# A3R: Agentic Affordance Reasoning via Cross-Dimensional Evidence in 3D Gaussian Scenes

arXiv: https://arxiv.org/abs/2604.01882 · HTML: https://mlsanity.com/paper/2604.01882/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- LLM agents and tool use / [Multimodal and embodied agents](https://mlsanity.com/agents/multimodal-and-embodied-agents/)

## Builds on (most cited first, 13 of 13)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [SAM 3: Segment Anything with Concepts](https://mlsanity.com/paper/2511.16719/) (2025)
- [ConceptFusion: Open-set Multimodal 3D Mapping](https://mlsanity.com/paper/2302.07241/) (2023)
- [OpenMask3D: Open-Vocabulary 3D Instance Segmentation](https://mlsanity.com/paper/2306.13631/) (2023)
- [Learning Social Affordance for Human-Robot Interaction](https://mlsanity.com/paper/1604.03692/) (2016)
- [ActiveVLA: Injecting Active Perception into Vision-Language-Action Models for Precise 3D Robotic Manipulation](https://mlsanity.com/paper/2601.08325/) (2026)
- [Tackling View-Dependent Semantics in 3D Language Gaussian Splatting](https://mlsanity.com/paper/2505.24746/) (2025)
- [AffordBot: 3D Fine-grained Embodied Reasoning via Multimodal Large Language Models](https://mlsanity.com/paper/2511.10017/) (2025)
- [Visibility-Aware Language Aggregation for Open-Vocabulary Segmentation in 3D Gaussian Splatting](https://mlsanity.com/paper/2509.05515/) (2025)
- [A4-Agent: An Agentic Framework for Zero-Shot Affordance Reasoning](https://mlsanity.com/paper/2512.14442/) (2025)
- [EgoSplat: Open-Vocabulary Egocentric Scene Understanding with Language Embedded 3D Gaussian Splatting](https://mlsanity.com/paper/2503.11345/) (2025)
- [SeqAffordSplat: Scene-level Sequential Affordance Reasoning on 3D Gaussian Splatting](https://mlsanity.com/paper/2507.23772/) (2025)

## Abstract (arXiv)

Affordance reasoning in 3D Gaussian scenes aims to identify the region that supports the action specified by a given text instruction in complex environments. Existing methods typically cast this problem as one-shot prediction from static scene observations, assuming sufficient evidence is already available for reasoning. However, in complex 3D scenes, many failure cases arise not from weak prediction capacity, but from incomplete task-relevant evidence under fixed observations. To address this limitation, we reformulate fine-grained affordance reasoning as a sequential evidence acquisition process, where ambiguity is progressively reduced through complementary 3D geometric and 2D semantic evidence. Building on this formulation, we propose A3R, an agentic affordance reasoning framework that enables an MLLM-based policy to iteratively select evidence acquisition actions and update the affordance belief through cross-dimensional evidence acquisition. To optimize such sequential decision making, we further introduce a GRPO-based policy learning strategy that improves evidence acquisition efficiency and reasoning accuracy. Extensive experiments on scene-level benchmarks show that A3R consistently surpasses static one-shot baselines, demonstrating the advantage of agentic cross-dimensional evidence acquisition for fine-grained affordance reasoning in complex 3D Gaussian scenes.