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arxiv: 2605.23898 · v1 · pith:VESSBQKWnew · submitted 2026-05-22 · 💻 cs.AI

SPACENUM: Revisiting Spatial Numerical Understanding in VLMs

Jianshu Zhang , Yijiang Li , Huifeixin Chen , Haoran Lu , Letian Xue , Bingyang Wang , Han Liu This is my paper

Pith reviewed 2026-05-25 03:54 UTC · model grok-4.3

classification 💻 cs.AI
keywords Vision-Language ModelsSpatial Numerical UnderstandingCoordinate GroundingEmbodied AISpatial ReasoningTask EvaluationNum2SpaceSpace2Num
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The pith

Vision-language models largely fail to ground numerical values in spatial perception, performing near random on bidirectional mapping tasks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a framework called SpaceNum to test whether VLMs can map between visual spatial structures and numerical representations in both dynamic exploration and static layout settings. It formulates two tasks, Num2Space and Space2Num, that require models to convert spatial observations into numbers or vice versa. Across multiple models, performance stays close to random, with analysis showing reliance on shallow visual cues rather than stable coordinate representations. If correct, this means VLMs deployed in embodied settings cannot reliably produce or interpret spatial coordinates for actions or navigation. The work also tests interventions like explicit reasoning and fine-tuning, finding only partial gains from the latter.

Core claim

Current VLMs fail to ground numbers in spatial meaning across dynamic transitions and static layouts, relying heavily on shallow spatial cues, struggling to build stable coordinate-aware representations, and failing to abstract structured spatial layouts from visual observations. Explicit reasoning yields only marginal gains, while tuning partially improves understanding and transfers to external spatial benchmarks.

What carries the argument

The SpaceNum framework with its bidirectional Num2Space and Space2Num tasks that test mapping between vision-side spatial structure and language-side numerical representations.

If this is right

  • Explicit chain-of-thought reasoning provides only marginal improvements on spatial numerical tasks.
  • Fine-tuning on the tasks can partially lift performance and transfer to other spatial reasoning benchmarks.
  • Models perform poorly on both dynamic transitions during spatial exploration and static layouts in reasoning.
  • Current VLMs cannot reliably produce action magnitudes or spatial coordinates grounded in perception.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Training corpora for VLMs may lack sufficient examples that force explicit coordinate-to-number alignment.
  • Applications in robotics could benefit from hybrid systems that add external coordinate tracking modules.
  • New benchmarks focused on blocking superficial cues might be needed to drive progress in spatial grounding.

Load-bearing premise

The Num2Space and Space2Num tasks measure genuine spatial numerical understanding rather than superficial visual or linguistic patterns unrelated to coordinate grounding.

What would settle it

A controlled experiment where a VLM achieves substantially above-chance accuracy on both tasks after interventions that block access to shallow visual patterns such as object counts or text overlays.

Figures

Figures reproduced from arXiv: 2605.23898 by Bingyang Wang, Han Liu, Haoran Lu, Huifeixin Chen, Jianshu Zhang, Letian Xue, Yijiang Li.

Figure 1
Figure 1. Figure 1: Overview of SPACENUM. We study spatial numerical understanding under two settings: numbers as dynamic transition in spatial exploration (left) and numbers as static layout in spatial understanding (right). We further investigate the mapping between vision-side space and language￾side numbers via two tasks: NUM2SPACE, which maps numbers to visual outcomes (top), and SPACE2NUM, which maps visual inputs to nu… view at source ↗
Figure 2
Figure 2. Figure 2: Dataset statistics. SPACE2NUM. The model is given an observation o and is required to infer the numerical coordinates p of a target object under the reference coordinate system. This task requires grounding visual spatial structure into numerical representations. 2.3 Statistics [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Structured analysis of model errors across spatial scenarios. Left: larger models tend to [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Additional analyses under dynamic transitions. Top left: blind testing by masking visual [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visual-side interventions. Left: adding anchors for dynamic transitions and reducing objects [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Representation-side interventions. Left: changing numerical representations in dynamic [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Tuning analysis for spatial numerical understanding. Left: transfer patterns across different [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces the SpaceNum framework with bidirectional Num2Space and Space2Num tasks to evaluate whether VLMs map between visual spatial structures and numerical representations in dynamic transitions and static layouts. It reports near-random performance across models, attributes this to reliance on shallow spatial cues rather than coordinate-aware representations, shows marginal benefits from explicit reasoning, and partial gains from tuning that transfer to other spatial benchmarks.

Significance. If the central empirical claims survive rigorous controls for task artifacts and full methodological disclosure, the work would document a concrete limitation in current VLMs for embodied settings that require numerical spatial grounding, providing diagnostic evidence via error and intervention analyses that could guide future architectural or training interventions.

major comments (3)
  1. [Abstract] Abstract: the claim of 'systematic evaluation, error analysis, and interventions' showing near-random performance is presented without any enumeration of the specific VLMs tested, dataset sizes or construction protocol, statistical tests, or control conditions, leaving the mapping from observed failure to 'failure to abstract structured spatial layouts' unverifiable.
  2. [§3] Task formulation (Num2Space/Space2Num): the manuscript does not report explicit ablation or verification that superficial cues (object counts, prompt-length statistics, or language-model priors over number words) have been removed from the image-generation and prompt-construction pipelines; without such checks the near-random result cannot be unambiguously attributed to absence of coordinate grounding rather than task artifacts.
  3. [§4] Experimental section: no details are supplied on model-selection criteria, number of models or runs, baseline comparisons that isolate spatial-numerical grounding from general visual or numerical competence, or the precise form of the 'controlled interventions,' all of which are load-bearing for the claim that VLMs 'rely heavily on shallow spatial cues.'
minor comments (2)
  1. [Abstract] Abstract: 'need produce' should read 'need to produce.'
  2. [Throughout] Ensure consistent capitalization and first-use definition of 'VLM' / 'VLMs' and 'SpaceNum.'

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. The comments highlight areas where additional methodological transparency will strengthen the paper. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of 'systematic evaluation, error analysis, and interventions' showing near-random performance is presented without any enumeration of the specific VLMs tested, dataset sizes or construction protocol, statistical tests, or control conditions, leaving the mapping from observed failure to 'failure to abstract structured spatial layouts' unverifiable.

    Authors: We agree the abstract is concise and omits enumeration of these details. The main text (Sections 3–4) contains the full list of evaluated VLMs, task construction protocol, dataset sizes, and the error/intervention analyses. In revision we will expand the abstract with a brief enumeration of the models tested and key dataset statistics while preserving length constraints, and will add explicit forward references to the statistical tests and controls. revision: yes

  2. Referee: [§3] Task formulation (Num2Space/Space2Num): the manuscript does not report explicit ablation or verification that superficial cues (object counts, prompt-length statistics, or language-model priors over number words) have been removed from the image-generation and prompt-construction pipelines; without such checks the near-random result cannot be unambiguously attributed to absence of coordinate grounding rather than task artifacts.

    Authors: This observation is correct; the original submission did not include dedicated ablations isolating object counts, prompt-length statistics, or LM priors over number words. While task construction in §3 varied spatial configurations to reduce such cues, we will add explicit ablation experiments in the revised §3 that systematically vary or control these factors and report the resulting performance to confirm the attribution to coordinate grounding. revision: yes

  3. Referee: [§4] Experimental section: no details are supplied on model-selection criteria, number of models or runs, baseline comparisons that isolate spatial-numerical grounding from general visual or numerical competence, or the precise form of the 'controlled interventions,' all of which are load-bearing for the claim that VLMs 'rely heavily on shallow spatial cues.'

    Authors: We acknowledge the need for greater detail. The revised experimental section will specify model-selection criteria, the exact number of models and runs, baseline comparisons that separate spatial-numerical grounding from general visual/numerical competence, and a precise description of each controlled intervention (including how they were implemented and what they isolate). These additions will directly support the claim regarding reliance on shallow cues. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical benchmarking study with no derivations or fitted predictions

full rationale

The paper is an empirical evaluation introducing Num2Space and Space2Num tasks to benchmark VLMs on spatial-numerical mapping. No mathematical derivation chain, first-principles predictions, or parameter fitting is present. Claims rest on observed model performance, error analysis, and interventions rather than any step that reduces by construction to its own inputs or self-citations. This matches the default expectation for non-circular empirical work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the validity of the new tasks as measures of spatial grounding; no free parameters or invented entities are introduced.

axioms (1)
  • domain assumption The bidirectional tasks Num2Space and Space2Num accurately isolate genuine spatial numerical understanding from superficial cues.
    The paper's conclusion that models fail to ground numbers rests on these tasks being faithful proxies.

pith-pipeline@v0.9.0 · 5754 in / 1136 out tokens · 22674 ms · 2026-05-25T03:54:22.720581+00:00 · methodology

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Reference graph

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