# MIRROR: Learning from the Other View for Multi-Modal Reasoning

arXiv: https://arxiv.org/abs/2607.21552 · HTML: https://mlsanity.com/paper/2607.21552/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 51 of its 61 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 30 of 51)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [InternVL: Scaling up Vision Foundation Models and Aligning for Generic Visual-Linguistic Tasks](https://mlsanity.com/paper/2312.14238/) (2023)
- [VQA: Visual Question Answering](https://mlsanity.com/paper/1505.00468/) (2015)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [LMMs-Eval: Reality Check on the Evaluation of Large Multimodal Models](https://mlsanity.com/paper/2407.12772/) (2024)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models](https://mlsanity.com/paper/2406.17294/) (2024)
- [Insight-V: Exploring Long-Chain Visual Reasoning with Multimodal Large Language Models](https://mlsanity.com/paper/2411.14432/) (2024)
- [Perception-Aware Policy Optimization for Multimodal Reasoning](https://mlsanity.com/paper/2507.06448/) (2025)

## Built on by (most cited first, 1 of 1)

- [Controlled Decoding Attacks on Black-Box LLMs](https://mlsanity.com/paper/2609.36956/) (2026)

## Abstract (arXiv)

Vision-language models (VLMs) can behave very differently depending on whether the same underlying problem is presented textually or visually. This inconsistency suggests that different views expose different reasoning paths and failure modes that standard multimodal post-training does not fully exploit. To study and exploit this phenomenon, we construct ODA-Data, a high-quality paired multimodal geometry dataset with text-dominant, image-dominant, and combined image+text views of the same problems, together with splits for training and evaluating view dependent reasoning behaviors. We then develop Modality-Informed Reciprocal Reasoning Optimization (MIRROR), a reinforcement learning approach that derives a cross-view self-distillation signal from the model's own modality-dependent capabilities. For each problem, MIRROR evaluates the model under all views, selects the best-performing view as a teacher, and trains the remaining views using a GRPO task-reward objective augmented with a reverse-KL regularizer toward that teacher. Across reasoning benchmarks that evaluate on multimodal mathematics problems, MIRROR improves over standard RL and yields more accurate and consistent behavior across different input modality representations.