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

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.