PerMix-RLVR: Preserving Persona Expressivity under Verifiable-Reward Alignment
Organizations: KAIST AI · Samsung Advanced Institute of Technology
Abstract
Persona prompting has been widely adopted to steer large language models (LLMs) behavior and improve their instruction performance by assigning specific characters. However, identifying an optimal persona is time-consuming, and its impact on output quality remains poorly understood. Prior work has mainly addressed this issue at the prompt level via inference-time strategies, incurring additional computation. In this work, we avoid inference-time prompt search by tackling persona sensitivity during training, aiming to train models that adapt their behavior to diverse personas while preserving task performance. In particular, we find that reinforcement learning with verifiable rewards (RLVR) systematically reduces sensitivity to persona prompts, but also reveals an inherent trade-off of outcome-based optimization: while RLVR improves robustness on tasks with verifiable goals, it can also degrade persona expressivity when needed, e.g., in-character role-playing. To address this limitation, we propose PerMix-RLVR, a persona-mixed RLVR strategy that mitigates the persona robustness-fidelity trade-off, preserving strong robustness to harmful persona variation while enabling faithful persona adoption when required. Concretely, PerMix-RLVR improves persona stability score (PSS) over RLVR by +21.2% on MATH500, while also enhancing persona fidelity by +11.4% on PersonaGym.
Figures & tables
| Model | WR | WR (no-tie) | Net margin |
| Llama3.1 (non-RLVR) | |||
| Qwen3 (RLVR) | |||
| Tie | – | – |
| Post-training | Input | Objective ( ) | GSM8K (i.d.) | MATH500 (o.o.d.) | PersonaGym | ||||||
| Worst | Best | Acc. Mean | PSS | Worst | Best | Acc. Mean | PSS | Consistency | |||
| Base ( ) | - | 81.1 | 84.9 | 83.5 | 0.956 | 28.6 | 46.0 | 42.5 | 0.619 | 3.19 | |
| SFT | 73.4 | 77.2 | 75.8 | 0.951 | 30.3 | 37.2 | 34.6 | 0.805 | 2.53 | ||
| PerMix-SFT | + | 74.3 | 76.2 | 75.2 | 0.974 | 33.0 | 35.3 | 34.2 | 0.880 | 2.88 | |
| 71.0 | 81.5 | 78.7 | 0.871 | 24.8 | 41.2 | 37.4 | 0.591 | 3.31 | |||
| RLVR | 84.0 | 87.6 | 86.1 | 0.959 | 34.0 | 49.6 | 46.8 | 0.675 | 3.06 | ||
| Post-training | Teacher | Input | Objective ( ) | GSM8K (i.d.) | MATH500 (o.o.d.) | PersonaGym | ||||||
| Worst | Best | Acc. Mean | PSS | Worst | Best | Acc. Mean | PSS | Consistency | ||||
| SeqKD | Qwen3-32B | 80.4 | 84.7 | 83.2 | 0.949 | 37.6 | 48.2 | 45.8 | 0.764 | 3.12 | ||
| + | 81.0 | 85.3 | 84.3 | 0.949 | 40.7 | 47.8 | 45.5 | 0.839 | 3.06 | |||
| SeqKD | Llama3.1-70B | 83.7 | 87.5 | 86.6 | 0.957 | 35.6 | 48.0 | 45.7 | 0.720 | 2.72 | ||
| + | 82.9 | 87.3 | 86.5 | 0.950 | 35.2 | 47.7 | 45.2 | 0.728 | 3.09 | |||
| SeqKD | Gemma3-27B | 62.1 | 85.2 | 82.0 | 0.729 | 31.7 | 47.2 | 45.3 | 0.656 | 3.06 | ||
| Post-training | Input | Objective ( ) | Easy | Medium | ||||||
| Worst | Best | Acc. Mean | PSS | Worst | Best | Acc. Mean | PSS | |||
| Base ( ) | - | 22.5 | 30.4 | 25.4 | 0.741 | 0.6 | 3.6 | 2.1 | 0.167 | |
| Supervised Fine-tuning | ||||||||||
| SFT | 19.0 | 25.4 | 22.5 | 0.750 | 0.6 | 3.0 | 1.7 | 0.200 | ||
| PerMix-SFT | + | 21.1 | 28.2 | 25.0 | 0.750 | 0.6 | 3.0 | 1.7 | 0.200 | |
| 18.3 | 24.7 | 21.2 | 0.743 | 0.8 | 2.9 | 1.8 | 0.292 | |||
Appendix figures & tables14 assets
Supplementary material from the paper’s appendix.
Appendix
| Name | Version |
| torch | 2.9.1 |
| transformers | 4.57.6 |
| accelerate | 1.12.0 |
| peft | 0.18.1 |
| CUDA toolkit | 11.8 |
| Hyperparameter | Value |
| Optimizer | PagedAdamW (8bit) |
| Data Type | bfloat16 |
| Learning Rate | |
| LR Scheduler | cosine |
| Batch Size | 128 |
| Max Sequence Length | 1024 (Non-Persona) / 2048 (PerMix-SFT) |
| Hyperparameter | Value |
| Optimizer | PagedAdamW (8bit) |
| Data Type | bfloat16 |
| Learning Rate | |
| LR Scheduler | cosine |
| Batch Size | 128 |
| Max Sequence Length | 1024 |
| Hyperparameter | Value |
| Optimizer | Fused AdamW |
| Data Type | bfloat16 |
| Learning Rate | |
| LR Scheduler | cosine |
| Batch Size | 64 |
| Max Prompt Length | 256 |
| Qwen3 | Llama3 | Gemma3 | ||||||||||
| Persona | 0.6B | 1.7B | 4B | 8B | 32B | 3.2-1B | 3.1-8B | 3.3-70B | 1B | 4B | 12B | 27B |
| math expert | 47.32 | 69.76 | 79.28 | 80.28 | 82.08 | 14.80 | 43.88 | 71.76 | 26.42 | 70.40 | 80.92 | 86.00 |
| software engineer | 46.28 | 68.68 | 77.48 | 80.12 | 82.80 | 15.72 | 44.8 | 72.44 | 20.92 | 69.24 | 78.92 | 85.16 |
| physics professor | 46.92 | 69.80 | 78.84 | 80.12 | 82.48 | 15.44 | 43.76 | 72.44 | 22.64 | 66.8 | 78.72 | 84.09 |
| semiconductor specialist | 46.64 | 70.00 | 77.92 | 81.60 | 81.84 | 16.16 | 45.00 | 71.28 | 22.08 | 64.72 | 77.56 | 82.48 |
| kindergarten | 45.48 | 68.08 | 78.16 | 78.24 | 83.84 | 9.16 | 32.16 | 70.76 | 25.00 | 49.56 | 70.20 | 78.88 |
| Qwen3 | Llama3 | Gemma3 | ||||||||||
| Persona | 0.6B | 1.7B | 4B | 8B | 32B | 3.2-1B | 3.1-8B | 3.3-70B | 1B | 4B | 12B | 27B |
| math expert | 1.98 | 12.62 | 21.33 | 28.00 | 23.99 | 0.66 | 6.66 | 24.00 | 2.00 | 7.33 | 25.33 | 27.33 |
| software engineer | 1.33 | 11.33 | 19.33 | 24.67 | 24.00 | 2.00 | 3.33 | 25.33 | 0.67 | 6.00 | 20.00 | 24.00 |
| physics professor | 1.33 | 10.67 | 18.67 | 28.00 | 24.67 | 0.67 | 4.00 | 24.00 | 0.67 | 9.33 | 22.67 | 24.00 |
| semiconductor specialist | 2.00 | 10.67 | 21.33 | 24.00 | 27.33 | 0.00 | 4.67 | 24.67 | 0.00 | 4.67 | 22.00 | 18.00 |
| kindergarten | 1.98 | 11.30 | 18.66 | 21.33 | 27.30 | 1.33 | 1.99 | 21.33 | 0.67 | 8.00 | 16.66 | 16.67 |
| Post-training | Input | Objective ( ) | EA | AJ | LH | PC | TC | Mean Score |
| Base ( ) | - | 2.69 | 2.59 | 2.44 | 3.19 | 2.91 | 2.76 | |
| Supervised Fine-tuning | ||||||||
| SFT | 2.38 | 2.03 | 2.31 | 2.53 | 2.72 | 2.39 | ||
| PerMix-SFT | + | 2.16 | 2.16 | 2.41 | 2.88 | 2.91 | 2.50 | |
| 2.56 | 2.59 | 2.25 | 3.31 | 3.13 | 2.77 | |||
| Distillation | ||||||||
| Post-training | Input | Objective ( ) | AIME24 | |||
| Worst | Best | Acc. Mean | PSS | |||
| Base ( ) | - | 1.33 | 4.67 | 2.67 1.11 | 0.286 | |
| Supervised Fine-tuning | ||||||
| SFT | 0.00 | 4.00 | 2.00 1.26 | 0.000 | ||
| PerMix-SFT | + | 0.00 | 3.33 | 1.42 0.99 | 0.000 | |
| 0.00 | 8.00 | 3.71 2.31 | 0.000 | |||
| Post-training | Input | Objective ( ) | LiveCodeBench (Hard) | |||
| Worst | Best | Acc. Mean | PSS | |||
| Base ( ) | - | 0.0000 | 0.0133 | 0.0085 | 0.0000 | |
| Supervised Fine-tuning | ||||||
| SFT | 0.0000 | 0.0222 | 0.0035 | 0.0000 | ||
| PerMix-SFT | + | 0.0000 | 0.0111 | 0.0042 | 0.0000 | |
| 0.0000 | 0.0222 | 0.0056 | 0.0000 | |||
| Persona key | System prompt |
| Tech Specialist | |
| statistician | You are a statistician with expertise in data analysis and probability. Approach problems by analyzing patterns, likelihoods, and logical inferences. |
| chemist | You are a chemist with a deep understanding of composition and reactions. Solve problems by breaking them down into their constituent elements and analyzing their interactions. |
| economist | You are an economist skilled in analyzing resources, incentives, and efficiency. Provide rational solutions that optimize outcomes based on the given constraints. |
| cryptographer | You are a cryptographer expert in patterns and security. Solve problems by looking for hidden structures, decoding logic, and validating the integrity of the solution. |
| architect | You are an architect focused on structure, balance, and design systems. Construct well-structured and logically sound solutions to the problems presented. |
| Persona key | System prompt |
| Character Traits | |
| anxious | You are anxious and cautious, always worried about making errors. Solve problems by carefully double-checking every step and considering all possible pitfalls before concluding. |
| arrogant | You are arrogant and supremely confident in your superior intellect. Provide the correct answer directly and concisely, acting as if the solution is obvious. |
| poetic | You are a poet who sees beauty in logic. Solve problems by weaving an elegant narrative and using metaphorical language to describe your reasoning process. |
| robotic | You are an AI unit focused purely on logic and efficiency. Process the input and output the solution with zero emotion, maximum precision, and standardized formatting. |
| energetic | You are highly energetic and enthusiastic! Tackle problems with excitement, using dynamic language and a very positive, encouraging tone. |
| Persona key | System prompt |
| STEM Expert | |
| math expert | You are a mathematical expert with deep knowledge of various mathematical concepts. Solve problems with precision and clarity. |
| software engineer | You are a software engineer with expertise in coding and algorithms. Provide clear and logical solutions to given problems. |
| physics professor | You are a physics professor with deep understanding of physical principles. Explain concepts clearly and solve problems methodically. |
| semiconductor specialist | You are a semiconductor specialist with extensive knowledge of semiconductor physics and technology. Provide accurate and detailed explanations. |
| Education Level | |
Personalized Language Model Alignment
Personalized language model alignment adapts model behavior to individual preferences while preserving safety, accuracy, and other shared constraints.
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