PolyComp: A Polycube-based Benchmark for Compositional 3D Spatial Reasoning in Multimodal Models

Multimodal large language models (MLLMs) excel at visual interpretation but fail on spatial reasoning tasks that humans solve reliably. Existing benchmarks evaluate these models as black boxes, limiting their ability to identify the underlying causes of lower performance: when a model fails a spatial reasoning task, it remains difficult to ascertain whether the hurdle is perceptual, such as recognizing object boundaries, or cognitive, such as reasoning about occlusion to infer hidden geometry. We introduce Spatial-IQ, a hierarchical diagnostic framework that decomposes object counting in stacked 3D structures into 9 perceptual and cognitive sub-tasks organized by the developmental stages of human spatial cognition, with mental rotation as an additional target probe. Using NVIDIA Isaac Sim, we procedurally generated a diverse dataset of roughly 80,000 stacked 3D structures with per-task ground truth. We evaluate models across three output formats (free-response text, multiple-choice images, and image editing) alongside a human baseline. The Spatial-IQ framework shows that top-performing models often succeed at the target task (object counting) without succeeding on the lower-level sub-tasks intended to support it, and that models differ in how much of these hierarchical chains they preserve, often revealing shortcut behavior that raw target-task accuracy alone would obscure. Finally, we demonstrate that training models with chain-of-thought (CoT) supervision over our hierarchical sub-tasks, combined with reinforcement learning with verifiable rewards, significantly improves both spatial consistency across sub-tasks and target-task accuracy, supporting the value of the proposed decomposition as both a diagnostic tool and a training signal.

Vision-language models are increasingly used for multimodal question answering, yet their ability to reconstruct latent spatial structure from a single image remains difficult to isolate. Broad benchmarks often combine perception, optical character recognition, domain knowledge, linguistic priors, and reasoning in the same evaluation. We introduce StateSight, a procedurally generated benchmark for cube-net opposite-face reasoning, occluded cube-tower counting, and 4-neighbor connected-component counting. Each task family contains 300 single-image prompts with deterministic oracle labels and exact-match scoring. OpenAI GPT-5.5, using the API model identifier gpt-5.5, achieved 59.3%, 33.3%, and 28.3% accuracy across the three tasks, while Claude Sonnet 5 achieved 53.3%, 18.7%, and 7.3%. All final direct runs had zero format errors. A 30-participant human baseline on 60 items exceeded both models on every task, with mean accuracies of 80.8%, 68.8%, and 64.3%. Visible-derivation analysis identified recurring errors in image-state reconstruction and reasoning procedure. We also introduce StateSight-Steps, a companion dataset of 900 interleaved image-text examples and 3,600 deterministic intermediate visual states. The results show that format-valid responses can mask failures to recover the spatial structure required for verifiable visual inference.

Spatial competence is the quality of maintaining a consistent internal representation of an environment and using it to infer discrete structure and plan actions under constraints. Prevailing spatial evaluations for large models are limited to probing isolated primitives through 3D transformations or visual question answering. We introduce the Spatial Competence Benchmark (SCBench), spanning three hierarchical capability buckets whose tasks require executable outputs verified by deterministic checkers or simulator-based evaluators. On SCBench, three frontier models exhibit monotonically decreasing accuracy up the capability ladder. Sweeping output-token caps shows that accuracy gains concentrate at low budgets and saturate quickly, and failures are dominated by locally plausible geometry that breaks global constraints. We release the task generators, verifiers, and visualisation tooling.