence level to yield a dependency graph faithful to the LLM's own computation (Hu et al., 6 Jan 2026).

3. Integration with LLMs and Reasoning Pipelines

Semantic-level reasoning graphs play diverse roles in LLM-centric pipelines:

• Chain-of-Thought (CoT) Alignment: By segmenting LLM-generated chains into reasoning steps and parsing them into graphs, retrieval or scoring can be explicitly synchronized with the evolution of the model's thought process. Structural retrieval over stepwise causal subgraphs ensures that evidence and reasoning paths are tightly coupled to the generated rationale (Luo et al., 24 Jan 2025, Xiong et al., 20 May 2025).
• Retrieval-Augmented Generation (RAG) Enhancement: By filtering knowledge graphs to retain only semantically or causally high-confidence relations, retrieval is made both more interpretable and more aligned with the reasoning required by the user query. Rationales can then reference explicit subgraphs, improving faithfulness and interpretability (Luo et al., 24 Jan 2025, Luo et al., 29 Sep 2025).
• Exemplar Retrieval and Reranking: In in-context learning, semantic-level graphs enable not only semantic but also structural alignment between the current query and candidate exemplars. R-convolution kernels or Weisfeiler–Lehman subtree kernels are used to measure graph similarity, and combined semantic-structural similarity drives reranking or selection of in-context examples (Lin et al., 2024).
• Verification and Consistency Checking: By aggregating reasoning steps across multiple candidate solutions, a combined reasoning graph supports GNN-based verification—selecting answers whose supporting paths are most structurally and semantically consistent (Cao, 2023).

Most integration strategies retain modularity: graphs are constructed or updated as external objects, often with no further LLM fine-tuning. Reasoning steps, supporting evidence, or prompt augmentations are generated via coordinated modules (filtering, construction, LLM completion), occasionally involving consistency checks or graph-guided pruning (Luo et al., 24 Jan 2025, Han et al., 14 Jan 2025).

4. Applications and Empirical Impact

Semantic-level reasoning graphs have demonstrated impact in a wide range of high-stakes and complex reasoning tasks:

• Multi-hop and Medical QA: Causal filtering and CoT-aligned graph retrieval in "CGMT" yielded a 6-10 point absolute accuracy gain over strong GPT-4o baselines on MedMCQA and MedQA; ablation studies confirm contributions from both graph filtering and CoT alignment (Luo et al., 24 Jan 2025).
• In-Context Learning: Reasoning Graph-Enhanced Exemplar Retrieval improves math and logic accuracy by 2-3 points over strong baselines, with graph re-ranking enabling more accurate and faithful reasoning trajectories (Lin et al., 2024).
• Fact Verification: SRL-based graphs combined with graph-aware positioning and graph convolutional attention yield state-of-the-art FEVER scores, with ablations showing each graph component contributing independently (Zheng et al., 2020, Zhong et al., 2019).
• Hallucination Detection: Fine-grained internal reasoning graphs based on semantic-level LRP vectors achieve substantially higher F1 scores (improvements of 3–6 points) on RAGTruth and Dolly-15k compared to previous scorer-based or self-consistency approaches (Hu et al., 6 Jan 2026).
• Reasoning Trace Analysis: Studies reveal structural graph metrics—exploration density, branching, convergence—correlate strongly with reasoning accuracy (+0.68 Pearson), and that prompt engineering significantly modulates internal graph structure (Xiong et al., 20 May 2025).
• Transferable Planning and Prediction: In autonomous driving, semantic spatial-temporal graphs enable domain-robust prediction, achieving 95%+ intention accuracy and near zero-shot transfer to novel intersection layouts (Hu et al., 2020).

Interpretability is enhanced by surfacing only high-strength paths or active facts, with answer rationales referencing explicit mini-graphs or causal chains.

5. Algorithmic Foundations and Graph Neural Architectures

Most recent systems employ specialized neural architectures for semantic-level graph encoding and reasoning:

• Graph Convolutional Networks (GCN/GAT): After construction, heterogeneous or semantic graphs are encoded with GCNs—propagating node and edge features, incorporating argument types, predicate semantics, or semantic similarity via adjacency structures (Zheng et al., 2020, Pan et al., 2020).
• Attention-based GGNNs: Edge-wise attention mechanisms guide propagation and gated updates—nodes aggregate incoming messages weighted by relational or semantic attention, supporting multi-hop compositionality (Pan et al., 2020).
• GNN Verifiers: For verification, attributed reasoning graphs are encoded via Graph Isomorphism Networks, aggregating features (e.g., verifier scores, occurrence counts) to vertices, and performing final answer selection via readout and classification (Cao, 2023).
• Differentiable Reasoning by Graph Transformation: Some frameworks model reasoning as a differentiable chain of graph transformation steps, with trainable rules as soft MATCH/CREATE operators; entire inference paths are modeled as matrix chains and trained end-to-end via loss on arrival at target concept nodes (Cetoli, 2021).

Structural similarity between candidate and query, or the propagation of token-level attribution up to semantic segments, is operationalized either via R-convolution kernels, Weisfeiler–Lehman relabelings, or stacking of GNN/GAT layers (Lin et al., 2024, Hu et al., 6 Jan 2026). Graph neural models often integrate directly with LLM outputs (embeddings, CoT steps, retrieved evidence) via feature concatenation, attention, or fusion layers in hybrid architectures (Luo et al., 29 Sep 2025, Zheng et al., 2020).

6. Theoretical Properties, Metrics, and Practical Considerations

Semantic-level reasoning graphs enable both empirical and theoretical advances:

• Theoretical Guarantees: Acyclicity and bounded edge counts are enforced in ReasoningFlow, enabling $O(n^2)$ parsing and sparse subgraph motif analysis (Lee et al., 3 Jun 2025).
• Metrics for Reasoning Quality: Structural metrics—exploration density, branching, convergence—quantify fidelity and diversity of LLM reasoning, offering model-agnostic signals beyond surface-level token metrics (Xiong et al., 20 May 2025).
• Scenario Transferability: Semantic abstraction (e.g., DIAs in traffic prediction) reduces distribution shift, theoretically shrinking cross-domain divergence and empirically supporting zero-shot transfer (Hu et al., 2020).
• Limitations and Future Directions: Attribution computation and graph construction can be expensive or exhibit high latency, and current frameworks often process local subgraphs or linearizations rather than globally optimizing over the full graph. Research directions include developing efficient semantic-level attribution, GNN-based discriminators that consume the full graph, and more robust prompt-to-graph parsing (Hu et al., 6 Jan 2026, Lee et al., 3 Jun 2025).

7. Interpretability, Explainability, and Cognitive Analysis

One of the principal advances enabled by semantic-level internal reasoning graphs is enhanced interpretability:

• Faithful Explanations: Surfaces the explicit logical or causal chains actually used in reasoning, allowing for stepwise auditing and human evaluation (Luo et al., 24 Jan 2025, Luo et al., 29 Sep 2025).
• Pattern and Motif Analysis: Enables the diagnosis of cognitive behaviors in LLMs—such as self-verification, backtracking, or branching—via motif counting and subgraph frequency analysis (Lee et al., 3 Jun 2025).
• Prompt Engineering: Structural analysis of generated graphs reveals prompt formats that preserve or degrade reasoning quality, offering actionable insights for LLM system developers (Xiong et al., 20 May 2025).

Semantic-level graphs serve not only as computational substrates but also as explicit, human-interpretable witnesses to the logical, causal, or procedural architectures of model reasoning—supporting error analysis, explanation, and the principled enhancement of model performance.