# FRISM: Fine-Grained Reasoning Injection via Subspace-Level Model Merging for Vision-Language Models

arXiv: https://arxiv.org/abs/2601.21187 · HTML: https://mlsanity.com/paper/2601.21187/

## 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 29 of its 69 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 29 of 29)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025)
- [Evaluating Object Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2305.10355/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [SEED-Bench: Benchmarking Multimodal LLMs with Generative Comprehension](https://mlsanity.com/paper/2307.16125/) (2023)
- [Are We on the Right Way for Evaluating Large Vision-Language Models?](https://mlsanity.com/paper/2403.20330/) (2024)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning](https://mlsanity.com/paper/2504.08837/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Multimodal Chain-of-Thought Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2503.12605/) (2025)
- [SoTA with Less: MCTS-Guided Sample Selection for Data-Efficient Visual Reasoning Self-Improvement](https://mlsanity.com/paper/2504.07934/) (2025)
- [No Task Left Behind: Isotropic Model Merging with Common and Task-Specific Subspaces](https://mlsanity.com/paper/2502.04959/) (2025)
- [Efficient and Effective Weight-Ensembling Mixture of Experts for Multi-Task Model Merging](https://mlsanity.com/paper/2410.21804/) (2024)
- [On Predictability of Reinforcement Learning Dynamics for Large Language Models](https://mlsanity.com/paper/2510.00553/) (2025)
- [ProxyThinker: Test-Time Guidance through Small Visual Reasoners](https://mlsanity.com/paper/2505.24872/) (2025)
- [SCI-Verifier: Scientific Verifier with Thinking](https://mlsanity.com/paper/2509.24285/) (2025)
- [SmallThinker: A Family of Efficient Large Language Models Natively Trained for Local Deployment](https://mlsanity.com/paper/2507.20984/) (2025)
- [Training-Free Reasoning and Reflection in MLLMs](https://mlsanity.com/paper/2505.16151/) (2025)
- [DRIFT: Transferring Reasoning Priors for Efficient MLLM Fine-Tuning](https://mlsanity.com/paper/2510.15050/) (2025)
- [Revisiting Multimodal KV Cache Compression: A Frequency-Domain-Guided Outlier-KV-Aware Approach](https://mlsanity.com/paper/2511.16786/) (2025)

## Abstract (arXiv)

Efficiently enhancing the reasoning capabilities of Vision-Language Models (VLMs) by merging them with Large Reasoning Models (LRMs) has emerged as a promising direction. However, existing methods typically operate at a coarse-grained layer level, which often leads to a trade-off between injecting reasoning capabilities and preserving visual capabilities. To address this limitation, we propose FRISM (Fine-grained Reasoning Injection via Subspace-level model Merging), a fine-grained reasoning injection framework based on subspace-level model merging. Observing that different SVD subspaces contribute differently to reasoning and perception, FRISM decomposes LRM task vectors via Singular Value Decomposition (SVD) and adaptively tunes the scaling coefficients of each subspace through learning to realize fine-grained reasoning injection. Furthermore, we introduce a label-free self-distillation learning strategy with dual-objective optimization using common vision-language perception datasets. Extensive experiments demonstrate that FRISM effectively improves reasoning capabilities while largely preserving the model's visual capabilities by consistently achieving strong performance across diverse visual-language reasoning benchmarks.