The Missing GAP: From Solving Square Jigsaw Puzzles to Handling Real World Archaeological Fragments

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 \textit{\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$16), we find that \textbf{zero-shot VLMs largely lack geometric reasoning}: only one of five frontier models (GPT-5.5) exceeds random baseline on 4$\times$4 puzzles, while all others perform at chance level. While supervised fine-tuning achieves $>$97% on 4$\times$4, \textbf{all models collapse on larger grids}: GPT-5.5 drops from 70% to near-random on 8$\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.

ARC-AGI-2 is a benchmark of human-intuitive visual puzzles that measures a machine's ability to generalize from limited examples, interpret symbolic meaning, and flexibly apply rules in varying contexts. In this paper, we discuss our approach to solving the ARC-AGI-2 puzzles with TinyLM, with additional fine-tuning at test time, including Test-Time-Training (TTT) and Products of Experts (POE). Our model achieves 96.1% accuracy on the training set and 21.7% accuracy on the evaluation set.

3D vision systems are fundamentally constrained by their reliance on visual overlap: reconstruction methods require it for geometric alignment, while generative models use it to enforce multi-view consistency. This limitation is particularly acute in real-world scenarios such as distributed swarm robotics or crowd-sourced data collection, where capturing overlapping perspectives, both in terms of spatial and appearance overlap, is often impossible. We introduce Generative Reconstruction from Disjoint Views as a new paradigm, establish a comprehensive dataset, and propose specialized evaluation metrics for zero-overlap scenarios. Our benchmarking demonstrates that existing state-of-the-art methods fail catastrophically on this task, producing disconnected geometries or semantically incoherent reconstructions. To address these limitations, we propose GLADOS, a general, modular framework that operates through three stages: (1) Generative Bridging, where foundation models synthesize intermediate perspectives to connect disjoint inputs; (2) Robust Coarse 3D Reconstruction, that establish coarse geometric scaffold via global alignment which absorbs local contradictions from generative process; and (3) Iterative Context Expansion and Consistency Optimization to fill missing regions and unify the reconstruction. As an architectureagnostic framework, GLADOS enables seamless integration of future advances in generation, reconstruction, and inpainting. The source code is available at: https://github.com/gwilczynski95/GLADOS.