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

Task-driven 3D affordance grounding aims to localize the functional region in a cluttered 3D scene that enables an action specified by a natural-language instruction. Existing methods either predict 3D masks directly or construct them by selecting and fusing intermediate 2D/3D regions. However, they remain vulnerable to two intertwined failure modes: the predicted or selected regions may miss the target interaction area or have unsuitable granularity, while language grounding may confuse visually similar alternatives under relational instructions. To this end, we introduce ThinkAfford, which decouples high-recall affordance proposal generation from instruction-grounded reasoning. Specifically, the Affordance Proposal Generation module first uses learnable affordance prompts and multi-level visual features to predict interaction-conditioned heatmaps, extracting a variable number of fine-grained proposals without parsed object or part names as segmentation prompts. Visual-Prompted Affordance Reasoning then reasons over labeled proposal overlays using the full instruction, returning identifiers in a structured "think-then-answer" response. Moreover, Group Relative Policy Optimization uses proposal-level rewards from lifted 3D overlap to align VPAR selection with final 3D grounding. On the SceneFun3D validation split, ThinkAfford achieves 10.69% AP50 and 25.46% AP25 under the official evaluator, outperforming comparable 3D open-vocabulary and vision-language-model-based 2D-to-3D baselines. Module-level diagnostics further show that APG attains 77.5% recall at 25% intersection-over-union, while GRPO-trained VPAR achieves 72.1% selection accuracy on APG-covered queries, compared with 63.4% under supervised fine-tuning.

Vision-language models (VLMs) have achieved strong performance in multimodal understanding and reasoning, yet grounded reasoning in 3D scenes remains underexplored. Effective 3D reasoning hinges on accurate grounding: to answer open-ended queries, a model must first identify query-relevant objects and regions in a complex scene, and then reason about their spatial and geometric relationships. Recent approaches have demonstrated strong potential for grounded 3D reasoning. However, they often rely on in-domain tuning or hand-crafted reasoning pipelines, which limit their flexibility and zero-shot generalization to novel environments. In this work, we present MAG-3D, a training-free multi-agent framework for grounded 3D reasoning with off-the-shelf VLMs. Instead of relying on task-specific training or fixed reasoning procedures, MAG-3D dynamically coordinates expert agents to address the key challenges of 3D reasoning. Specifically, we propose a planning agent that decomposes the task and orchestrates the overall reasoning process, a grounding agent that performs free-form 3D grounding and relevant frame retrieval from extensive 3D scene observations, and a coding agent that conducts flexible geometric reasoning and explicit verification through executable programs. This multi-agent collaborative design enables flexible training-free 3D grounded reasoning across diverse scenes and achieves state-of-the-art performance on challenging benchmarks.

Functional affordance grounding requires more than recognizing an object: an agent must localize the specific region that supports an interaction, such as the handle to pull or the button to press. This is difficult for training-free vision-language pipelines because actionable regions are often small, visually ambiguous, and repeated across multiple same-category instances in a scene. We propose AFFORDMEM, a framework that grounds 3D functional affordances by remembering geometry at two levels. The first is cross-scene affordance memory: the agent maintains a category-level memory bank of RGB images with affordance regions rendered as overlays, and recalls the most informative examples at query time to guide a frozen VLM toward small operable subregions that text-only prompting consistently misses. The second is in-scene spatial memory: as the agent processes the scene, it organizes candidate instances and their 3D spatial relations into a structured scene graph, enabling the language model to resolve references over distant or currently unobserved candidates such as "the second handle from the top." AFFORDMEM requires no model fine-tuning and no target-scene annotation, using a reusable memory bank built from source scenes. On SceneFun3D, our method improves AP50 over the prior training-free state of the art by 3.23 on Split 0 and 3.7 on Split 1. Ablation studies support complementary benefits: cross-scene affordance memory improves fine-grained localization, while in-scene spatial memory provides the larger gain on spatially qualified queries. The project homepage is available at the project page.