Self-Evolving Spatial Reasoning in Vision Language Models via Geometric Logic Consistency

Vision-Language Models (VLMs) have made striking progress, yet their spatial reasoning remains fragile. Models that answer an original input correctly can still fail under valid transformations with predictable answer mappings, revealing a gap between instance-level correctness and robust spatial reasoning. To address this, we propose **S**patial **A**lignment via **G**eometric **E**volution (SAGE), a self-evolving framework that improves robust spatial reasoning through geometric and linguistic duality operations. SAGE incorporates duality consistency into GRPO training, encouraging models to produce coherent answers across original and transformed inputs. SAGE co-evolves duality generation and solution, allowing the model to continually expose and address its own reasoning weaknesses. A dynamic operation pool identifies challenging operations and retires mastered ones, keeping training focused on informative duality signals. SAGE is model-agnostic, data-efficient compared to prior post-training methods, and can be applied as a lightweight adaptation stage to any existing VLM. Experiments on video and spatial reasoning benchmarks demonstrate consistent improvements over strong baselines and enhanced generalization to unseen data.