FARCA: Fact-Aligned Reliability-Aware Credit Assignment for Reinforcement Learning with Factual Supervision
Organizations: School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China · School of Intelligence Science and Technology, Nanjing University, China
Abstract
To reduce the hallucination risk caused by outcome-driven rewards in large language models trained through reinforcement learning with verifiable rewards, existing mitigation approaches introduce process-level factual supervision. However, due to coarse-grained aggregation of factual signals and the lack of reliability assessment for these signals, they create a mismatch between fact verification and policy updates. We term this noisy factual credit assignment and decompose it into two aspects: credit localization ambiguity and credit reliability ambiguity. To address these issues, we propose FARCA (Fact-Aligned Reliability-Aware Credit Assignment), a policy optimization framework that transforms factual supervision into localized, reliability-weighted token-level training signals. FARCA achieves fine-grained credit localization by aligning the granularity of fact verification with that of policy updates. It further introduces counterfactual evidence attribution, which uses the dependence of a factual judgment on key evidence as an empirical proxy for verification reliability to compute reliability weights. These weights modulate factual rewards and local policy advantages, reducing the influence of potentially unreliable signals on policy optimization. Experiments across different models and multiple factual reasoning benchmarks show that FARCA significantly improves model factuality while preserving general reasoning capabilities.
Figures & tables
| Method | Hallucination | Math | ||||||
|---|---|---|---|---|---|---|---|---|
| SimpleQA | TruthfulQA | HalluQA | HaluEval-QA | AIME2026 | AIME2025 | MATH-500 | GSM8K | |
| Qwen2.5-3B-Instruct | ||||||||
| Zero-shot | 1.33 | 30.41 | 16.44 | 23.56 | 0.00 | 0.00 | 32.20 | 65.96 |
| GRPO (Math only) | 0.79 | 18.12 | 9.56 | 10.22 | 3.33 | 3.33 | 54.80 | 77.18 |
| GRPO (Full) | 2.52 | 42.59 | 22.67 | 25.05 | 3.33 | 3.33 | 53.22 | 75.82 |
| KnowRL | 2.42 | 41.98 | 20.67 | 25.57 | 0.00 | 0.00 | 51.80 | 75.59 |
| Variant | Hallucination | Math | ||||||
|---|---|---|---|---|---|---|---|---|
| SimpleQA | TruthfulQA | HalluQA | HaluEval-QA | AIME2026 | AIME2025 | MATH-500 | GSM8K | |
| FARCA | 3.56 | 45.41 | 25.78 | 26.67 | 6.67 | 10.00 | 63.20 | 84.46 |
| w/o token provenance | 3.23 | 44.52 | 23.94 | 25.90 | 6.67 | 6.67 | 61.00 | 82.87 |
| w/o reliability estimation | 3.04 | 43.88 | 24.51 | 26.28 | 3.33 | 6.67 | 61.40 | 82.26 |
| w/o continuous factual score | 3.31 | 44.78 | 25.40 | 26.06 | 6.67 | 10.00 | 62.80 | 83.85 |
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Instruction: You are an atomic fact extractor. Given a SENTENCE, extract all atomic facts from it. An atomic fact is the smallest, self-contained, and independently verifiable factual statement. 1. Each atomic fact must be a complete and self-contained statement that can be understood independently. 2. Remove subjective opinions, speculation, reasoning steps, and discourse connectors; only keep factual content. 3. If the SENTENCE does not contain any verifiable facts (e.g., pure reasoning, mathematical derivations, or subjective judgments), return an empty list. 4. For each atomic fact, provide its corresponding source_span , which must be an exact substring of the SENTENCE. 5. Atomic facts should be ordered according to their appearance in the SENTENCE. 6. The source_span should include only the minimal, distinctive part corresponding to that fact. Avoid repeating shared subjects or prefixes across multiple facts. 7. Your task is to do this for the SENTENCE under “Your Task.” Some examples have been provided for you to learn how to do this task. EXAMPLE #1: SENTENCE: Beijing is the capital of the United States, Tiananmen is one of the most famous landmarks of Beijing. ATOMIC FACTS: json {"atomic_facts": [{"fact": "Beijing is the capital of the United States", "source_span": "Beijing is the capital of the United States"}, {"fact": "Tiananmen is one of the most famous landmarks of Beijing", "source_span": "Tiananmen is one of the most famous landmarks of Beijing"}]} EXAMPLE #2: SENTENCE: Therefore, we can conclude that this reasoning is correct. ATOMIC FACTS: json {"atomic_facts": []} EXAMPLE #3: SENTENCE: Tiananmen Square in Beijing is the largest city square in the world and attracts millions of visitors each year. ATOMIC FACTS: json {"atomic_facts": [{"fact": "Tiananmen Square in Beijing is the largest city square in the world", "source_span": "Tiananmen Square in Beijing is the largest city square in the world"}, {"fact": "Tiananmen Square in Beijing attracts millions of visitors each year", "source_span": "attracts millions of visitors each year"}]} EXAMPLE #4: SENTENCE: Beijing is the capital of the United States, its landmark building is Tiananmen. ATOMIC FACTS: json {"atomic_facts": [{"fact": "Beijing is the capital of the United States", "source_span": "Beijing is the capital of the United States"}, {"fact": "Beijing’s landmark building is Tiananmen", "source_span": "its landmark building is Tiananmen"}]} EXAMPLE #5: SENTENCE: Marie Curie was a famous chemist, physicist, and writer. ATOMIC FACTS: json {"atomic_facts": [{"fact": "Marie Curie was a famous chemist", "source_span": "Marie Curie was a famous chemist"}, {"fact": "Marie Curie was a famous physicist", "source_span": "physicist"}, {"fact": "Marie Curie was a famous writer", "source_span": "writer"}]} Your Task: SENTENCE: [SENTENCE] ATOMIC FACTS: |
LLM Reliability
Large language model reliability studies whether outputs remain correct, calibrated, robust, and controllable across prompts, contexts, and deployment conditions.
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