---
title: "Improving Multimodal Reasoning via Worst Dimension Optimization"
authors:
  - "Haocheng Lv"
  - "Huaping Zhang"
  - "Qiuchi Li"
  - "Lei Li"
  - "Chunxiao Gao"
doi: "10.24963/ijcai.2026/166"
url: "https://ijcai.org/proceedings/2026/166"
pdf: "https://ijcai.org/proceedings/2026/0166.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "1487-1495"
track: "Main Track"
keywords:
  - "Knowledge Representation and Reasoning: Learning and reasoning"
  - "Natural Language Processing: Question answering"
  - "Computer Vision: Vision, language and reasoning"
---

# Improving Multimodal Reasoning via Worst Dimension Optimization

Haocheng Lv, Huaping Zhang, Qiuchi Li, Lei Li, Chunxiao Gao

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 1487-1495. DOI: [10.24963/ijcai.2026/166](https://doi.org/10.24963/ijcai.2026/166)

## Abstract

Multimodal reasoning requires a path that retains integrity over a wide range of constraints, from visual grounding to logic consistency. However, the current Process Reward Models (PRMs) focus on heuristically defined rewards that equally weigh these factors, which may lead to the concealment of individual dimension failures (such as visual hallucinations) by the dominating factors, without guaranteeing the validity of the reasoning process in general. Therefore, to overcome the limitation, the paper proposes the concept of Multimodal Multi-Dimensional Scalarization Process Reward Modeling (MMS-PRM), a paradigm specifically developed to enforce the worst dimension’s robustness in multimodal reasoning. Specifically, a hierarchical fine-grained reward space is developed to represent the multimodal risks in the reasoning tasks, and a Chebyshev-based Monte Carlo Tree Search (MCTS) algorithm is introduced, in which the primary focus during the path searching is given to the worst-performing dimension. Moreover, a curriculum-based Direct Preference Optimization (DPO) approach is developed to gradually learn the balanced reasoning skills in the policy. The experimental results show that, without the dimension collapse issue, the MMS-PRM approach significantly improves the reliability of the multimodal reasoning performance and reaches competitive results in various challenging tasks. The code is available at https://github.com/leibniz-Man/MMS-PRM