# Improving Multimodal Reasoning via Worst Dimension Optimization

arXiv: https://arxiv.org/abs/2606.07801 · HTML: https://mlsanity.com/paper/2606.07801/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 20 of 20)

- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [MiniCPM-V: A GPT-4V Level MLLM on Your Phone](https://mlsanity.com/paper/2408.01800/) (2024)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [R1-VL: Learning to Reason with Multimodal Large Language Models via Step-wise Group Relative Policy Optimization](https://mlsanity.com/paper/2503.12937/) (2025)
- [Enhancing the Reasoning Ability of Multimodal Large Language Models via Mixed Preference Optimization](https://mlsanity.com/paper/2411.10442/) (2024)
- [InternLM-XComposer-2.5: A Versatile Large Vision Language Model Supporting Long-Contextual Input and Output](https://mlsanity.com/paper/2407.03320/) (2024)
- [Ovis: Structural Embedding Alignment for Multimodal Large Language Model](https://mlsanity.com/paper/2405.20797/) (2024)
- [VisualPRM: An Effective Process Reward Model for Multimodal Reasoning](https://mlsanity.com/paper/2503.10291/) (2025)
- [Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTS](https://mlsanity.com/paper/2411.18478/) (2024)
- [3DSceneEditor: Controllable 3D Scene Editing with Gaussian Splatting](https://mlsanity.com/paper/2412.01583/) (2024)
- [Training Vision-Language Process Reward Models for Test-Time Scaling in Multimodal Reasoning: Key Insights and Lessons Learned](https://mlsanity.com/paper/2509.23250/) (2025)
- [RAM: Recover Any 3D Human Motion in-the-Wild](https://mlsanity.com/paper/2603.19929/) (2026)
- [Graph Canvas for Controllable 3D Scene Generation](https://mlsanity.com/paper/2412.00091/) (2024)
- [Learning an Efficient Optimizer via Hybrid-Policy Sub-Trajectory Balance](https://mlsanity.com/paper/2511.00543/) (2025)
- [PSGS: Text-driven Panorama Sliding Scene Generation via Gaussian Splatting](https://mlsanity.com/paper/2602.00463/) (2026)

## Abstract (arXiv)

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 focus on heuristically defined rewards that equally weigh these factors, which may lead to the concealment of individual dimension failures by the dominating factors, without guaranteeing the validity of the reasoning process in general.