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SPACENUM: Revisiting Spatial Numerical Understandin... | AI Research

Key Takeaways

  • Vision-Language Models (VLMs) are increasingly used to navigate environments and interpret spatial scenes, tasks that require them to output precise numbers...
  • Vision-Language Models (VLMs) are increasingly deployed in embodied environments, where they need produce numerical outputs such as action magnitudes and spatial coordinates.
  • Although these numbers appear meaningful, it remains unclear whether these numerical outputs are genuinely grounded in spatial perception.
  • We formulate two bidirectional tasks, Num2Space and Space2Num, to evaluate how well VLMs map between vision-side spatial structure and language-side numerical representations.
  • We systematically study whether current VLMs truly understand numerical values in spatial settings.
Paper AbstractExpand

Vision-Language Models (VLMs) are increasingly deployed in embodied environments, where they need produce numerical outputs such as action magnitudes and spatial coordinates. Although these numbers appear meaningful, it remains unclear whether these numerical outputs are genuinely grounded in spatial perception. Therefore, in this work, we revisit spatial numerical understanding through SpaceNum, a unified framework that captures two complementary settings: numbers as dynamic transitions during spatial exploration, and numbers as static layouts in spatial reasoning. We formulate two bidirectional tasks, Num2Space and Space2Num, to evaluate how well VLMs map between vision-side spatial structure and language-side numerical representations. We systematically study whether current VLMs truly understand numerical values in spatial settings. Across dynamic transitions and static layouts, we find that models largely fail to ground numbers in spatial meaning and often perform close to random guess. Through error analysis, reasoning trace analysis, and controlled interventions, we show that current VLMs rely heavily on shallow spatial cues, struggle to build stable coordinate-aware representations, and fail to abstract structured spatial layouts from visual observations. We further show that explicit reasoning provides only marginal gains, while tuning can partially improve spatial numerical understanding and transfer to external spatial reasoning benchmarks.

Vision-Language Models (VLMs) are increasingly used to navigate environments and interpret spatial scenes, tasks that require them to output precise numbers like coordinates or movement distances. This research introduces SpaceNum, a framework designed to test whether these models truly understand the spatial meaning behind numbers or if they are simply guessing. By evaluating 18 different models, the authors reveal that current VLMs struggle to ground numerical values in spatial reality, often performing no better than random chance.

Testing Spatial Numerical Understanding

To determine if VLMs possess genuine spatial awareness, the researchers developed two bidirectional tasks: Num2Space and Space2Num. In Num2Space, a model is given a number and must predict the corresponding visual outcome (such as how a scene changes after a 20-degree rotation). In Space2Num, the model is given visual observations and must infer the correct numerical value (such as the distance between two objects). These tasks were applied to two scenarios: dynamic transitions, which involve movement through an environment, and static layouts, which involve understanding the relative positions of objects in a scene.

Key Findings on Model Performance

The study found that most VLMs fail to ground numbers in spatial meaning. Across all tested models, performance was consistently low, often hovering near the random guess threshold. The researchers identified several critical weaknesses:

  • Shallow Cues: Models often rely on simple visual patterns rather than building a stable, coordinate-aware understanding of the environment.

  • Lack of Geometric Consistency: Models struggle to maintain consistent numerical predictions when faced with symmetric transformations, such as rotating left versus rotating right.

  • Inability to Compare: Even when models generate reasoning traces, they often stop at coarse observations (e.g., "the object moved") rather than performing the fine-grained comparisons necessary to determine exact magnitudes.

The Limits of Reasoning and Intervention

The authors explored whether prompting models to "think" or reason explicitly would improve their performance. Surprisingly, explicit reasoning provided only marginal gains, suggesting that the models lack the underlying spatially calibrated operations needed to solve these problems. Furthermore, the researchers attempted to simplify the tasks by adding visual anchors or reducing the number of objects in a scene, but these interventions failed to produce significant improvements. This indicates that the models' difficulties are deeply rooted in their architecture and training, rather than just a lack of visual clarity.

Implications for Future Development

The research concludes that while scaling up model size can help with coarse spatial sensitivity—leading to "less wrong" mistakes—it does not necessarily lead to precise numerical grounding. However, the study shows that targeted tuning can partially improve spatial numerical understanding and help models perform better on external spatial reasoning benchmarks. These findings highlight a significant gap in current VLM capabilities, suggesting that future development must focus on building more robust, coordinate-aware representations rather than relying on superficial spatial cues.

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