# Consistency as Inductive Bias: Learning Cross-View Invariance for Robust Multimodal Reasoning

arXiv: https://arxiv.org/abs/2606.29812 · HTML: https://mlsanity.com/paper/2606.29812/

## 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 25 of its 58 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Evaluating Object Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2305.10355/) (2023)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [VLM-R1: A Stable and Generalizable R1-style Large Vision-Language Model](https://mlsanity.com/paper/2504.07615/) (2025)
- [Visual-RFT: Visual Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.01785/) (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)
- [AMBER: An LLM-free Multi-dimensional Benchmark for MLLMs Hallucination Evaluation](https://mlsanity.com/paper/2311.07397/) (2023)
- [Reason-RFT: Reinforcement Fine-Tuning for Visual Reasoning of Vision Language Models](https://mlsanity.com/paper/2503.20752/) (2025)
- [NoisyRollout: Reinforcing Visual Reasoning with Data Augmentation](https://mlsanity.com/paper/2504.13055/) (2025)
- [Look Twice Before You Answer: Memory-Space Visual Retracing for Hallucination Mitigation in Multimodal Large Language Models](https://mlsanity.com/paper/2410.03577/) (2024)
- [Eagle 2: Building Post-Training Data Strategies from Scratch for Frontier Vision-Language Models](https://mlsanity.com/paper/2501.14818/) (2025)
- [R1-ShareVL: Incentivizing Reasoning Capability of Multimodal Large Language Models via Share-GRPO](https://mlsanity.com/paper/2505.16673/) (2025)
- [Perception-R1: Advancing Multimodal Reasoning Capabilities of MLLMs via Visual Perception Reward](https://mlsanity.com/paper/2506.07218/) (2025)
- [EDGE-GRPO: Entropy-Driven GRPO with Guided Error Correction for Advantage Diversity](https://mlsanity.com/paper/2507.21848/) (2025)
- [Reefknot: A Comprehensive Benchmark for Relation Hallucination Evaluation, Analysis and Mitigation in Multimodal Large Language Models](https://mlsanity.com/paper/2408.09429/) (2024)

## Abstract (arXiv)

Inductive biases steer learning toward generalizable solutions by encoding task structure. In this work, we identify a crucial missing bias in MLLMs: cross-view consistency, textiti.e., semantically invariant views of the same instance should lead to the same answer. Standard reinforcement learning with verifiable rewards (RLVR) objectives do not impose this constraint, but instead assign pointwise rewards to each visual input. Even with data augmentation (DA), transformed views are typically rewarded independently, providing little signal once within-view rewards saturate. We propose ConsistRoll, a simple but effective method that injects cross-view consistency into RLVR training by reusing the group-sampling mechanism of GRPO. Specifically, ConsistRoll places original and semantically invariant transformed views in the same generation group, and assigns a joint reward only when paired completions are both correct and consistent. In this way, ConsistRoll turns consistency into an online credit-assignment signal, without extra generation overhead and annotations. Theoretically, we show that cross-view consistency is a valid inductive bias, and ConsistRoll introduces a cross-view correction term absent from DA, penalizing view dependence and alleviating advantage collapse. Comprehensive benchmarks across math, general-purpose, hallucination domains confirm that ConsistRoll achieves robust improvements in multimodal reasoning.