MathFlow: Enhancing the Perceptual Flow of MLLMs for Visual Mathematical
  Problems
Authors: name: Felix Chen, name: Hangjie Yuan, name: Yunqiu Xu, name: Tao Feng, name: Jun Cen, name: Pengwei Liu, name: Zeying Huang, name: Yi Yang

Despite impressive performance across diverse tasks, Multimodal Large
Language Models (MLLMs) have yet to fully demonstrate their potential in visual
mathematical problem-solving, particularly in accurately perceiving and
interpreting diagrams. Inspired by typical processes of humans, we hypothesize
that the perception capabilities to extract meaningful information from
diagrams is crucial, as it directly impacts subsequent inference processes. To
validate this hypothesis, we developed FlowVerse, a comprehensive benchmark
that categorizes all information used during problem-solving into four
components, which are then combined into six problem versions for evaluation.
Our preliminary results on FlowVerse reveal that existing MLLMs exhibit
substantial limitations when extracting essential information and reasoned
property from diagrams and performing complex reasoning based on these visual
inputs. In response, we introduce MathFlow, a modular problem-solving pipeline
that decouples perception and inference into distinct stages, thereby
optimizing each independently. Given the perceptual limitations observed in
current MLLMs, we trained MathFlow-P-7B as a dedicated perception model.
Experimental results indicate that MathFlow-P-7B yields substantial performance
gains when integrated with various closed-source and open-source inference
models. This demonstrates the effectiveness of the MathFlow pipeline and its
compatibility to diverse inference frameworks. The FlowVerse benchmark and code
are available at https://github.com/MathFlow-zju/MathFlow.