Geometry-Aware Test-Time Learning for Quantitative Spatial Reasoning

Summary

The paper introduces TTL-SR, a test-time learning framework that improves quantitative spatial reasoning (metric distance and size estimation from single images) in vision-language models without any labeled target data. Instead of confidence-based objectives like entropy minimization — which the authors show homogenize the feature space for continuous predictions (Fig. 3) — TTL-SR augments each query with geometrically coupled variants (direct/vertical/horizontal distance, width, height), checks whether the model's own predictions satisfy Pythagorean, aspect-ratio, and semantic consistency within a tolerance τ, and only for coherent groups converts the reconciled numeric value into structured token-level pseudo-labels (one-hot for decimal/unit tokens, uniform over a tolerance interval for digits). LoRA adapters are updated cumulatively over the unlabeled test stream with a multi-objective loss (multi-label positive learning, unlikelihood loss, KL to the frozen model, restricted entropy minimization). On Q-Spatial-ScanNet, average accuracy rises from 40.00% to 46.47% for Qwen3-VL-4B-Instruct and from 34.12% to 43.53% for SpatialRGPT-VILA-1.5-8B, with gains also on Q-Spatial++, SPAR-Bench, and SpatialRGPT-Bench; the 4B model with TTL-SR becomes competitive with frontier closed models. Limitations: very small per-category test sets (accuracy granularity implies roughly 20-60 samples), no confidence intervals or significance testing, transductive adaptation on the evaluation stream, LoRA and template details deferred to supplementary materials, and no code release stated.