Large Language Models (LLMs) have gained widespread adoption in various natural language processing tasks, but suffer from hallucination issues where they generate unfaithful or inconsistent content. While Reinforcement Learning with Verifiable Rewards (RLVR) has shown promising applications in reasoning tasks, its application to span-level hallucination detection is challenged by localization ambiguity, reward sparsity on hard examples, and uncontrolled length inflation. To address these issues, we introduce Socratic Guided Policy Optimization (SOPO), a multi-turn RL framework for robust hallucination detection. The key innovation of SOPO is a Socratic feedback mechanism, where a teacher model guides the reasoning trajectories during rollout by providing indirect hints inferred from the ground truth. This teacher-guided approach enables the model to generate more effective reasoning trajectories for hard examples, thus alleviating reward sparsity. Furthermore, we incorporate Turn-based Advantage Scaling to penalize verbosity bias, encouraging the model to develop efficient and autonomous reasoning capabilities. Empirical results on RAGTruth demonstrate that SOPO (4B) achieves state-of-the-art performance, surpassing leading proprietary models (e.g., GPT-5) and standard RL baselines, while obtaining higher reported mean scores than GRPO on four out-of-domain benchmarks, with mixed evidence against CAPO. We release our training and evaluation code alongside the 1.7B and 4B SOPO models at https://github.com/patsnap/SOPO.
Figures & tables
Figure 1: Overview of SOPO.
Figure 2Figure 3Table 4
Method
Training
Span-F1
Case-F1
SOPO
Interactive RL
63.34±0.22
84.65±0.21
SOPO-FLOP
Interactive RL
62.96±0.24
83.72±0.32
80B-CoT-Distill
Teacher-trace SFT
50.09±0.77
79.05±0.39
Table 6: Overall RAGTruth F1 (%, mean ± standard deviation over 10 selected full-set, single-turn inference runs per checkpoint). All students share the cold-start initialization.
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
Hyperparameter
SFT (Cold-start)
RL
Learning Rate
7×10−6
1×10−6
Batch Size
16
64
Epochs
3
4
Warmup Epoch
1
1
LR Scheduler
Cosine
Constant
Optimizer
Adam
Adam
Appendix
Table 7: Hyperparameter of SFT and RL training.
Statistic
GRPO
SOPO
Difference
Generation Length (multi-turn sum)
2700.1
2529.4
-6.3%
Dynamic Sampling Rate ( ρ )
41.30%
48.02%
+6.7%
Turns Per Trajectory
1
1.57
-
Teacher Gen Length Per Feedback
-
172.8
-
Student Gen Length Per Turn
2700.1
1534.4
-43.2%
Appendix
Table 8: Trajectory statistics.
Training Phase
Component
GRPO
SOPO
Difference
Forward ( 2ND )
Student
9.37
8.62
-8.0%
Teacher
0.00
3.46
-
Backward ( 6ND )
Student
11.61
12.87
+10.6%
Total
20.98
24.95
+18.9%
Appendix
Table 9: FLOPs calculation (ExaFLOPs).
Metric
GRPO
SOPO
Difference
Training Time (Hours)
17.88
15.82
-11.5%
GPU Hours (NVIDIA-A800)
286.08
316.40
+10.6%
Appendix
Table 10: Wall-clock time and GPU hours.
Figure 10
SOPO checkpoint
Baseline
SOPO mean
Base mean
Δ F1
95% CI for Δ
One-sided p
Overall span-F1
SOPO
CAPO
63.34
59.75
+3.59
[1.52, 5.75]
0.0005
GRPO
59.49
+3.85
[1.33, 6.57]
0.0008
SOPO-FLOP
CAPO
62.96
59.75
+3.21
[0.98, 5.38]
0.0031
GRPO
59.49
+3.47
[0.93, 6.00]
0.0039
SOPO-GPUh
CAPO
62.74
59.75
+2.99
[0.95, 5.07]
0.0016
Appendix
Table 12: Repeated-inference RAGTruth results (%, 10 runs per method). Nominal paired-bootstrap 95% CIs and one-sided p -values use 10,000 replicates (seed 42), drawing one run per pool and resampling matched test examples. Pools were selected by span-F1 (including baseline runs from multiple evaluation campaigns); case-F1 uses the same runs. Estimates are conditional on these pools and do not measure training-seed variability.
Checkpoint
PsiloQA span-F1
Math-Shepherd span-F1
AggreFact mean BAcc
HaluEval accuracy
SOPO
73.90±0.36
89.02±0.49
75.93±0.15
69.77±0.03
SOPO-FLOP
74.17±0.20
87.59±0.62
75.23±0.10
69.23±0.06
CAPO
72.67±0.18
85.89±0.60
75.29±0.11
69.19±0.19
GRPO
72.51±0.17
85.68±0.61
72.55±0.90
67.52±0.35
Appendix
Table 13: OOD primary-metric means ± standard deviations (%) over 10 inference runs per checkpoint or baseline group. These are repeated inference evaluations, not independent training seeds.
Benchmark
SOPO checkpoint
Baseline
Δ
95% CI for Δ
One-sided p
PsiloQA
SOPO
CAPO
+1.28
[−0.26,2.92]
0.0524
GRPO
+1.47
[−0.05,3.12]
0.0282
SOPO-FLOP
CAPO
+1.48
[−0.15,3.19]
0.0353
GRPO
+1.66
[0.08,3.43]
0.0212
Math-Shepherd
SOPO
CAPO
+3.04
[0.35,5.99]
0.0131
GRPO
+3.19
[−0.03,6.73]
0.0267
Appendix
Table 14: OOD primary-metric sample-paired bootstrap comparisons (percentage points). Reported Δ , 95% CIs, and one-sided p -values pair the median-scoring run from each method’s 10 inference runs and use B=10,000 paired example-resampling replicates (seed 42). These nominal intervals and p -values are conditional on the paired inference runs. p<10−4 indicates zero nonpositive differences among the bootstrap replicates.
Figure 8: Probability density histogram of QA, data2text and summary task on RAGTruth Test set.
Retrieval-Augmented Generation (RAG) is widely used to augment the input to Large Language Models (LLMs) with external information, such as recent or domain-specific knowledge. Nonetheless, current models still produce closed-domain hallucinations and generate content that is unsupported by the retrieved context. Current detection approaches typically treat hallucination as a post-hoc problem, relying on black-box consistency checks or probes over frozen internal representations. In this work, we demonstrate that hallucination detection based on internal state representation can also serve as a direct training signal. We introduce RAGognize, a dataset of naturally occurring closed-domain hallucinations with token-level annotations, and RAGognizer, a hallucination-aware fine-tuning approach that integrates a lightweight detection head into an LLM, allowing for the joint optimization of language modeling and hallucination detection. This joint objective forces the model to improve the separability of its internal states regarding hallucinations while simultaneously learning to generate well-formed and meaningful responses. Across multiple benchmarks, RAGognizer achieves state-of-the-art token-level hallucination detection while substantially reducing hallucination rates during generation, without degrading language quality or relevance.
Fabian Ridder, Laurin Lessel, Malte Schilling
Computer Science Department, University of Münster, Münster, Germany
Hallucinations remain a major obstacle to deploying large language models (LLMs) in knowledge-intensive settings, where generated responses must be faithfully grounded in provided evidence. Reinforcement learning (RL) is a promising direction for hallucination mitigation, but response-level faithfulness rewards suffer from a granularity mismatch: localized hallucinations can cause supported content to receive spurious penalties. Although recent work introduces fine-grained feedback such as claim-level verification and token-level rewards, unbalanced credit assignment can still induce length, verbosity, or optimization-noise biases. We propose BALTO, a Balanced Token-level Policy Optimization framework for hallucination mitigation. BALTO extracts checkable factual claims, verifies them against the reference context, and projects claim-level judgments to token-level labels. A balanced token-level credit assignment mechanism is introduced into the framework. This design redistributes probability mass from unsupported content toward faithful content, rather than suppressing the entire response. We systematically analyze the limitations of response-level rewards from a theoretical standpoint, and prove BALTO's advantages in training stability and optimization efficiency for hallucination mitigation. Experiments on ConFiQA, RAGTruth, and FinLLM-Eval show that BALTO achieves the highest faithfulness across all six model--benchmark settings and consistently outperforms existing post-training baselines in Q-Score, demonstrating a stronger faithfulness--informativeness trade-off.
With the rapid advancement of large language models (LLMs), modern systems not only possess strong foundational capabilities and extensive knowledge, but can also solve complex problems via long, multi-step reasoning. However, as reasoning traces become longer, LLMs may produce a substantial amount of hallucinated content during the reasoning process, which is often difficult to detect. In this work, we conduct a fine-grained analysis of hallucinations arising in LLM reasoning and find that the reasoning traces are particularly prone to Context-Sensitive Factual Hallucinations: cases where the model actually has the relevant knowledge, yet makes factual errors due to contextual interference during reasoning. To address this issue, we propose Step-level Self-Consistency Group Relative Policy Optimization (SSC-GRPO), which assigns step-level rewards to reasoning traces by computing self-consistency scores of individual steps across multiple rollouts. Compared with prior methods, SSC-GRPO achieves state-of-the-art performance on both mathematical reasoning benchmarks and hallucination leaderboards. Our results offer a new perspective for detecting and mitigating hallucinations in the reasoning process of large language models.