Vertical-Domain Accounting Reasoning

• Vertical-domain accounting reasoning is a process that integrates multi-step numerical computations with rule-based logic within established accounting standards.
• It employs advanced methodologies like FEVO, EQD, and Fin-PRM to automate tasks such as journal entry generation and financial statement synthesis.
• Key challenges include semantic alignment, arithmetic precision, and regulatory compliance, driving ongoing research in hybrid, structure-aware architectures.

Vertical-domain accounting reasoning refers to the capacity of AI systems, particularly LLMs, to carry out multi-step numerical computations and rule-based logical inference under the explicit constraints of professional accounting standards, data structures, and workflows. This capability integrates specialized corpus knowledge, formal process supervision, structured dataset curation, domain-aligned reward mechanisms, and regulatory quality control, enabling advanced automation of tasks such as journal entry generation, financial statement synthesis, tax and compliance logic, and detailed audit traceability.

1. Formal Definition and Conceptual Foundations

Vertical-domain accounting reasoning is formally defined as a reasoning process, $R = (s_1, \ldots, s_k)$, elicited by an LLM in response to a query $Q$ and domain fact set $D$ (e.g., US-GAAP, IFRS, local regulatory manuals), where each subproblem $s_i$ represents a numerical computation or rule application, such that:

• Each intermediate result $v_i$ propagates to $v_{i+1} = f_i(v_i)$ via an accounting transformation $f_i$,
• The final answer $A$ is consistent with all domain constraints in $D$,
• The reasoning chain $R$ is logically valid and verifiable by domain experts (Zhou et al., 27 Dec 2025).

This approach subsumes both accounting logic (e.g., proper account mapping, double-entry checks) and quantitative reasoning (e.g., ratio analysis, depreciation computation, multi-period aggregations), requiring models to strictly implement business rules, preserve intermediate state, and guarantee format and regulatory correctness.

2. Methodological Paradigms for Model Enhancement

The leading methodologies for instilling vertical-domain accounting reasoning in LLMs are characterized by multi-stage post-pretraining, reward engineering, and structured data filtering:

• Three-Stage Enhancement (FEVO) Framework: The FEVO architecture (Pang et al., 8 Jul 2025) comprises:
  • Continued Pre-training (CPT): Expansion of accounting knowledge via domain corpus aggregation (CPA texts, QA datasets, filings, general anchors), rigorous deduplication, and mixed denoising loss:

  $$L_\text{total} = L_\text{CPT} + \lambda_\text{denoise}\,E_{x\sim D_\text{gen}}[\| x - \text{decode}(\text{encode}(x)+\text{noise}) \|_2]$$

  with $\lambda_\text{denoise}$ controlling preservation of linguistic stability. - Supervised Fine-Tuning (SFT): Multi-stage template supervision (<PLAN>, <STEP>, <REFLECT>, <BACKTRACK>, <ENTRY>) to explicitly chunk reasoning and enforce interpretability, using cross-entropy loss over the concatenated tokenized segments. - Reinforcement Learning (RL): Proximal Policy Optimization (PPO) with reward shaping over domain criteria—journal entry balancing, logical step accuracy, format compliance:

  $$r(\tau) = \alpha\,\mathbf{1}\{\text{all\_entries\_balanced}\} - \beta\, (\text{\# illogical\_steps}) - \gamma\,\mathbf{1}\{\text{format\_violation}\}$$

  Combined with auxiliary NLL loss on reference chains for style retention.

• Expert Question Decomposition (EQD): Low-rank adaptation scheme generating minimal, high-yield sub-questions for decomposition, optimized via reward that compares direct- and decomposed-QA answer correctness. In practice, a single targeted supporting question is often more effective than explicit multi-step chains (Wang et al., 1 Oct 2025).
• Process Reward Models (Fin-PRM): Dual-level evaluators offering step-, trajectory-, and knowledge-coverage rewards for both offline selection and online RL. These models operationalize dense, domain-specific reward signals, quantifying both process correctness (balanced entries, valid steps) and final outcome alignment (Zhou et al., 21 Aug 2025).
• Retrieval-Augmented Generation (RAG): Dual-retriever systems pairing a domain-specialized retriever (SecBERT, DPR external definitions) with a symbolic or prompt-based generator, ensuring accounting fact completeness and regulatory memory (Zhang et al., 29 Dec 2025).

3. Benchmark Datasets and Evaluation Metrics

Empirical progress in this area is grounded in the systematic creation of domain-aligned evaluation sets, with metrics targeting end-to-end numerical correctness, logical chain completeness, and regulatory compliance:

Benchmark / Task	Key Evaluation Metrics	Source
Fin CPA, FinCCR, MATH500	Entry-Accuracy, Calculation-Accuracy, Coherence Score	(Pang et al., 8 Jul 2025)
Accounting-Reasoning-Benchmark	Exact Match Accuracy, Step Consistency, Error-Propagation	(Zhou et al., 27 Dec 2025)
CFLUE, FinQA, CCC	Structured output reward, final answer correctness, compliance	(Zhu et al., 22 Apr 2025)
FinAuditing (FinSM, FinRE, FinMR)	Hit-Rate@k, Macro-F1, Multi-class Accuracy, Strict JSON output	(Wang et al., 10 Oct 2025)
FRA (FinMR), BizBench	Ratio error rate, stepwise F1, code-based program execution	(Deng et al., 22 Apr 2025, Koncel-Kedziorski et al., 2023)

Weighted composite scores are frequently adopted, e.g.,

$$\text{Overall} = 0.4 \cdot \text{Entry-Acc} + 0.4 \cdot \text{Calc-Acc} + 0.2 \cdot \text{Coherence}$$

FEVO and DianJin-R1 approaches use auxiliary structure and correctness rewards for alignment.

4. Specialized Data Curation and Knowledge Resources

Vertical-domain accounting models rely on domain-specific corpora and layered filtering:

• Corpus Sources: CPA/IFRS textbooks, accounting Q&A forums, regulatory filings, industry news, in-house dialogue logs (e.g., Kuaiji's CAtAcctQA (Luo et al., 2024), FEVO's AccLearn, FinCorpus-QA).
• Formal Structuring: Hierarchical knowledge graphs, ontology triples (e.g., (Inventory, “subclassOf”, Current Asset)), RAG vector stores, and taxonomy-aligned linkbase segmentation (FinAuditing’s US-GAAP/XBRL (Wang et al., 10 Oct 2025)).
• Filtering: Rule-based (double-entry balance, account validity, completeness), model-based (logical chain validation with LLM-as-judge, template conformance), and deduplication via MinHash or string similarity.
• Multilingual and Regulatory Context: Localized rules (Chinese GAAP, PBOC circulars), cross-standard corpora, and federated training across institution silos (Hong et al., 8 May 2025).

5. Characteristic Challenges and Error Modes

Despite progress, several classes of persistent challenge are documented:

• Semantic and Structural Alignment: Significant accuracy drops (60–90%) in taxonomy-aligned, multi-document benchmarks (FinAuditing) caused by LLMs’ inability to traverse calculation linkbases or resolve semantic tag mismatches; best human-aligned performance still below 15% on multi-step consistency (Wang et al., 10 Oct 2025).
• Arithmetic and Table Parsing: High error rates in quantity extraction and ratio computation, notably due to header misinterpretation and arithmetic slip-ups, even in multimodal LLMs (Deng et al., 22 Apr 2025).
• Fact Grounding and Regulatory Drift: Hallucination around regulatory standards, incorrect frequency/threshold retrieval, and incomplete knowledge coverage, especially for non-localized models (Hong et al., 8 May 2025).
• Step Error Propagation: Error amplification from early-stage computation into downstream steps, with error-type breakdowns indicating principle-level misunderstandings, coverage gaps, and logic inconsistency (Zhou et al., 27 Dec 2025).

Explicit modeling of chain-of-thought and constraint-reinforced supervision (e.g., via structural rewards or chain completeness tracking) are key mitigation strategies.

6. Notable Systems and Application Scenarios

Several open-domain and localized LLMs have demonstrated substantial, though not complete, gains in vertical-domain accounting reasoning:

• FEVO Series (Qwen2.5-32B-based): Demonstrates superiority over much larger general or specialist models on financial reasoning, achieving state-of-the-art on five financial benchmarks via CPT–SFT–RL (Pang et al., 8 Jul 2025).
• DianJin-R1 and Fin-PRM: Enforce structured output via dual rewards (structure, correctness), optimizing for both answer correctness and chain transparency. Reported 8–40pp gains over non-reasoning LLMs, with empirical accuracy jumps from 77.95% to 86.74% (CFLUE), and 56.5% to 96% (CCC compliance) (Zhu et al., 22 Apr 2025, Zhou et al., 21 Aug 2025).
• Kuaiji (Chinese Baichuan2-13B-based): Combines Quanted LoRA adapters, continuous pre-training on accounting text, and expert-annotated dialogue data, achieving 88% accuracy on a real-world test set and rapid inference on commodity GPUs (Luo et al., 2024).
• QualBench: Reveals that localized models (Qwen2.5-7B) vastly outperform non-Chinese models in Chinese financial/accounting tasks (77.52% vs. 58.2% for GPT-4o), validating the need for regulatory and linguistic adaptation (Hong et al., 8 May 2025).
• BizBench: Benchmark for code-based accounting workflows, indicating programmatic solution generation as a method for robust chain-of-thought auditability and error tracing (Koncel-Kedziorski et al., 2023).

Application domains range from adjusting entry generation, multi-period ratio analysis, audit trace construction, and tax compliance, to regulatory error detection in XBRL filings (Wang et al., 10 Oct 2025).

7. Outlook, Limitations, and Research Frontiers

While SOTA LLMs and process-reward frameworks have advanced vertical-domain accounting reasoning towards near-professional performance, open technical problems remain:

• Scaling and Generalization: Existing systems underperform on long-context and multi-document inputs, and remain sensitive to prompt or demonstration schema.
• Hybrid Architectures: Hybrid symbolic–neural approaches (integration of programmatic calculations, knowledge graphs, and retrieval-augmented generation) are a research frontier for structure-aware reasoning (Zhang et al., 29 Dec 2025, Wang et al., 10 Oct 2025).
• Federated and Continual Learning: For privacy-sensitive financial institutions, federated fine-tuning over distributed ledgers without raw data sharing is proposed, as is continual pretraining on evolving regulatory texts (Hong et al., 8 May 2025).
• Automated Audit, End-to-End Flows: Benchmarks are extending from discrete QA or code synthesis toward fully-automated flow coverage (journal entry → ledger → statement → audit trail) (Koncel-Kedziorski et al., 2023).

Advancing vertical-domain accounting reasoning will require continued innovation in data curation, process-aware reward modeling, structured output supervision, and cross-domain multimodal integration. The combination of statistical, symbolic, and process-constrained components is central to closing the remaining gap between automated and expert-level accounting performance.