Measure the error
Convert geometric distance and clock-direction errors into preference margins. Larger spatial errors require stronger separation.
MEASURED PREFERENCE MARGINS VISION–LANGUAGE MODELS / SPATIAL REASONING
GaugeVLM.Structuring Spatial Supervision
with Measured Geometric Interventions
Measure the error. Preserve the relation. Learn the change.
1 Institute of Automation, Chinese Academy of Sciences
2 School of Artificial Intelligence, UCAS · 3 School of Advanced Interdisciplinary Sciences, UCAS
4 National University of Singapore · 5 The Chinese University of Hong Kong
UCAS: University of Chinese Academy of Sciences.† Corresponding Author
MULTI-INSTITUTION COLLABORATION
CASIAInstitute of Automation,
Chinese Academy of Sciences
Chinese Academy of Sciences
UCASUniversity of Chinese
Academy of Sciences
Academy of Sciences
NUSNational University
of Singapore
of Singapore
CUHKThe Chinese University
of Hong Kong
of Hong Kong
+15.0ppMSMU distancevs. GaugeSFT · Qwen 7B
+18.9ppQSpatial+vs. GaugeSFT · Qwen 7B
30/ 30Spatial metrics improved10 metrics × 3 backbones · vs. SFT
50.4KSpatial preference pairsGauge-50K · 5 task families
01 / THE IDEASpatial understanding,
Spatial understanding,
grounded in geometry.
A good spatial model should know how wrong an answer is, stay correct across camera views, and respond when the world changes.
Beyond right or wrong. GaugeVLM connects measured error magnitude, shared spatial truths across views, and controlled changes to a scene.
Original PDF ↗Abstract
Vision-language models (VLMs) can contradict themselves across views of the same spatial relation and fail to respond when that relation changes. Addressing these failures requires supervision that captures error magnitude and geometric dependencies across observations, both of which remain implicit in training on individual answers or ordinal preferences.
Therefore, we introduce GaugeVLM, which makes this structure explicit through controlled object and camera interventions in explicit 3D scenes, producing linked observations with measured differences between spatial relations and shared truths across views. To translate this structure into learning signals, its core objective, GaugeDPO, converts measured errors into preference margins, directly supervises correct canonical rankings across views, and links intervention-induced answer-odds contrasts to measured relation changes with view-specific scales.
Our analysis bounds canonical prediction error and establishes that the cross-view and intervention constraints can be jointly satisfied. Empirically, GaugeVLM improves all 10 established spatial metrics over supervised fine-tuning across three VLM backbones, with the main 7B model gaining 15.0 and 18.9 percentage points on MSMU distance and QSpatial+, respectively. These gains also extend to autonomous driving and embodied reasoning, demonstrating the robust generalization across domains.
02 / THE METHODFrom measured change
From measured change
to structured supervision.
GaugeDPO brings three complementary learning signals into one objective, while allowing confidence to vary across views.
Keep the truth consistent
Directly rank the true canonical relation above incorrect candidates in every camera view, including the hardest one.
DIRECT CROSS-VIEW SUPERVISIONLearn how relations change
Align intervention-induced changes in answer odds with measured relation changes, using a separate scale for each view.
INTERVENTION PROFILESOne objective, three constraints. Measured preference margins, correct rankings across views, and intervention profiles work together.
Original PDF ↗PLAY WITH THE GEOMETRY
One scene. A different perspective.
Orbit the camera, then move the object. Discover what should stay true.
LIVE GEOMETRYCamera · 35°
↔ Drag to orbit · ← → keys also workA · anchor B · target
CENTROID DISTANCE2.00 m
ANCHOR-RELATIVE CLOCK2 o’clock
FIXED ANCHOR FRAME
The camera changes the image, not the relation.
01 / CHANGE THE VIEW
Camera movement preserves both measurements.
02 / CHANGE THE WORLD
Object movement changes the true relation.
Interactive illustration · geometry is computed live; no model is running.Try moving the camera first.
MEASURE THE MISTAKE
α = 0.5 · κ = ln 5Not every wrong answer is equally wrong.
Change a candidate answer and see its measured preference margin.
SCENE TRUTH2.00 m · 2 o’clock
Use the scene above to change the ground truth. “Test this scene’s error” imports it here.
GEOMETRIC MARGIN0.293
Measured error0 · correct1 · maximum
Direction contribution0.1672 hours / 6 × 0.5
Distance contribution0.126|ln(3.00 / 2.00)| / ln 5 × 0.5
Larger geometric errors require larger preference gaps during training.
How is the margin computed?
m = 0.5 × eclock + 0.5 × edistance
Clock error uses the shortest arc around a 12-hour circle, divided by 6. Distance error is |ln(d / d*)| / ln 5, capped at 1. Equal over- and under-estimation ratios receive equal errors.
This illustrates the paper’s fully measured branch. It is a geometric error, not a model confidence or a predicted benchmark score.
03 / DATA & EVALUATIONBuilt in 3D.
Built in 3D.
Measured, not guessed.
Controlled object and camera interventions create linked observations with known geometry, shared truths, and measurable changes.
GAUGE-50K50,436Preference pairs.
Preference pairs.
Five spatial task families.
Objects from Objaverse-LVIS and 3D-FUTURE are placed in 3D-FRONT scenes and rendered with BlenderProc.
30,000 preference pairs form the training pool. Pair counts are separate from intervention-block counts.
One construction across training and evaluation. Measured pairs, controlled object movements, and matched camera groups. Counts above follow the appendix; the original figure labels clock direction as 7,129 instead of 7,219.
Original PDF ↗CONSTANCY-BENCH
Evaluate distance ranking, photometric consistency at a fixed camera, and correct responses to object relocation. A separate cross-view audit checks whether models agree on the correct relation across cameras.
04 / RESULTSConsistent gains.
Consistent gains.
Across three backbones.
All 10 established spatial metrics improve over GaugeSFT on each evaluated backbone. Explore the matched comparisons below.
Qwen2.5-VL · 7B
GaugeSFTGaugeVLM
MSMU Distance
QSpatial+ δ₂
SURDS Depth
SpatialRGPT Qualitative
GaugeVLM improves all 10 spatial metrics over GaugeSFT on Qwen2.5-VL-7B.
All 10 spatial metrics
| Benchmark / metric | Base VLM | GaugeSFT | GaugeVLM | Gain vs. SFT |
|---|---|---|---|---|
| MSMU · Distance | 17.5 | 47.5 | 62.5 | +15.0 pp |
| MSMU · Width | 3.4 | 48.3 | 55.1 | +6.8 pp |
| MSMU · Height | 12.1 | 67.0 | 71.4 | +4.4 pp |
| QSpatial+ · δ₂ | 42.6 | 45.5 | 64.4 | +18.9 pp |
| SURDS · Distance | 20.0 | 22.4 | 30.4 | +8.0 pp |
| SURDS · Depth | 22.3 | 24.3 | 35.7 | +11.4 pp |
| SpatialRGPT · Quantitative | 25.0 | 33.5 | 43.1 | +9.6 pp |
| SpatialRGPT · Qualitative | 70.0 | 74.7 | 81.6 | +6.9 pp |
| 3DSRBench · Accuracy | 44.9 | 48.2 | 56.9 | +8.7 pp |
| BLINK · Accuracy | 49.5 | 50.5 | 56.7 | +6.2 pp |
Source: paper, spatial understanding results. Scores in %. Gains are percentage points, computed from the displayed scores. The 10 metrics exclude Constancy-Bench probes.
Download results ↓Correct across the group
Cross-view group accuracy rises from 50.0% to 69.5% over SFT initialization. Agreement alone is not enough: the shared answer must be correct.
Overall block accuracy
Up from 60.0% for pair + direct supervision, across familiar, held-out magnitude, and held-out combination settings.
Of the preference budget
GaugeDPO with 25% of the preference data surpasses full-data DPO on all five evaluated data-efficiency metrics.
WHY MEASUREMENT MATTERSThe preference gap follows
The preference gap follows
the geometric error.
With measured margins, larger geometric errors produce larger policy gaps. Constant or shuffled margins do not preserve this structure.
05 / BUILD ON THIS WORKA little more
A little more
spatial sense.
If you find GaugeVLM useful for your research, please consider citing our work.
Explore the full paper@misc{wang2026gaugevlm,
title = {GaugeVLM: Structuring Spatial Supervision
with Measured Geometric Interventions},
author = {Hongbo Wang and Zihan Lin and Wenkui Yang
and Shiran Ge and Yuang Ai and Jie Cao
and Huaibo Huang and Ran He},
year = {2026},
url = {https://github.com/wafer-bob/GaugeVLM},
note = {Preprint}
}