*Equal contribution. †Corresponding authors.
VeriEvol asks a simple scaling question: what if harder multimodal math prompts are not enough unless their answers are also verifiably reliable?
In visual mathematical reasoning, wrong answers become especially damaging at the RL stage: every rollout can repeatedly convert a noisy label into reward signal. VeriEvol moves answer reliability into the data-construction stage, before any policy update.
Prompt difficulty scales through route-specific evolution operators, while answer reliability scales through offline hypothesis-test falsification. This decoupling makes each part extensible and auditable.
Accepted examples are materialized as standard prompt-answer-reward tuples, so the resulting VeriEvol-RL data can plug into existing GRPO-style recipes without changing the optimizer.
The framework turns low-difficulty image-question seeds into verified training samples through prompt difficulty control, answer reliability control, and closed-loop refinement.
Task routing sends seeds to route-specific operators such as decomposition, rephrasing, constraint strengthening, multi-hop reasoning, inverse solving, and visual grounding.
HTV-Agent accepts an answer only after multiple solver hypotheses and counter-evidence channels fail to refute it.
Rollout-based difficulty estimates prioritize useful samples and refresh the seed pool, keeping the construction loop focused on learnable challenges.
VeriEvol combines data-volume scaling with explicit verification, then validates the effect through training dynamics and verifier ablations.
All internal rows share the Qwen2.5-VL-7B-Instruct backbone and evaluate on five held-out visual mathematical reasoning benchmarks.
| Method | MathVista Mini ↑ |
MathVision Mini ↑ |
MathVerse VO ↑ |
DynaMath Worst ↑ |
We-Math Strict ↑ |
Avg. ↑ |
|---|---|---|---|---|---|---|
| External 7B-size baselines | ||||||
| OpenMMReasoner-7B | 79.50 | 43.60 | 63.80 | 34.90 | 53.81 | 55.12 |
| ReVisual-R1-7B | 73.10 | 48.80 | 53.60 | 27.50 | 42.00 | 49.00 |
| OVR-7B | 72.10 | 38.20 | 54.60 | 33.50 | 44.60 | 48.60 |
| MMR1-Math-v0 | 72.00 | 29.00 | 55.40 | 27.90 | 31.90 | 43.24 |
| WeThink-7B | 70.90 | 27.20 | 44.70 | 24.40 | 48.00 | 43.04 |
| VLAA-Thinker-7B | 68.00 | 26.40 | 48.20 | 22.40 | 41.50 | 41.30 |
| VL-Rethinker-7B | 73.70 | 28.40 | 46.40 | 17.80 | 36.30 | 40.52 |
| ThinkLite-VL-7B | 71.60 | 24.60 | 42.90 | 16.50 | 41.80 | 39.48 |
| MM-Eureka-Qwen-7B | 72.60 | 32.10 | 45.40 | 23.00 | 21.80 | 38.98 |
| InternVL3-8B | 70.50 | 28.60 | 33.90 | 23.00 | 37.50 | 38.70 |
| Qwen2.5-VL-7B-Instruct | 69.20 | 21.80 | 34.10 | 18.00 | 32.30 | 35.08 |
| Supervised Fine-Tuning (ours) | ||||||
| Seed-only SFT | 74.10 | 36.16 | 65.02 | 26.96 | 56.76 | 51.80 |
| VeriEvol-SFT | 76.60 | 39.80 | 67.01 | 30.94 | 59.33 | 54.73 |
| Reinforcement Learning (ours) | ||||||
| RL-Origin | 77.00 | 41.45 | 69.04 | 30.54 | 58.19 | 55.24 |
| RL-Evol | 78.10 | 45.39 | 69.67 | 32.14 | 60.00 | 57.06 |
| RL-Evol + Verifier (full VeriEvol) | 79.00 | 47.37 | 70.46 | 35.73 | 63.05 | 59.12 |
Full VeriEvol adds +3.88 average points over RL-Origin, including +1.82 from evolved prompts and +2.06 from HTV-Agent verification.
The paper describes the release of prompts, data, models, code, and the full verifier trace of every accepted sample. Public links were not included in the provided PDF, so this page keeps the paper live and reserves release slots for upcoming artifacts.
@article{li2026verievol,
title={VeriEvol: Scaling Multimodal Mathematical Reasoning via Verifiable Evol-Instruct},
author={Li, Haoling and Zheng, Kai and Wu, Jie and Xu, Can and Sun, Qingfeng and Hu, Han and Yang, Yujiu},
year={2026}
}