Geometry-Aware Test-Time Learning for Quantitative Spatial Reasoning

Quantitative spatial reasoning in visual-language models (VLMs) aims to infer spatial distances and directional relationships among objects in 3D space from a 2D image and a natural language query. Despite recent progress, VLM spatial reasoning remains brittle under distribution shifts, largely due to the high cost of 3D supervision. As a result, models often produce inconsistent or contradictory predictions when faced with novel object configurations or rephrased spatial queries, revealing a misalignment between learned representations and underlying geometry. To address this, we propose TTL-SR, a geometry-aware Test-Time Learning framework for quantitative Spatial Reasoning that leverages geometric consistency constraints and unlabeled test data to adapt models to target domains. Specifically, TTL-SR augments the input query with geometrically coupled auxiliary queries, filters unreliable predictions via adaptive geometric triggering to construct structured token-level pseudo-labels, and updates model parameters under a geometry-aware multi-objective loss using only test data. Experimental results demonstrate that TTL-SR significantly boosts spatial reasoning performance, yielding 6.47% and 9.41% accuracy gains for Qwen3-VL-4B-Instruct and SpatialRGPT-VILA-1.5-8B on Q-Spatial-ScanNet dataset, respectively.