BareBones: Benchmarking Zero-Shot Geometric Comprehension in VLMs

Jigsaw puzzle solving requires jointly reasoning about visual content and geometric constraints, yet existing benchmarks use rectangular cuts that create ambiguous ground truth in texture-repeated regions. We introduce \ours{}, a benchmark with tab-and-blank interlocking pieces where geometric constraints provide strong local compatibility requirements that, combined with visual content, yield unambiguous ground truth. Across 95K instances at four grid densities (4$\times$4 to 16$\times$16), we find that zero-shot VLMs largely lack geometric reasoning: only one of five frontier models (GPT-5.5) exceeds random baseline on 4$\times$4 puzzles, while all others perform at chance level. While supervised fine-tuning achieves $>$97% on 4$\times$4, all models collapse on larger grids: GPT-5.5 drops from 70% to near-random on 8$\times$8, and even fine-tuned models fall below 5% on 12$\times$12. This ``scaling cliff'' suggests current architectures cannot maintain consistent constraint satisfaction as the number of pieces increases. \ours{} establishes scalable geometric reasoning as an open challenge for vision-language models.

This work investigates the fundamental fragility of state-of-the-art Vision-Language Models (VLMs) under basic geometric transformations. While modern VLMs excel at semantic tasks such as recognizing objects in canonical orientations and describing complex scenes, they exhibit systematic failures at a more fundamental level: lack of robust spatial invariance and equivariance required to reliably determine object identity under simple rotations, scaling, and identity transformations. We demonstrate this limitation through a systematic evaluation across diverse visual domains, including symbolic sketches, natural photographs, and abstract art. Performance drops sharply as semantic content becomes sparse, and this behavior is observed across architectures, model capacities, and prompting strategies. Overall, our results reveal a systematic gap between semantic understanding and spatial reasoning in current VLMs, highlighting the need for stronger geometric grounding in future multimodal systems.

Vision-language models (VLMs) often struggle with geometric reasoning due to their limited perception of fundamental diagram elements. To tackle this challenge, we introduce GeoPerceive, a benchmark comprising diagram instances paired with domain-specific language (DSL) representations, along with an efficient automatic data generation pipeline. This design enables the isolated evaluation of geometric perception independently from reasoning. To exploit the data provided by GeoPerceive for enhancing the geometric perception capabilities of VLMs, we propose GeoDPO, a translator-guided reinforcement learning (RL) framework. GeoDPO employs an NL-to-DSL translator, which is trained on synthetic pairs generated by the data engine of GeoPerceive, to bridge natural language and DSL. This translator facilitates the computation of fine-grained, DSL-level scores, which serve as reward signals in reinforcement learning. We assess GeoDPO on both in-domain and out-of-domain datasets, spanning tasks in geometric perception as well as downstream reasoning. Experimental results demonstrate that, while supervised fine-tuning (SFT) offers only marginal improvements and may even impair performance in out-of-domain scenarios, GeoDPO achieves substantial gains: $+26.5\%$ on in-domain data, $+8.0\%$ on out-of-domain data, and $+39.0\%$ on downstream reasoning tasks. These findings underscore the superior performance and generalization ability of GeoDPO over SFT. All codes are released at https://github.com/Longin-Yu/GeoPerceive to ensure reproducibility.