# Thinking with Deltas: Incentivizing Reinforcement Learning via Differential Visual Reasoning Policy

arXiv: https://arxiv.org/abs/2601.06801 · HTML: https://mlsanity.com/paper/2601.06801/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 69 of its 97 references that are in the map.
- First posted on arXiv 11 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 69)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [LLaVA-Med: Training a Large Language-and-Vision Assistant for Biomedicine in One Day](https://mlsanity.com/paper/2306.00890/) (2023)
- [Shikra: Unleashing Multimodal LLM's Referential Dialogue Magic](https://mlsanity.com/paper/2306.15195/) (2023)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [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)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [PathVQA: 30000+ Questions for Medical Visual Question Answering](https://mlsanity.com/paper/2003.10286/) (2020)
- [SLAKE: A Semantically-Labeled Knowledge-Enhanced Dataset for Medical Visual Question Answering](https://mlsanity.com/paper/2102.09542/) (2021)
- [AFlow: Automating Agentic Workflow Generation](https://mlsanity.com/paper/2410.10762/) (2024)
- [DeepEyes: Incentivizing "Thinking with Images" via Reinforcement Learning](https://mlsanity.com/paper/2505.14362/) (2025)
- [Med-Flamingo: a Multimodal Medical Few-shot Learner](https://mlsanity.com/paper/2307.15189/) (2023)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [PMC-VQA: Visual Instruction Tuning for Medical Visual Question Answering](https://mlsanity.com/paper/2305.10415/) (2023)
- [VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning](https://mlsanity.com/paper/2504.08837/) (2025)
- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (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)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)

## Built on by (most cited first, 6 of 6)

- [Beyond SFT-to-RL: Pre-alignment via Black-Box On-Policy Distillation for Multimodal RL](https://mlsanity.com/paper/2604.28123/) (2026)
- [VAD: Attributing Visual Evidence for Target Reconstruction in Multimodal On-Policy Distillation](https://mlsanity.com/paper/2607.28590/) (2026)
- [Thinking With Tools, Not With Pixels: Tool Calls as Text Scaffolds for Visual Reasoning](https://mlsanity.com/paper/2608.09682/) (2026)
- [When Does a Video-Language Model Stop Watching? Reward Strength Controls the Formation and Reversal of Visual Shortcuts in Multimodal RLVR](https://mlsanity.com/paper/2606.22043/) (2026)
- [SIVA-RL: Sensitivity-Invariance Visual Alignment for Multimodal Reinforcement Learning](https://mlsanity.com/paper/2607.13931/) (2026)
- [Evidence-Aligned Multimodal On-Policy Self-Distillation for Fine-Grained Visual Understanding](https://mlsanity.com/paper/2609.34672/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced reasoning capabilities in Large Language Models. However, adapting RLVR to multimodal domains suffers from a critical textitperception-reasoning decoupling. Existing paradigms, driven by text-centric outcome rewards, reasoning in language medium, inadvertently encourage models to bypass visual perception. We empirically validate this through blind experiments: state-of-the-art policies maintain or surprisingly improve performance even when visual inputs are entirely removed. This reveals that these models degenerate into textitblind reasoners, exploiting linguistic priors to generate plausible answers instead of attending to visual evidence. In response, we propose Thinking with Deltas, a framework driven by a Differential Visual Reasoning Policy (DVRP). DVRP introduces intrinsic supervision via visual triplets, comprising original, masked, and perturbed inputs. It optimizes the model to maximize reasoning divergence from masked inputs (enforcing textitvisual sensitivity) while minimizing divergence from perturbed inputs (ensuring textitvisual robustness). By aligning reasoning variations strictly with the textitDelta of visual information, DVRP inherently bolsters visual understanding capabilities and significantly outperforms state-of-the-art methods on both general and medical benchmarks, without requiring external annotations or auxiliary tools.