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MentalBlackboard : Evaluating Spatial Visualization via Mathematical Transformations

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
spatial visualizationspatial cognitionspatial reasoningVLMs
Abstract:

Spatial visualization is the mental ability to imagine, transform, and manipulate the spatial characteristics of objects and actions. This intelligence is a part of human cognition where actions and perception are connected on a mental level. Do state-of-the-art Vision-Language Models (VLMs) also exhibit this ability? To explore this, we develop MentalBlackboard, an open-ended spatial visualization benchmark for Paper Folding and Hole Punching tests within two core tasks: prediction and planning. Our prediction experiments reveal that models mostly overpredict the final hole numbers and struggle with applying symmetrical transformations, even when they predict the sequence of unfolding steps correctly. The backward folding process (folding the paper away from the camera/observer), which leads to limited vision, reduces the accuracy of spatial arrangement construction for certain models. Rotations, which alter the orientation of the unfolding actions, introduce a significant challenge for models to understand the physical orientation of the paper. The planning task, in which models are required to identify the sequence of folds that match the final hole pattern, shows models' limitations in analyzing symmetrical relations and creating the multi-stage symmetry process. In the task of generalization, which does not require spatial visualization, models reason through the visual analogies involving two visual examples of the same paper-folding process, along with a distinct spatial property and text-based hole information. Although the best-performing model, o3, achieves a peak performance of 71.6% in transferring spatial data, it only obtains 25% accuracy on text-based prediction tasks. Claude Opus 4.1 achieves the highest planning score with 10%. The field-wise performance shows that models struggle more with locating and orienting the holes.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces MentalBlackboard, a benchmark evaluating vision-language models on paper folding and hole punching tasks through prediction and planning challenges. It resides in the 'Vision-Language and Multimodal Model Evaluation' leaf, which contains four papers total including this one. This leaf sits within the broader 'Computational and AI-Based Spatial Reasoning Models' branch, indicating a moderately populated research direction focused on AI systems rather than human cognition. The taxonomy shows this is one of three computational subtopics alongside cognitive architectures and neuroimaging approaches, suggesting the field balances AI evaluation with human-centered studies.

The taxonomy reveals neighboring work in cognitive architecture models using symbolic representations and brain-connectivity studies examining neural correlates of spatial reasoning. The paper's leaf excludes symbolic or cognitive architecture approaches, positioning it specifically within neural network and multimodal LLM evaluation. Nearby branches include extensive human psychometric assessment work (four subtopics, twenty-three papers) and educational interventions (four subtopics, thirteen papers), indicating the broader field emphasizes human spatial abilities while computational evaluation remains a smaller but active frontier. The scope note clarifies this work targets large-scale model benchmarking rather than human-subject studies.

Among twenty-six candidates examined across three contributions, none were identified as clearly refuting the work. The MentalBlackboard benchmark contribution examined ten candidates with zero refutable matches, the automated data pipeline examined six with none refutable, and the VLM limitations evaluation examined ten with none refutable. This suggests that within the limited search scope of top-K semantic matches, the specific combination of paper folding tasks, automated 3D animation generation, and systematic VLM evaluation appears relatively unexplored. However, the analysis explicitly notes this reflects a limited literature search rather than exhaustive coverage.

The contribution-level statistics indicate the work occupies a relatively open space within the examined candidates, though the modest search scale (twenty-six papers) and the presence of three sibling papers in the same taxonomy leaf suggest caution. The taxonomy structure shows computational spatial reasoning evaluation is less crowded than human psychometric assessment, but the field is actively developing benchmarks for multimodal models. The analysis covers semantic neighbors and citation-expanded candidates but does not claim comprehensive field coverage.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
26
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Evaluating spatial visualization through paper folding and hole punching transformations. This field encompasses diverse approaches to understanding and measuring how individuals mentally manipulate spatial information, particularly through classic tasks like imagining folded paper with punched holes. The taxonomy reveals five major branches: Computational and AI-Based Spatial Reasoning Models explore how modern vision-language systems and multimodal architectures handle spatial tasks, often benchmarking models like MentalBlackboard[0] or GamiBench[15] against human-like reasoning; Human Spatial Ability Assessment and Psychometrics focuses on measurement instruments, individual differences, and validation studies such as those examining traits and experience effects[3][14]; Educational Interventions and Training Programs investigate how spatial skills can be taught or enhanced through classroom activities, puzzles, or origami-based exercises[2][10]; Spatial Reasoning in Domain-Specific Contexts applies these abilities to fields like geometry education[5], scientific inquiry[4], or even groundwater visualization[18]; and Theoretical and Methodological Foundations address the cognitive structures, strategy use, and conceptual frameworks underlying spatial transformations[16][25]. Recent work shows particularly active development in computational evaluation and educational design. On one hand, AI-based benchmarks like Unfolding Spatial Cognition[6] and LLMs and Spatial Reasoning[20] probe whether large models can replicate human-like mental folding and unfolding, revealing gaps in current architectures' ability to handle multi-step spatial transformations. On the other hand, educational studies explore training interventions ranging from paper-based activities[10][33] to interactive games[22], debating whether improvements transfer across different spatial subtasks. MentalBlackboard[0] sits within the computational branch, emphasizing vision-language model evaluation on paper folding tasks, closely aligned with neighbors like Unfolding Spatial Cognition[6] that similarly test AI spatial reasoning but differing in its focus on blackboard-style iterative processing. This contrasts with psychometric work on human performance[3][43], which prioritizes individual differences and cognitive mechanisms over model architectures, highlighting ongoing questions about whether computational and human spatial reasoning share common principles or require distinct theoretical accounts.

Claimed Contributions

MentalBlackboard benchmark for spatial visualization evaluation

The authors introduce MentalBlackboard, a large-scale benchmark that evaluates vision-language models' spatial visualization abilities through paper folding and hole punching tasks. The benchmark features open-ended evaluation across prediction and planning tasks with multiple modalities (video, 2D image, text).

10 retrieved papers
Automated data creation pipeline for 3D animation generation

The authors develop an automated pipeline using VPython to generate physically valid 3D animations of paper folding sequences. This pipeline produces over 12,000 unique configurations with validation rules ensuring physical feasibility and supports multiple representation formats.

6 retrieved papers
Comprehensive evaluation revealing VLM limitations in spatial visualization

The authors conduct extensive evaluations of state-of-the-art vision-language models, revealing significant limitations in spatial visualization tasks. Their analysis identifies specific challenges including symmetry transformation, sequential reasoning, and physical orientation understanding through open-ended evaluation.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

MentalBlackboard benchmark for spatial visualization evaluation

The authors introduce MentalBlackboard, a large-scale benchmark that evaluates vision-language models' spatial visualization abilities through paper folding and hole punching tasks. The benchmark features open-ended evaluation across prediction and planning tasks with multiple modalities (video, 2D image, text).

Contribution

Automated data creation pipeline for 3D animation generation

The authors develop an automated pipeline using VPython to generate physically valid 3D animations of paper folding sequences. This pipeline produces over 12,000 unique configurations with validation rules ensuring physical feasibility and supports multiple representation formats.

Contribution

Comprehensive evaluation revealing VLM limitations in spatial visualization

The authors conduct extensive evaluations of state-of-the-art vision-language models, revealing significant limitations in spatial visualization tasks. Their analysis identifies specific challenges including symmetry transformation, sequential reasoning, and physical orientation understanding through open-ended evaluation.

Table of Contents

MentalBlackboard : Evaluating Spatial Visualization via Mathematical Transformations | Novelty Validation