URSA: Understanding and Verifying Chain-of-Thought Reasoning in Multimodal Mathematics

Ruilin Luo* , Zhuofan Zheng* , Yifan Wang , Yiyao Yu , Xinzhe Ni , Zicheng Lin, Jin Zeng†, Yujiu Yang†

* Equal Contribution † Corresponding Authors

Tsinghua University, Bytedance

📣 Updates

• [2025.09.19]: 🎉🎉🎉 URSA has been accepted to NeurIPS2025 Main Track. See you in San Diego!

• [2025.01.27]: URSA-8B has taken the lead in the 4-10B size MLLMs on the Opencampass LMM Reasoning Leaderboard, contributing to the SOTA on Math-Vision. Evaluation of URSA has been supported by VLMEvalKit.

• [2025.01.22]: URSA-8B and URSA-RM-8B have been released, along with open-sourced inference code powered by vLLM!

• [2025.01.08]: Our paper is released on Arxiv Paper. And training data is open-sourced on Huggingface Dataset!

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🔥 Highlights

URSA-8B is the first small-sized MLLM specifically focused on Chain-of-thought multimodal mathematical reasoning.

URSA-RM-8B is the first open-source, small-sized reward model that operates in multimodal mathematics.

• We conduct extensive evaluations on six mathematical benchmarks (MathVista, MathVerse, Dynamath, GeoQA, Math-Vision and We-Math). URSA-8B outperforms similarly sized general and math MLLMs such as Qwen2-VL, InternVL2.5-8B, and InfiMM-Math, as well as closed-source models like GPT-4V, Gemini-1.5-002-Flash, and Gemini1.5-Pro.

• When conducting system-2 reasoning with the verification of URSA-RM-8B, URSA-8B is able to surpass state-of-the-art MLLMs such as GPT-4o on datasets like MathVision and MathVerse! (55.0 vs. 50.8, 35.2 vs. 30.4)

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📚 Introduction

Three stages training

We adopt a three-stage training strategy, including Vision-Language Alignment, Math Instruction Fine Tuning, and PRM Training. Our model architecture employs a hybrid vision tower and Qwen-2.5-Math-Instruct, connecting them using an MLP.

CoT Reasoning Augmentation

We design the CoT reasoning data synthesis through a triple strategy of distillation, trajectory rewriting, and style naturalization, resulting in the MMathCoT-1M instruction fine-tuning data.

System2 reasoning-like Scaling

We continue training the reward model based on URSA-8B, aiming to transform CoT reasoning capabilities into supervised capabilities. We design a Dual-view process supervision data synthesis, including binary error localization and visual misinterpretation insertion, to construct data that focuses on both logical and visual perspectives. It results in DualMath-1.1M.

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🏆 Leaderboards

Table 1: Comparison of major MLLMs on six widely-used multimodal mathematical benchmarks. For WE-MATH, we employ strict metrics. For DYNAMATH, we report average accuracy. For Math-Vision, we use full set for comprehensive evaluation. The notation URSA-8B + URSA-RM-8B indicates that URSA-8B is used as a 32-time reasoning trajectory sampler, and URSA-RM-8B is utilized to select the final answer.

Model	MathVerse	MathVista-GPS	WE-MATH	DYNAMATH	Math-Vision	GeoQA
GPT-4o	50.8	64.7	42.9	63.7	30.4	-
GPT-4V	39.4	50.5	31.1	-	22.8	45.2
Gemini-1.5-Pro	35.3	-	26.4	60.5	19.2	-
Gemini-1.5-Flash-002	49.4	-	-	-	-	-
Qwen2-VL	33.6	40.9	25.6	42.1	16.3	-
InternVL2-8B	35.9	62.0	26.6	39.7	18.4	-
InternVL2-26B	33.4	58.2	-	41.0	17.0	-
InternVL2-40B	37.6	54.8	-	41.8	16.9	-
InternVL2.5-8B	39.5	64.9	-	-	19.7	-
InternVL2.5-26B	40.1	68.8	-	-	23.1	-
Math-LLaVA-13B	22.9	57.7	11.1	-	15.7	-
Multimath	27.7	66.8	-	-	16.3	67.7
Math-PUMA-Qwen2-7B	33.6	48.1	19.2	-	14.0	63.6
URSA-8B (Ours)	45.7	79.3	32.2	44.7	26.2	73.5
URSA-8B + URSA-RM-8B (Ours)	55.0	86.4	-	-	35.2	-

Please refer to our paper to see the specific performance on these benchmarks!

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🔨 Usage

Dataset

The total training datasets are available on Huggingface: URSA-MATH.

Inference

We have adapted the URSA-8B architecture into the vllm project, so you can enjoy faster inference using vllm!

Step 1: Configure vllm.

bash start.sh

Step 2: Configure the inference script located at ./inference/start_vllm_infer.sh. We use mathvista as an example.

TEMPERATURE=0.2
DATASET="mathvista" # dynamath, wemath, mathvista, mathverse, mathvision
IMAGE_ROOT="" # PATH_TO_IMAGE_ROOT
GENERATE_NUM=1

OUTPUT_FILE="./mathvista_$GENERATE_NUM.jsonl"
DATA_PATH="./data/mathvista/mathvista_testmini.jsonl"
MODEL_PATH="./URSA-8B"

echo "Running inference on data_path: $DATA_PATH"
echo "Save output at $OUTPUT_FILE"

CUDA_VISIBLE_DEVICES=0 python3 inference/vllm_infer.py \
  --model $MODEL_PATH \
  --dataset $DATASET \
  --temperature $TEMPERATURE \
  --data_path $DATA_PATH \
  --output_file $OUTPUT_FILE \
  --image_root $IMAGE_ROOT \
  --num_return_sequences $GENERATE_NUM \

Step 3: Start vllm.

bash ./inference/start_vllm_infer.sh

📝 Citation

If you find our paper, model, or data helpful, please give this repo a star 🌟 and cite our article ✏️.

@article{luo2025ursa,
  title={URSA: Understanding and Verifying Chain-of-thought Reasoning in Multimodal Mathematics},
  author={Luo, Ruilin and Zheng, Zhuofan and Wang, Yifan and Yu, Yiyao and Ni, Xinzhe and Lin, Zicheng and Zeng, Jin and Yang, Yujiu},
  journal={arXiv preprint arXiv:2501.04686},
  year={2025}
}