(VLMs) struggle with spatial reasoning because they are trained on 2D projections and lack understanding of 3D geometry and temporal continuity. FactoSR tackles this by decomposing the monolithic problem into three orthogonal sub-objectives: planar correspondence (XY), depth consistency (Z), and temporal reversibility (T). It uses with verifiable rewards for each dimension, guided by a multi-objective reward framework that includes format, accuracy, and geometric rewards.
The framework combines supervised fine-tuning (FactoSR-SFT) with reinforcement learning (FactoSR-RL) to transition from initial spatial perception to explicit reasoning. Evaluated on multi-view and video benchmarks, FactoSR achieves a 5.9% boost on VSI-Bench and a 4.5% boost on All-Angles-Bench. This is significant because it provides a principled way to inject explicit 4D reasoning into VLMs without requiring monolithic 4D optimization.