Geometric Parrots: Rule Absence vs. Rule Fragility in Spatial and Physical Reasoning for Vision-Language Models

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.

Physical reasoning over images requires integrating perception, domain knowledge, and multi-step symbolic inference, yet Vision-Language Models (VLMs) fall far short of human performance on physics benchmarks. Reinforcement learning can improve reasoning via reward signals, but it remains unclear whether these signals must come from outside the model or can be derived from the model itself. We compare external rewards, which rely on an outside verifier (rule-based format and answer-correctness checks, or an LLM-judge rubric), with an internal attention-based reward computed from the model's own attention over image regions, requiring no labels or judge. We find that external rewards drive most of the accuracy gains, while preserving more coherent reasoning when rewarded for reasoning tokens. The internal attention-based reward, provides an annotation-free grounding signal that improves spatial-relation reasoning and is complementary to external rewards: adding it to format and accuracy rewards, at no additional annotation cost, improves average accuracy on Molmo~2 while generalizing to out-of-distribution tasks. Our results suggest that internal attention rewards can supplement external supervision and lead to improved physical reasoning.

Vision-language model (VLM) errors on visual reasoning may come from missing visual structure, from mistakes after that structure is extracted, or from both. We introduce VRIQ, a benchmark of 1,391 human-verified IQ-style visual reasoning puzzles spanning five psychometric categories, each instantiated in category-matched abstract and natural-image domains. To study perception and reasoning more directly, we also introduce DiagVRIQ, a 209-item diagnostic subset paired with human-verified, rule-neutral textual descriptions. Across 21 VLMs, the 17 non-frontier models reach a 26.8% unweighted category mean on abstract puzzles, while three 2026 frontier models improve substantially but unevenly, with unweighted category means of 41.3--70.9% on abstract puzzles and at most 78.2% on natural-image puzzles; all remain below human performance. On DiagVRIQ, even when their descriptions are judged correct, the strongest models still answer approximately 9--12% of those items incorrectly. Two interventions, ground-truth description augmentation and tool-augmented inference, improve accuracy, with the largest tool gains on spatially demanding categories, but neither eliminates errors. VRIQ and DiagVRIQ provide a framework for studying visual reasoning through complementary end-to-end, description-based, and intervention-based analyses rather than treating it as a single monolithic capability.