Reinforcement learning (RL) as post-training is crucial for enhancing the reasoning ability of large language models (LLMs) in coding and math. However, their capacity for visual semantic arithmetic, inferring relationships from images, remains underexplored. The classic text analogy "king"-"man"+"woman" = "queen" illustrates relational reasoning, yet replacing text with images of "king" and "man" significantly reduces performance because it requires commonsense knowledge and the extraction of concise concepts from irrelevant visual details. This capability is important for service and domestic robotics in unstructured environments, where robots must infer semantic relationships among objects, agents, and actions. In a kitchen, recognizing from images that "powder" and "cake" are related by "is made of" grounds symbolic relations in perception, enabling tool substitution, task generalization, and improved semantic reasoning. Prior work approaches semantic arithmetic by decoding image features after vector arithmetic, but suffers from modality gaps and lacks systematic evaluation. In this paper, we formulate two novel tasks, two-term subtraction and three-term operations, and construct the Image-Relation-Pair Dataset (IRPD) for benchmarking. We further propose Semantic Arithmetic Reinforcement Fine-Tuning (SAri-RFT), which post-trains large vision-language models (LVLMs) using a verifiable function and Group Relative Policy Optimization (GRPO). Our method achieves state-of-the-art results on IRPD and the real-world Visual7W-Telling dataset. By equipping LVLMs with robust cross-modal relational reasoning, this work advances domestic robots' ability to ground symbolic reasoning in perception, enhancing decision-making, tool adaptability, and human-robot interaction in complex environments. Datasets and source code are provided in the supplementary material.
Recent progress in large-scale reinforcement learning (RL) has notably enhanced the reasoning capabilities of large language models (LLMs), especially in mathematical domains. However, current multimodal LLMs (MLLMs) for mathematical reasoning often rely on one-to-one image-text pairs and single-solution supervision, overlooking the diversity of valid reasoning perspectives and internal reflections. In this work, we introduce MathV-DP, a novel dataset that captures multiple diverse solution trajectories for each image-question pair, fostering richer reasoning supervision. We further propose Qwen-VL-DP, a model built upon Qwen-VL, fine-tuned with supervised learning and enhanced via group relative policy optimization (GRPO), a rule-based RL approach that integrates correctness discrimination and diversity-aware reward functions. Our method emphasizes learning from varied reasoning perspectives and distinguishing between correct yet distinct solutions. Extensive experiments on the MathVista's minitest and Math-V benchmarks demonstrate that Qwen-VL-DP significantly outperforms prior base MLLMs in both accuracy and generative diversity, highlighting the importance of incorporating diverse perspectives and reflective reasoning in multimodal mathematical reasoning.
Chain-of-Thought (CoT) improves the performance of Large Language Models (LLMs) and has been extended to Multimodal Large Language Models (MLLMs). More recent work further moves from text-based multimodal reasoning toward interleaved-modal reasoning, where intermediate steps can incorporate both textual rationales and visual evidence. In this work, we propose a bolder and more ambitious idea: could images alone serve as the reasoning medium for both language and multimodal tasks? To explore this, we propose optical reasoning, which treats images as a standalone reasoning medium. We instantiate this concept with two variants: typographic-based optical reasoning, which optimizes visual layouts for compact rationale rendering, and graphical-based optical reasoning, which composes text and graphical elements into structured visual rationales. Across mathematical, scientific, and interleaved-modal reasoning benchmarks, optical reasoning can match or even exceed traditional text reasoning while reducing reasoning tokens by an average of 28.57% on language tasks and 16% on multimodal tasks, achieving 1.96 times the token efficiency of text reasoning. These results show that images can effectively and efficiently encode rationales while providing a unified visual canvas for reasoning.
Despite their popularity and success, Multimodal Large Language Models (MLLMs) often struggle to interpret images accurately, which limits their reasoning capability in complex scenarios (e.g., high object density and complex background clutter). Prior work mainly addresses this limitation by incorporating explicit visual cues like bounding boxes that require extra annotations. In addition, the resulting low-resolution crops often miss fine-grained details that MLLMs require for accurate reasoning. Therefore, we propose Mags-RL, an Agentic Reinforcement Learning (RL) framework that equips MLLMs with an external super-resolution "magnifying glass" agent for high-resolution fine-grained inspection. Specifically, the model performs two-round reasoning: in the first round, it generates an initial rationale and autonomously identifies regions of interest without relying on additional annotations; in the second round, it invokes a super-resolution agent to crop and upscale those regions, then revisits and verifies its earlier reasoning to produce the final answer. We also introduce a novel curriculum learning strategy that enables data-efficient RL training, needing as few as only 40 training samples to achieve reasonable performance. Experiments on VSR, TallyQA, and GQA subsets show its superior performance against recent strong competing methods, demonstrating high-quality reasoning with precise visual grounding. Code and weights will be released soon.