# We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?

## Abstract

Visual mathematical reasoning, as a fundamental visual reasoning ability, has received widespread attention from the Large Multimodal Models (LMMs) community. Existing benchmarks, such as MathVista and MathVerse, focus more on the result-oriented performance but neglect the underlying principles in knowledge acquisition and generalization. Inspired by human-like mathematical reasoning, we introduce WE-MATH, the first benchmark specifically designed to explore the problem-solving principles beyond end-to-end performance. We meticulously collect and categorize 6.5K visual math problems, spanning 67 hierarchical knowledge concepts and five layers of knowledge granularity. We decompose composite problems into sub-problems according to the required knowledge concepts and introduce a novel four-dimensional metric, namely Insufficient Knowledge (IK), Inadequate Generalization (IG), Complete Mastery (CM), and Rote Memorization (RM), to hierarchically assess inherent issues in LMMs' reasoning process. With WE-MATH, we conduct a thorough evaluation of existing LMMs in visual mathematical reasoning and reveal a negative correlation between solving steps and problem-specific performance. We confirm the IK issue of LMMs can be effectively improved via knowledge augmentation strategies. More notably, the primary challenge of GPT-4o has significantly transitioned from IK to IG, establishing it as the first LMM advancing towards the knowledge generalization stage. In contrast, other LMMs exhibit a marked inclination towards Rote Memorization - they correctly solve composite problems involving multiple knowledge concepts yet fail to answer sub-problems. We anticipate that WE-MATH will open new pathways for advancements in visual mathematical reasoning for LMMs. The WE-MATH data and evaluation code are available at https://github.com/We-Math/We-Math.

### Community

Visual mathematical reasoning, as a fundamental visual reasoning ability, has received widespread attention from the Large Multimodal Models (LMMs) community. Existing benchmarks focus more on the result-oriented performance, but neglecting the underlying principles in knowledge acquisition and generalization.

Inspired by human-like mathematical reasoning, we introduce WE-MATH, the first benchmark specifically designed to explore the problem-solving principles beyond the end-to-end performance. As shown in upon figure, we meticulously collect and categorize 6.5K visual math problems, spanning 67 hierarchical knowledge concepts and 5 layers of knowledge granularity.

We firstly decompose composite problems into sub-problems according to the required knowledge concepts and introduce a novel four-dimensional metric, namely Insufficient Knowledge (IK), Inadequate Generalization (IG), Complete Mastery (CM), and Rote Memorization (RM) to hierarchically assess inherent issues in LMMs' reasoning process (as shown in upon figure).

With WE-MATH, we conduct a thorough evaluation of existing LMMs in visual mathematical reasoning and reveal a negative correlation between solving step and problem-specific performance. We confirm the IK issue of LMMs can be effectively improved via knowledge augmentation strategy. More notably, the primary challenge of GPT-4o has significantly transitioned from IK to IG, establishing it as the first LMM advancing towards the knowledge generalization stage. In contrast, other LMMs exhibit a marked inclination towards Rote Memorization -- they correctly solve composite problems involving multiple knowledge concepts, yet fail in answering sub-problems. We anticipate that WE-MATH will open new pathways for advancements in visual mathematical reasoning for LMMs.

All our resources are open source !

Project link: https://we-math.github.io/

Code: https://github.com/We-Math/We-Math

Dataset: https://huggingface.co/datasets/We-Math/We-Math

Hi @dongguanting congrats on this work!

I see your dataset is currently hosted here: https://github.com/We-Math/We-Math/tree/main/data, would you be up for pushing it to the hub and linking it to this paper?

See here for a guide: https://huggingface.co/docs/datasets/loading#json.

Let me know if you need any help.

Kind regards,

Niels

Thanks, we will push to the hub.

Our dataset link on huggingface dataset: https://huggingface.co/datasets/We-Math/We-Math

Thanks, would it be possible to link it to the paper? https://huggingface.co/datasets/We-Math/We-Math/discussions/1

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