Fact Decomposition Methodology

• Fact decomposition methodology is a process that divides complex claims into minimal, interpretable atomic facts to enable precise fact verification and reasoning.
• It employs various algorithmic paradigms—such as iterative extract-verify loops, graph-based, and program-guided approaches—to boost retrieval accuracy and manage adversarial scenarios.
• This method is vital for applications in fact-checking, knowledge base completion, and table-based validation by enhancing clarity and mitigating noise.

Fact decomposition methodology encompasses a family of algorithmic and modeling strategies for breaking down complex claims, statements, answers, tables, or other structured or unstructured data into minimal, interpretable subcomponents—often framed as "atomic facts." These methods are especially prominent in fact verification, natural language inference (NLI), attributed question answering (AQA), adversarial fact-checking, knowledge base completion, and fact evaluation of LLMs. Fact decomposition enables more fine-grained retrieval, focused reasoning, enhanced interpretability, and robustness to noise and adversarial perturbations.

1. Formal Definitions and Atomic Fact Typologies

Fact decomposition derives from the principle that complex, compositional statements can be divided into "atomic" units, where each atomic fact expresses a minimal, standalone, irreducible proposition. Definitions and implementation details vary by task:

• In claim verification and NLI, an atomic fact may be a contiguous span in the premise that forms a minimal, semantically coherent assertion (Popovič et al., 23 Sep 2025).
• In knowledge base settings, atomic facts correspond to (subject, relation, object) triples (Huang et al., 10 Mar 2025, Fu et al., 2019).
• Temporal decomposition extends atomicity to (subject, relation, object, qualifier, time) quintuples (Chen et al., 16 May 2024).
• For attributed question answering, atomicity is enforced at the level of "molecular clauses" split further into atomic facts, each intended to contain precisely one proposition with low self-information (Yan et al., 22 Oct 2024).
• In matrix factorization, "atomic" components are formal concepts covering the minimal rectangular submatrices required for exact or approximate reconstruction (Belohlavek et al., 2013).

The central desiderata in all cases are minimality (irreducibility), interpretability (standalone semantics), and completeness (joint coverage of the original input) (Schmidt et al., 1 Sep 2025, Zheng et al., 9 Jun 2025). Taxonomic guidelines for splitting include clause conjunction, conditional boundaries, and explicit anaphora resolution (Schmidt et al., 1 Sep 2025).

2. Paradigms and Algorithmic Pipelines

A variety of decomposition and verification frameworks have been developed, differing in the mechanism of decomposition, the structure of intermediate representations, and the means of recombination:

• Iterative Extract-Verify Loops: Complex claims are decomposed stepwise, with each atomic fact extracted conditioned on prior facts and rationales; evidence is retrieved and reranked per atomic fact, and aggregation of sub-verdicts yields the final label (e.g., AFEV (Zheng et al., 9 Jun 2025), SUCEA (Liu et al., 5 Jun 2025)).
• Graph-based Decomposition: Claims are mapped into triplet graphs, with known and unknown entity nodes, ensuring co-reference and relational constraints are preserved. A parallel evidence graph enables fine-grained matching and graph-guided planning for verification (Huang et al., 10 Mar 2025).
• Program-guided Decomposition: For table-based verification, statements are parsed into symbolic programs; operator skeletons determine decomposition types (conjunction, comparative, superlative, uniqueness), and subproblems are solved over assigned table regions (Yang et al., 2021).
• Instruction-tuned LLM Decomposition: Instruction-tuned LLMs split text into molecular clauses and atomic facts, with dedicated editing and verification stages mapping evidence and attribution at the atomic level (ARE framework (Yan et al., 22 Oct 2024)).
• Joint Extractive Architectures: Encoder-only models (e.g., JEDI) extract atomic fact spans and perform interpretable inference in a single forward pass, obviating the need for generative LLMs during inference (Popovič et al., 23 Sep 2025).
• Temporal Decomposition: Complex sentences are mapped to timeline-indexed event lists, with in-context learning prompting large LMs and fine-tuning downstream PLMs for quintuple extraction (Chen et al., 16 May 2024).
• Numerical/Compositional Pipelines: Numerical claims are decomposed into sub-queries reflecting all required information facets, emulating human fact-checkers’ stepwise information needs (Venktesh et al., 24 Oct 2025).

Table: Representative Fact Decomposition Frameworks

Framework / Study	Task Domain	Decomposition Mechanism
AFEV (Zheng et al., 9 Jun 2025)	Multi-hop Verification	Iterative atomic extraction + pooling
GraphFC (Huang et al., 10 Mar 2025)	Fact-checking	Triplet claim/evidence graphs
Table-Program (Yang et al., 2021)	Table-based Verification	Program-guided skeleton parsing
JEDI (Popovič et al., 23 Sep 2025)	NLI, Fact-checking	Joint span extraction/classification
ARE (Yan et al., 22 Oct 2024)	Attributed QA	Clause/atomic fact LLM decomposition
FCDecomp (Venktesh et al., 24 Oct 2025)	Numerical Verification	Justification-driven query mining

3. Training, Supervision, and Data Construction

Complex decomposition frameworks typically require either (a) explicit pseudo-gold decompositions or (b) weak or synthetic supervision:

• Pseudo-gold Construction: In the table-based setting, symbolic programs are used to auto-generate annotated decompositions with type templates (e.g., “Find X, Find Y, Compare”), sometimes augmented via entity substitutions or semantic inversion (Yang et al., 2021).
• Synthetic Rationale Generation: Large instruction-tuned LMs, guided by human-in-the-loop prompt engineering, output fine-grained salient spans which are further bootstrapped for gold fact spans (Popovič et al., 23 Sep 2025).
• Knowledge-graph Sampling: Datasets for instruction-tuning can be assembled by transforming KG one-hop neighborhoods into text, from which corresponding clause/atomic mappings are induced (Yan et al., 22 Oct 2024).
• Temporal Annotation: Time expressions are extracted with deterministic parsers; prompts structure LLM outputs into timeline-aligned decompositions (Chen et al., 16 May 2024).

Supervision strategies often employ cross-entropy, margin-ranking, InfoNCE-style contrastive, or multi-component loss functions combining extraction, classification, and span-matching objectives (Yang et al., 2021, Popovič et al., 23 Sep 2025).

4. Integration with Retrieval and Verification

Fact decomposition acts as the entry point to retrieval-intensive or reasoning-centric verification pipelines:

• Each atomic fact or sub-proposition becomes a focused query for dedicated evidence, enhancing yield and reducing distraction compared to monolithic queries (Venktesh et al., 24 Oct 2025, Yan et al., 22 Oct 2024).
• Retrieved evidence is ranked either via dense bi-encoder/cross-encoder scoring or via semantic similarity in SBERT-embedding space; aligned evidence-fact pairs are fused for final veracity prediction (Zheng et al., 9 Jun 2025, Yan et al., 22 Oct 2024).
• Iterative or editing-enhanced pipelines further refine sub-claims based on partial retrieval results, thereby mitigating adversarial phrasing or ambiguity (Liu et al., 5 Jun 2025).
• In graph-based approaches, evidence graphs are constructed in parallel, and triplets are matched or completed in order dictated by referential constraints, allowing global early-stopping if a mismatch occurs (Huang et al., 10 Mar 2025).
• Decomposition outputs serve as the unit of both evidence attribution and post-hoc answer editing in AQA (Yan et al., 22 Oct 2024).

5. Empirical Performance, Challenges, and Error Taxonomies

Numerous studies demonstrate systematic improvements in retrieval accuracy, precision of attribution, downstream fact verification, and robustness, across tasks and datasets:

• Decomposition frameworks consistently outperform non-decomposition (single-query) baselines in evidence coverage and retrieval diversity (Venktesh et al., 24 Oct 2025, Yang et al., 2021).
• Iterative extraction and span-wise architectures (e.g., AFEV and JEDI) yield marked gains in adversarial and out-of-distribution robustness (Zheng et al., 9 Jun 2025, Popovič et al., 23 Sep 2025).
• Fine-grained triplet/atomic decompositions alleviate referential ambiguity and under-decomposition limitations in multi-hop and multi-entity verification (Huang et al., 10 Mar 2025).

However, decomposition introduces characteristic sources of noise:

• Over-fragmentation / Over-decomposition: Excessively splitting claims can yield trivial or redundant sub-claims, diluting verification signal (Hu et al., 17 Oct 2024).
• Omissions: Poor decomposition may omit context, causal relations, or critical components required for global veracity (Hu et al., 17 Oct 2024).
• Ambiguity/Semantic Drift: Decomposition errors can alter original meaning, cause pronoun/reference ambiguities, or fabricate unsupported sub-claims (Schmidt et al., 1 Sep 2025, Hu et al., 17 Oct 2024).

As a result, the impact of decomposition exhibits an accuracy–noise tradeoff depending on input complexity, verifier strength, and precise decomposition prompt/objective (Hu et al., 17 Oct 2024). Fine-tuned reflection loops or error-detection modules can partially mitigate decomposition-induced errors.

6. Applications Beyond Fact Verification

Fact decomposition methodologies extend beyond pure verification to other structured tasks:

• Knowledge Base Completion/Discovery: Decomposition into "facets" (e.g., head-relation, tail-relation, tail inference) allows more efficient KB enrichment, with autoencoder and feedback learning components for ranking candidate triples (Fu et al., 2019).
• Matrix Factorization: "Fact decomposition" as formal concept extraction enables lossless/parsimonious factor models for multigraded data, with interpretability via "rectangle" patterns (Belohlavek et al., 2013).
• Attribute-grounded QA and Editing: Atomic fact decomposition underpins selective evidence retrieval, attribution precision ($Attr_{p}$), and minimally invasive editing of long-form answers (Yan et al., 22 Oct 2024).
• Benchmarking and Dataset Construction: Fact decomposition provides the backbone for generating high-coverage datasets for temporal extraction, adversarial claims, and open-domain numerical verification (Chen et al., 16 May 2024, Venktesh et al., 24 Oct 2025).

7. Future Directions, Best Practices, and Open Challenges

Emerging work highlights several future pathways:

• Joint, End-to-End Optimization: Aligning decomposition objectives directly with downstream verification utility to close the retrieval–verification gap (Venktesh et al., 24 Oct 2025).
• Human-in-the-Loop Annotation Tools: Visual analytics frameworks to stabilize fact-level gold standards and resolve ambiguity in annotation guidelines for atomicity (Schmidt et al., 1 Sep 2025).
• Dynamic, Adaptive Decomposition: Iterative, context-sensitive pipelines that flexibly refine atomic fact extraction based on ongoing verification state and retrieved evidence (Zheng et al., 9 Jun 2025).
• Error Tradeoff Management: Adaptive selection of decomposition granularity and explicit monitoring of over-/under-decomposition errors (e.g., limiting number of sub-claims to input complexity) (Hu et al., 17 Oct 2024).
• Cross-domain Generalization: Fact decomposition for non-textual modalities, relational tables, temporal sequences, and fact-structured matrix/tensor data (Yang et al., 2021, Belohlavek et al., 2013).

In brief, fact decomposition methodology has emerged as a foundational mechanism for interpretable, scalable, and robust fact-centric machine learning, especially in the era of complex, blended, or adversarial information environments. The design of effective decomposition pipelines, taxonomy of atomicity, and integration with retrieval/remediation modules remain active areas of research and critical levers for progress in factual inference systems.