Thinking with Images as Continuous Actions: Numerical Visual Chain-of-Thought

TL;DR

This paper introduces NV-CoT, a novel framework enabling multimodal large language models to perform visual reasoning using continuous numerical coordinates, improving localization and accuracy over existing methods.

Contribution

NV-CoT allows MLLMs to reason over images with continuous coordinates, reducing modality mismatch and architectural complexity, and supports both supervised and reinforcement learning training.

Findings

Significantly improves localization precision.

Enhances final answer accuracy.

Accelerates training convergence.

Abstract

Recent multimodal large language models (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 eight 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. The code is available in https://github.com/kesenzhao/NV-CoT.