Fact-based Decomposition Methods

• Fact-based Decomposition Methods are frameworks that break down complex information into independent, verifiable sub-claims, improving retrieval precision and reasoning transparency.
• They employ iterative, graph-based, and program-guided techniques to extract atomic units, ensuring minimal ambiguity and facilitating multi-hop evidence retrieval.
• Empirical benchmarks reveal notable gains in accuracy and recall, while also highlighting challenges such as error propagation and over-fragmentation in complex domains.

Fact-based decomposition methods encompass a family of frameworks for breaking down complex information—typically natural language claims, tabular assertions, or long-form answers—into minimal, independently verifiable units (“atomic facts” or sub-claims). These approaches are foundational in automated fact verification, interpretable natural language inference (NLI), question answering (QA), knowledge base expansion, and counterfactual reasoning. The central goals are to increase retrieval precision, enable multi-hop and modular reasoning, and provide transparent rationales for verdicts, especially in adversarial or high-noise settings.

1. Formal Principles and Definitions

Fact-based decomposition replaces monolithic verification with a pipeline centered on minimal factual units. For a complex claim $C$, decomposition yields a set of atomic facts or sub-claims $\{F_1, F_2, \dots, F_T\}$, each designed to:

• Be maximally independent and context-free;
• Convey a single piece of information (atomicity) as in $C = \{c_i\,:\, C\models c_i \ \forall i\}$, where $\models$ is either explicit entailment or, in knowledge graphs, triple inclusion;
• Be suitable for direct retrieval or entailment scoring.

Granularity is strictly regulated: in graph-based frameworks, minimal units correspond to subject–predicate–object triplets; in sequence-based approaches, units are concise declarative sentences or questions; and in structured contexts (tables, temporal extraction) they become programmatic subqueries or event-time quintuples.

Atomicity is quantified via information-theoretic metrics—$\text{atomicity}(c) = \log_2 K$ for $K$ underlying facts, with dynamic decomposition seeking to align this granularity to verifier preferences (Lu et al., 19 Mar 2025).

2. Methodological Taxonomy

Major classes of fact-based decomposition—spanning text, knowledge base, tabular, and reasoning domains—can be organized by the units of analysis and downstream task:

Paradigm	Atomic Units	Use Case
Sub-claim extraction	Context-free clauses	Textual fact-checking
Triplet graph extraction	(s, p, o) triples	Multi-hop/graph FC
Program-guided	Sub-programs/questions	Table/num. verification
Timeline/event	(entity, rel, obj, qual, time)	Temporal IE
Question decomposition	Evidence-seeking Qs	QA/fact-checking

2.1 Sub-claim and atomic fact extraction

SUCEA (Liu et al., 5 Jun 2025) employs claim segmentation (via LLM prompting), decontextualization, iterative claim editing grounded in retrieved evidence, and aggregation into a final entailment verdict. AFEV (Zheng et al., 9 Jun 2025) introduces an iterative loop: extract atomic fact $F_t$ (conditioning on prior facts and rationales), retrieve and rerank evidence, gather context-specific demonstrations, verify, and aggregate.

2.2 Graph-based decomposition

GraphFC (Huang et al., 10 Mar 2025) maps claims and supporting evidence into directed graphs of (subject, predicate, object) triplets, explicitly handling referential ambiguity via placeholder nodes. This produces a fine-grained, unambiguous substrate for planning and graph-guided checking.

2.3 Program-guided and query-based

Table fact verification leverages latent semantic programs to decompose statements into simpler, template-generated subproblems (Yang et al., 2021). For numerical claims, decomposition yields web-search sub-queries optimized for diversity and coverage using Maximal Marginal Relevance (MMR) (Venktesh et al., 24 Oct 2025).

2.4 Timeline and temporal decomposition

Temporal fact extraction uses timeline-aligned sentence decomposition: time expression recognition (e.g., via SUTime), LLM-based mapping to (time, event-sentence) pairs, then fine-tuned seq2seq for fact extraction (Chen et al., 16 May 2024).

2.5 Question-based decomposition

Recent QA and fact-checking pipelines employ fine-tuned or instruction-tuned models to map claims into evidence-seeking questions, covering all facets of the claim for retrieval and modular NLI aggregation (Setty et al., 31 Jul 2024).

3. Algorithms and Implementation Techniques

Decomposition methods operationalize the above principles through modular, often iterative, pipelines. Key algorithmic components include:

• Iterative decomposition and verification: AFEV (Zheng et al., 9 Jun 2025), SUCEA (Liu et al., 5 Jun 2025), and Dynamic Decomposition RL (Lu et al., 19 Mar 2025) employ loops where extraction, evidence retrieval, and (optionally) prior rationales inform further decomposition or halt conditions.
• Evidence-guided editing: SUCEA introduces LLM-based claim editing, paraphrasing sub-claims using retrieved snippets to bridge lexical gaps and improve retriever recall—a critical component not present in static decomposition.
• Joint encoder architectures: JEDI (Popovič et al., 23 Sep 2025) performs extractive atomic fact decomposition and span-wise NLI in one forward pass, leveraging synthetic rationale corpora for supervision.
• Graph-guided scheduling: In GraphFC (Huang et al., 10 Mar 2025), triplets are prioritized by how many entities are grounded, avoiding under- or over-decomposition and referential ambiguity.
• Fine-tuned generation and reranking: Silver or gold decompositions are mined from weak supervision or LLMs, then distilled into small generative models (e.g., FLAN-T5, GPT-2) for efficient deployment (Venktesh et al., 24 Oct 2025).
• Joint evidence aggregation and label prediction: Retrieved evidence is aggregated (union, reranking, or CombMAX-Norm fusion), then scored (LLM/reranker, NLI model, entailment aggregation) for a final claim verdict.

Iterative RL-based policies (Lu et al., 19 Mar 2025) and bilevel optimization emerge as solutions to the nontrivial task of aligning decomposition granularity to downstream verifier capability.

4. Empirical Benchmarks and Performance Insights

Fact-based decomposition shows statistically significant gains—both in evidence retrieval (Recall@10 up to +11 pp) and final label accuracy (+7–8% absolute)—on adversarial or multi-hop fact-checking datasets (Liu et al., 5 Jun 2025). In AFEV (Zheng et al., 9 Jun 2025), iterative extraction yields +1.2% accuracy and +1 F1 over static splits; Table-based pipelines (Yang et al., 2021) report up to +4 pp accuracy for decomposed program-guided variants.

• GraphFC (Huang et al., 10 Mar 2025) outperforms prior multi-hop and program-based baselines on HOVER, FEVEROUS, and SciFact by 3–8 points macro-F1, with ablations confirming the necessity of explicit triplet decomposition and graph-guided reasoning.
• Fact-based question decomposition approaches (e.g., T5-based QGen in (Setty et al., 31 Jul 2024)) outperform much larger LLMs by up to 8% in downstream NLI Macro-F1 despite being orders of magnitude smaller.
• Decomposition noise is non-negligible: errors such as omission, ambiguity, over-fragmentation, or alteration can counteract the benefits of finer atomicity (Hu et al., 17 Oct 2024); reflection and error mitigation can recoup F1 losses.

A plausible implication is that decomposition’s impact is highly contingent on the strength of retrieval and verification models, as well as the granularity alignment to input/domain complexity. Dynamic RL-trained decomposers (Lu et al., 19 Mar 2025) consistently improve confidence (+0.07) and accuracy (+0.12) over static policies.

5. Error Analysis, Theoretical Trade-offs, and Best Practices

Decomposition can introduce systematic errors, categorized as:

• Omission: Lost context, missing relations or critical facts.
• Ambiguity: Vague or underspecified sub-claims propagating noise downstream.
• Over-fragmentation: Excessively granular units inflating retrieval noise and aggregation complexity.
• Alteration: Unintended inversion or fabrication of facts (Hu et al., 17 Oct 2024).

The trade-off is formalized as: $$A_{\mathrm{decomposed}} = A(k_d)\cdot (1-E_d)\cdot (1-E_r)$$ where $A(k)$ is verifier accuracy at complexity $k$, $E_d$ is decomposition noise, and $E_r$ is cumulative retrieval error. Decomposition helps only when the reduction in atomicity (and thus $A(k_d)-A(k_0)$) outweighs the introduction of $E_d$ and $E_r$.

Authors recommend:

• Limiting sub-claim count to the number of original sentences;
• Enforcing atomicity without excessive fragmentation;
• Including necessary context in each unit;
• Using error-aware reflection (e.g., prompting LLMs to self-check and repair decomposition outputs);
• Explicitly modeling decomposition and retrieval error, adaptively tuning granularity (Hu et al., 17 Oct 2024, Lu et al., 19 Mar 2025).

6. Specialized Domains and Extensions

Fact-based decomposition generalizes across modalities:

• Clinical notes: FactEHR (Munnangi et al., 17 Dec 2024) demonstrates sub-sentence to atomic fact rewriting for clinical factuality, highlighting high precision but variable recall and strong model sensitivity.
• Knowledge base expansion: Fact Facet Decomposition (FFD) (Fu et al., 2019) decomposes triple discovery into facet subproblems (head-relation, tail-relation, tail-inference), augmenting KBC’s limited scope with substantial MAP and precision gains.
• Temporal reasoning: Timeline-aligned decompositions formalize the alignment of facts to time anchors, increasing recall in event extraction (Chen et al., 16 May 2024).
• Counterfactual analysis in games: Decomposition coincides with equilibrium forecasts under selection-invariance (Canen et al., 2020), streamlining counterfactual analysis in strategic environments.

Emerging directions include joint learning of decomposition and verification, integration of knowledge graph-specific reasoning, and extension to multi-lingual or domain-specific settings.

7. Impact, Limitations, and Future Directions

Fact-based decomposition methods now underpin state-of-the-art in adversarial, open-domain, multi-hop, clinical, tabular, and temporal fact verification.

Limitations include:

• Error propagation when decomposition is suboptimal;
• Domain and prompt sensitivity of LLM-based decomposers;
• Bottlenecks in current retrievers and verifiers, especially for non-textual domains (e.g., table, number, or temporal reasoning).

A recurring insight is that improved retrieval (via decomposition) does not fully close the verification gap: NLI and entailment models remain limiting factors in multi-evidence, compositional reasoning (Venktesh et al., 24 Oct 2025).

Future work is trending toward:

• End-to-end decomposition-verifier co-training;
• Iterative, evidence-guided dynamic decomposition at scale (Lu et al., 19 Mar 2025);
• Hybrid symbolic–neural approaches (e.g., integrating explicit graph decomposition);
• Robust evaluation and intervention for decomposition errors, especially in safety-critical domains.

Fact-based decomposition, while not universally beneficial in every task or domain, forms the foundational architecture for interpretable, robust, and scalable automated factuality and verification systems. Its evolution is closely connected to advances in LLM prompting, retrieval-augmented architectures, and interpretable learning for complex compositional reasoning.