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

The paper introduces Numerical Visual Chain-of-Thought (NV‑CoT), a framework that expands multimodal large language models (MLLMs) to reason over images using continuous numerical coordinates instead of discrete tokens or fixed patches. NV‑CoT allows MLLMs to generate bounding‑box coordinates directly as actions with minimal architectural changes, supporting both supervised fine‑tuning and reinforcement learning via a Gaussian or Laplace policy. Experiments on three benchmarks show that NV‑CoT improves localization precision, answer accuracy, and training convergence compared to 11 visual reasoning baselines.

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• reinforcement-learning
• fine-tuning
• benchmarks