# Thinking with Images without Coordinates

arXiv: https://arxiv.org/abs/2610.14265 · HTML: https://mlsanity.com/paper/2610.14265/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 49 of its 56 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 49)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Evaluating Object Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2305.10355/) (2023)
- [Kosmos-2: Grounding Multimodal Large Language Models to the World](https://mlsanity.com/paper/2306.14824/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Visual-RFT: Visual Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.01785/) (2025)
- [Video-R1: Reinforcing Video Reasoning in MLLMs](https://mlsanity.com/paper/2503.21776/) (2025)
- [V*: Guided Visual Search as a Core Mechanism in Multimodal LLMs](https://mlsanity.com/paper/2312.14135/) (2023)
- [LLaVA-CoT: Let Vision Language Models Reason Step-by-Step](https://mlsanity.com/paper/2411.10440/) (2024)
- [DeepEyes: Incentivizing "Thinking with Images" via Reinforcement Learning](https://mlsanity.com/paper/2505.14362/) (2025)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [Pix2seq: A Language Modeling Framework for Object Detection](https://mlsanity.com/paper/2109.10852/) (2021)
- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [MME-RealWorld: Could Your Multimodal LLM Challenge High-Resolution Real-World Scenarios that are Difficult for Humans?](https://mlsanity.com/paper/2408.13257/) (2024)
- [Visual CoT: Advancing Multi-Modal Language Models with a Comprehensive Dataset and Benchmark for Chain-of-Thought Reasoning](https://mlsanity.com/paper/2403.16999/) (2024)
- [Pixel Reasoner: Incentivizing Pixel-Space Reasoning with Curiosity-Driven Reinforcement Learning](https://mlsanity.com/paper/2505.15966/) (2025)
- [LMM-R1: Empowering 3B LMMs with Strong Reasoning Abilities Through Two-Stage Rule-Based RL](https://mlsanity.com/paper/2503.07536/) (2025)
- [Bias Runs Deep: Implicit Reasoning Biases in Persona-Assigned LLMs](https://mlsanity.com/paper/2311.04892/) (2023)
- [Thinking with Images for Multimodal Reasoning: Foundations, Methods, and Future Frontiers](https://mlsanity.com/paper/2506.23918/) (2025)

## Abstract (arXiv)

Recent advances in multi-modal large language models have shifted toward the "thinking with images" paradigm to improve reasoning faithfulness, yet existing methods rely heavily on explicit coordinate- based grounding. We identify two fundamental limitations in this approach, i.e., a semantic gap where sparse regressions miss high-dimensional latent structures, and a resolution gap due to the granularity mismatch between patch-level tokens and pixel-level coordinates. To address these, we propose TiCO (Thinking with images without COordinates). It reformulates visual reasoning as a semantic evidence discovery process within the latent space, and evidence is injected as token-level regions without pixel coordinates. Specifically, TiCO utilizes a dedicated probe token to estimate similarity distributions and performs importance sampling over spatially connected components to generate diverse, semantically dominant evidence rollouts. Extensive experiments across multiple high-resolution and general visual reasoning benchmarks demonstrate that our TiCO consistently outperforms state-of-the-art coordinate-based methods with significantly improved inference efficiency.