Canvas-of-Thought: Grounding Reasoning via Mutable Structured States

While Chain-of-Thought (CoT) prompting has significantly advanced the reasoning capabilities of Multimodal Large Language Models (MLLMs), relying solely on linear text sequences remains a bottleneck for complex tasks. We observe that even when auxiliary visual elements are interleaved, they are often treated as static snapshots within a one-dimensional, unstructured reasoning chain. We argue that such approaches treat reasoning history as an immutable stream: correcting a local error necessitates either generating verbose downstream corrections or regenerating the entire context. This forces the model to implicitly maintain and track state updates, significantly increasing token consumption and cognitive load. This limitation is particularly acute in high-dimensional domains, such as geometry and SVG design, where the textual expression of CoT lacks explicit visual guidance, further constraining the model's reasoning precision. To bridge this gap, we introduce \textbf{Canvas-of-Thought (Canvas-CoT)}. By leveraging a HTML Canvas as an external reasoning substrate, Canvas-CoT empowers the model to perform atomic, DOM-based CRUD operations. This architecture enables in-place state revisions without disrupting the surrounding context, allowing the model to explicitly maintain the "ground truth". Furthermore, we integrate a rendering-based critique loop that serves as a hard constraint validator, providing explicit visual feedback to resolve complex tasks that are difficult to articulate through text alone. Extensive experiments on VCode, RBench-V, and MathVista demonstrate that Canvas-CoT significantly outperforms existing baselines, establishing a new paradigm for context-efficient multimodal reasoning.

Guided Verifier: Collaborative Multimodal Reasoning via Dynamic Process Supervision

Reinforcement Learning (RL) has emerged as a pivotal mechanism for enhancing the complex reasoning capabilities of Multimodal Large Language Models (MLLMs). However, prevailing paradigms typically rely on solitary rollout strategies where the model works alone. This lack of intermediate oversight renders the reasoning process susceptible to error propagation, where early logical deviations cascade into irreversible failures, resulting in noisy optimization signals. In this paper, we propose the \textbf{Guided Verifier} framework to address these structural limitations. Moving beyond passive terminal rewards, we introduce a dynamic verifier that actively co-solves tasks alongside the policy. During the rollout phase, this verifier interacts with the policy model in real-time, detecting inconsistencies and providing directional signals to steer the model toward valid trajectories. To facilitate this, we develop a specialized data synthesis pipeline targeting multimodal hallucinations, constructing \textbf{CoRe} dataset of process-level negatives and \textbf{Co}rrect-guide \textbf{Re}asoning trajectories to train the guided verifier. Extensive experiments on MathVista, MathVerse and MMMU indicate that by allocating compute to collaborative inference and dynamic verification, an 8B-parameter model can achieve strong performance.