Thinking with Images without Coordinates

Recent MLLMs increasingly rely on visual chain-of-thought to perform region-grounded reasoning over images. However, existing approaches ground regions via either textified coordinates (causing modality mismatch and semantic fragmentation) or fixed-granularity patches that both limit precise region selection and often require non-trivial architectural changes. In this paper, we propose Numerical Visual Chain-of-Thought (NV-CoT), a framework that enables MLLMs to reason over images using continuous numerical coordinates. NV-CoT expands the MLLM action space from discrete vocabulary tokens to a continuous Euclidean space, allowing models to directly generate bounding-box coordinates as actions with only minimal architectural modification. The framework supports both supervised fine-tuning and reinforcement learning. In particular, we replace categorical token policies with a Gaussian (or Laplace) policy over coordinates and introduce stochasticity via reparameterized sampling, making NV-CoT fully compatible with GRPO-style policy optimization. Extensive experiments on three benchmarks against 11 representative visual reasoning baselines demonstrate that NV-CoT significantly improves localization precision and final answer accuracy, while also accelerating training convergence, validating the effectiveness of continuous-action visual reasoning in MLLMs. Project page: https://kesenzhao.github.io/NV-CoT/

Recently, Interleaved-modal Chain-of-Thought (ICoT) reasoning has achieved remarkable success by leveraging both multimodal inputs and outputs, attracting increasing attention. While achieving promising performance, current ICoT methods still suffer from two major limitations: (1) Static Visual Thought Positioning, which statically inserts visual information at fixed steps, resulting in inefficient and inflexible reasoning; and (2) Broken Visual Thought Representation, which involves discontinuous and semantically incoherent visual tokens. To address these limitations, we introduce Interleaved-modal Chain-of-Thought reasoning with Dynamic and Precise Visual Thoughts (DaP-ICoT), which incorporates two key components: (1) Dynamic Visual Thought Integration adaptively introduces visual inputs based on reasoning needs, reducing redundancy and improving efficiency. (2) Precise Visual Thought Guidance ensures visual semantically coherent and contextually aligned representations. Experiments across multiple benchmarks and models demonstrate that DaP-ICoT achieves state-of-the-art performance. In addition, DaP-ICoT significantly reduces the number of inserted images, leading to a 72.6% decrease in token consumption, enabling more efficient ICoT 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.