What they did

The authors divided spatial reasoning into three geometric objectives: planar correspondence in the image plane (XY), depth consistency (Z), and temporal reversibility (T), which tests whether reasoning remains consistent across changes over time.

They optimized these separately verifiable constraints within a unified reinforcement-learning framework, then evaluated the resulting vision-language models on multi-view and video-based spatial-reasoning benchmarks.

Key findings

• FactoSR improved performance on VSI-Bench by 5.9%, according to the authors.
• It produced a 4.5% gain on All-Angles-Bench.
• The results indicate that explicitly training planar, depth, and temporal consistency can outperform treating spatial reasoning as a single undivided objective.

Why it matters

Visual inputs collapse a 3D, changing world into 2D projections. FactoSR offers a structured way to train models against that information loss, suggesting that verifiable geometric sub-objectives may be more effective than relying on general multimodal training alone for world-consistent reasoning.

Caveats

The reported evidence is benchmark-based and does not by itself establish robust reasoning in unconstrained physical environments. The abstract also does not provide absolute scores, model-specific results, ablations for each geometric objective, or evidence that the gains transfer beyond the evaluated multi-view and video tasks.