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Why Far Looks Up: Probing Spatial Representation in Vision-Language Models

Conference: ECCV 2026
Paper: ECCV
Area: Multimodal VLM
Keywords: vision-language model, spatial reasoning, contrastive probing, perspective projection bias, representation analysis

TL;DR

The paper builds a representation-level analysis framework that extracts delta vectors from the final-token hidden states of minimal contrastive question pairs (same image, swapped object order) to measure how the three spatial axes are organized inside VLMs, finds a pervasive vertical-distance entanglement in which image-plane height is used as a proxy for depth, and uses SpatialTunnel — a synthetic benchmark that geometrically decouples vertical position from depth — to show the bias is model-intrinsic and that models with a more coherent distance axis are the ones that stay robust on counter-heuristic examples.

Background & Motivation

Vision-language models keep posting higher scores on spatial reasoning benchmarks — EmbSpatial-Bench, CV-Bench, BLINK — so much so that the results invite the reading that these systems genuinely reason about 3D structure. Yet almost all of them are trained on 2D image-text pairs, and monocular images carry a strong statistical regularity of their own: on a common ground plane, farther objects appear higher in the image (the classical elevation cue). A model can therefore score well on a large share of depth questions simply by learning "higher in the image ⇒ farther away," without understanding any 3D structure. The harder problem is that behavioral benchmarks only record whether the answer is right, never how it was reached: two models with nearly identical scores may look the same while one encodes left/right, above/below, and near/far as structured, separable directions, and the other merely latches onto whatever image cues happen to correlate with depth and collapses the moment the evaluation distribution shifts. Telling these two cases apart requires looking inside the model rather than at the output layer.

Existing efforts fall into two groups. One line builds controlled behavioral evaluations — What's Up, COMFORT and related work — and exposes systematic failures in basic positional judgments and frame-of-reference consistency. The other line has begun probing internal mechanisms: ADAPTVIS analyzes attention dynamics during spatial reasoning, DepthCues uses linear probes to show that vision encoders themselves represent monocular depth cues, other work finds geometric coordinates bound to object activations in early layers, and Spatial Forcing explicitly aligns intermediate layers with 3D structure. But these either measure success or failure on a single task, or detect whether some individual spatial primitive exists, or adjust local attention behavior. None of them asks the more global question: do different spatial dimensions occupy separate directions in representation space, or are they packed into the same one? Isolated probing is blind to precisely this entanglement — a model can probe well for "above" and for "far" separately while encoding both into the very same direction.

This paper therefore attacks the problem from two complementary angles. On the behavioral side, depth questions are partitioned by whether their ground truth agrees with the "far is up" prior, and the accuracy difference Δ between the consistent and counter groups is measured; a single-point-perspective synthetic corridor, SpatialTunnel, then moves objects up and down the tunnel cross-section while holding the depth ordering fixed, geometrically breaking the "higher ⇒ farther" correlation so that Δ can be attributed to the model rather than to the evaluation set. On the representation side, swapping the two objects in a question yields a minimal contrastive pair that differs only in the flipped relation; the difference of their intermediate-layer final-token hidden states forms a delta vector, and axis coherence plus the VD-Entanglement Index describe how the spatial axes are geometrically laid out. Core idea: rewrite the question "does the model rely on 3D structure or on a perspective shortcut" — which output scores cannot settle — as a direction relation between spatial axes in representation space (axis coherence plus an entanglement index), and use a synthetic benchmark that geometrically decouples vertical position from depth to separate model bias from evaluation-set skew.

Method

Overall Architecture

The input is an image plus a spatial-relation question (left/right, above/below, near/far), and the output is a diagnosis of whether the model's spatial ability is structured or shortcut-driven. The analysis runs in two legs. The behavioral leg first partitions depth questions into consistent / counter / ambiguous by the "far is up" prior and measures the consistent-versus-counter accuracy gap Δ on real benchmarks (Section 3); SpatialTunnel then repeats the same partition and measurement on synthetic tunnel scenes, stripping evaluation-set skew out of Δ (Section 4). The representational leg constructs, for each image, a pair of questions that differ only in object order, takes the difference of the final-token hidden states at a fixed intermediate layer as a delta vector, and aggregates those vectors by spatial category into axis coherence and VD-EI — a description of what the model's left/right, above/below, and near/far axes actually look like (Section 5). Finally, the representation metrics are matched against counter-example accuracy and cross-benchmark performance to see whether representational structure and robustness move together.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["image + spatial-relation VQA"] --> B["consistent / counter split<br/>decide prior direction by y"]
    B --> C["SpatialTunnel<br/>decouples height from depth"]
    C --> D["minimal contrastive pairs<br/>swap object order, take delta"]
    D --> E["axis coherence and VD-EI<br/>geometry of the spatial axes"]
    E --> F["structure vs counter accuracy<br/>cross-model / cross-benchmark"]

Key Designs

1. Consistent / counter partitioning: turning the "far is up" prior into a measurable behavioral gap

Claiming that a model takes a shortcut is easy; proving it is not. The paper restricts itself to depth-comparison questions and compares the vertical center coordinates of the two queried objects in pixel space: if the farther object has the smaller y coordinate (i.e., sits higher in the image), the sample is labeled consistent; otherwise it is counter; if the two differ by less than 5% of the image height, the vertical position carries almost no directional information and the sample is labeled ambiguous and excluded. The partition uses only annotations and coordinates and no model output at all, so it acts as a purely prior-based criterion. Its use is direct: a model that does not rely on vertical position should score comparably on both groups, so a substantially higher score on the consistent group is behavioral evidence that the model is treating vertical position as a proxy for depth.

Applying the partition to existing benchmarks is itself revealing. Of the 1,206 depth questions in EmbSpatial-Bench, 976 (80.9%) are consistent and only 129 (10.7%) are counter; in CV-Bench-3D, 363 of 600 (60.5%) are consistent and 65 (10.8%) counter. Those distributions are essentially a mirror of natural photographic statistics, so a model that leans purely on the vertical cue still earns a respectable average score. The value of this design is that it is free and portable: any depth-annotated spatial question set can be sliced by the same criterion and re-scored, with no new data collection.

2. SpatialTunnel: a tunnel geometry that decouples vertical image position from depth

In real photographs, vertical position, size gradients, and occlusion all vary together, so no individual depth cue can be isolated for intervention. SpatialTunnel builds a single-point-perspective corridor in Blender: walls, ceiling, and floor are symmetric about the camera's optical axis, and objects can only be placed on the interior tunnel surfaces, so each object is parameterized by a depth z and an angular position θ on the tunnel cross-section. Holding z fixed while varying θ moves the object up, down, left, and right in the image without changing the depth ordering at all — an object near the tunnel ceiling and one near the floor can be equally far from the camera, so "higher in the image ⇒ farther" is broken by construction. The benchmark discretizes the cross-section into 16 angular positions and places two objects, yielding a 16 × 16 grid over (θ1, θ2) that can be rendered as heatmaps showing exactly which configurations a model gets right and which it gets wrong; object color, size, shape, and scene lighting are randomized across renders so that models cannot memorize appearances.

For evaluation, the model sees a rendered RGB image with two objects and is asked a binary depth-comparison question ("Is {obj1} closer to or farther from the camera than {obj2}?"). Rather than reading generated text, the authors take the local probability at the first generated token by normalizing the Yes/No logits into the probability p of Yes (⚠️ the equation is corrupted in the cached text; it is reconstructed here from the prose description, refer to the original paper), and a single query scores v = p when the ground truth is Yes and v = 1 − p when it is No. Using a continuous probability rather than a hard answer lets the analysis see which side a model leans toward even when it hovers near chance. Four metrics are aggregated: mean accuracy v, consistent accuracy v_cons, counter accuracy v_ctr, and the gap Δ = v_cons − v_ctr, which is the direct behavioral reading of vertical-distance entanglement and should be ≈ 0 for an unbiased model.

3. Minimal contrastive question pairs and delta vectors: isolating the spatial relation from the visual content

Probing hidden states directly mostly recovers shared components — object identity, scene style, question wording — rather than the spatial relation itself. The paper's countermeasure is a minimal contrastive pair: the same image with the two objects swapped in the question, "Is A to the left or right of B?" against "Is B to the left or right of A?". The visual input is identical and the ground-truth relation is the exact inverse (left becomes right, far becomes near, above becomes below). For each question the final-token hidden state at a fixed intermediate layer L is extracted, and subtracting the two gives the delta vector δ = h_q2 − h_q1. Because the visual content and most of the linguistic content cancel in the subtraction, the residual displacement carries approximately only the flipping of the relation — which is exactly what isolates the relational encoding from confounds. Pooling delta vectors over many images within a spatial category (above, below, far, close, left, right) yields one cluster of vectors per direction in representation space, and this is the sole input to the two metrics below. L is fixed per model family, with the selection following prior layer-selection work (Appendix D.3 / D.4).

4. Axis coherence and VD-EI: two comparable scalars for how spatial axes are organized

Once delta-vector clusters exist, cross-model and cross-scale comparison needs scalars. Axis coherence answers "does this axis have a stable direction": for one axis, the delta vectors of its two opposing categories (say far and close) are pooled, the vectors of the opposite category are negated so that all of them point toward the same canonical direction, and the mean pairwise cosine similarity is computed over that sign-corrected set (⚠️ the equation is corrupted in the cached text; reconstructed here from the prose, refer to the original paper):

\[\tilde{\delta}^{(i)} = \begin{cases}\delta^{(i)}, & \text{canonical (e.g. far)}\\ -\delta^{(i)}, & \text{opposite (e.g. close)}\end{cases}\]
\[\text{Coh}_{\text{axis}} = \frac{2}{N(N-1)}\sum_{i<j}\cos\left(\tilde{\delta}^{(i)}, \tilde{\delta}^{(j)}\right)\]

A high value means the axis corresponds to a stable direction in representation space and the model encodes it self-consistently; a value near zero means the vectors point in all directions and the model cannot say which way "farther" moves. The VD-Entanglement Index (VD-EI) then answers "are the two axes tied together, and in the way perspective projection predicts": it takes the mean delta vector μ_c for each of above, below, far, and close, and compares four cosine terms —

\[\text{VD-EI} = \frac{1}{4}\left[\cos(\mu_{\text{above}},\mu_{\text{far}}) + \cos(\mu_{\text{below}},\mu_{\text{close}}) - \cos(\mu_{\text{above}},\mu_{\text{close}}) - \cos(\mu_{\text{below}},\mu_{\text{far}})\right]\]

The first two terms are the perspective-aligned pairs (above↔far, below↔close) and the last two the perspective-opposing pairs; a positive value means the vertical and distance representations are genuinely coupled the way perspective projection predicts, while zero means they are independent. This metric is far stricter than "probing above and far separately both work well": separate probes are blind to two concepts being encoded along a single shared direction, whereas VD-EI measures the angle relation between the two axes directly — precisely the blind spot of isolated probing.

Loss & Training

The paper does not train a new method, but to relate data scale to entanglement it runs recipe-controlled spatial SFT on three model families: five spatial understanding datasets (SAT, RoboSpatial, SPAR-7M, RefSpatial, PRISM) are mixed uniformly and subsampled to 80k / 400k / 800k / 2M samples, with everything else held constant; "base" denotes the original pretrained weights without spatial fine-tuning. RoboRefer-2B-SFT (same base as NVILA-Lite-2B, but trained on more than 20M samples including RGB-D images) and Qwen3-VL-235B-A22B-Instruct are added as references from two different training regimes. The paper does not report optimization hyper-parameters such as learning rate; on the probing side it only specifies that one intermediate layer L* is fixed per model family, with details in the appendix. It is worth stating plainly that the entire evidence chain — the behavioral Δ gap, the persistence of Δ on the synthetic benchmark, the low CohD and high VD-EI in representation space, and the cross-benchmark correlation between CohD and counter accuracy — is correlational. No causal intervention (activation patching, or removing a direction and re-measuring) is performed, so "entangled representations cause the reasoning failures" and "the readout fails to exploit structure that is already there" cannot yet be strictly separated.

Key Experimental Results

Main Results

Table 1 gives the sample composition of the evaluation sets themselves (ambiguous means the two objects differ by less than 5% of the image height):

Benchmark Consistent Counter Ambiguous
EmbSpatial-Bench 976 (80.9%) 129 (10.7%) 101 (8.4%)
CV-Bench-3D 363 (60.5%) 65 (10.8%) 172 (28.7%)

Table 2 is the core behavioral evidence: accuracy on depth questions for the consistent versus counter groups, with the difference in percentage points in parentheses. Only the base and 2M endpoints are listed; the intermediate scales are discussed after the table.

Model EmbSpatial Cons. EmbSpatial Ctr. CV-3D Cons. CV-3D Ctr.
Molmo-7B-O-0924 63.5 34.9 (−28.6) 93.1 75.4 (−17.7)
Molmo + 2M 65.3 39.5 (−25.8) 90.6 72.3 (−18.3)
NVILA-Lite-2B 49.0 27.1 (−21.9) 74.4 40.0 (−34.4)
NVILA + 2M 60.7 41.1 (−19.6) 97.2 93.8 (−3.4)
RoboRefer-2B-SFT 87.0 59.7 (−27.3) 98.9 95.4 (−3.5)
Qwen2.5-VL-3B-Instruct 54.7 32.6 (−22.1) 75.5 55.4 (−20.1)
Qwen2.5-VL + 2M 60.9 24.0 (−36.9) 62.0 53.8 (−8.2)
Qwen3-VL-235B-A22B 73.3 41.7 (−31.6) 98.1 90.8 (−7.3)

Every model scores lower on the counter group on both benchmarks, with gaps ranging from 3.4 points (NVILA 2M on CV-Bench-3D) to 36.9 points (Qwen2.5-VL 2M on EmbSpatial-Bench), independent of model family, parameter count, or fine-tuning data volume. More tellingly, data scale does not monotonically fix the problem: Qwen2.5-VL widens from −22.1 at base to −36.9 at 2M, its consistent score rising to 60.9 while its counter score falls to 24.0, which suggests it learned to apply the prior harder; NVILA moves the other way and compresses the CV-Bench-3D gap to −3.4, yet still sits at −19.6 on EmbSpatial. Intermediate scales even regress: NVILA at 400k / 800k gives −27.0 / −24.4 on EmbSpatial and −22.8 / −16.9 on CV-3D, while Molmo at 400k / 800k gives −35.6 / −31.1 on EmbSpatial.

Beyond accuracy, the paper compares five tasks of differing format and difficulty (EmbSpatial overall, CV-Bench-2D Relation, CV-Bench-3D Depth / Distance, and BLINK's Rel. Depth and Spat. Rel.), and finds that fine-tuned variants fluctuate wildly across benchmarks so that no single score reflects how well 3D concepts were internalized: NVILA (2M) reaches 93.8% on CV-3D Depth but only 62.9% on BLINK Spatial Relation, while Qwen2.5-VL (2M) scores 78.3% on BLINK Spatial Relation but only 52.2% on CV-3D Distance. RoboRefer-2B-SFT and Qwen3-VL-235B-A22B, by contrast, stay consistently high across all tasks (RoboRefer: 92.0 / 96.5 / 95.7 / 90.5 / 84.7 / 79.7; Qwen3-VL-235B: 82.0 / 96.5 / 93.3 / 91.0 / 84.7 / 90.2, in the same column order). The representation analysis subsequently identifies exactly these two models as having the most structured spatial representations.

Ablation Study

The first analysis experiment repeats the consistent / counter partition on the synthetic SpatialTunnel benchmark, where v is the mean score, v_cons and v_ctr are the two subset scores, and Δ = v_cons − v_ctr:

Model v v_cons v_ctr Δ
Molmo-7B-O-0924 0.528 0.565 0.487 +0.078
Molmo + 2M 0.666 0.703 0.630 +0.073
NVILA-Lite-2B 0.488 0.504 0.471 +0.033
NVILA + 2M 0.812 0.875 0.749 +0.127
RoboRefer-2B-SFT 0.793 0.816 0.770 +0.046
Qwen2.5-VL-3B-Instruct 0.570 0.776 0.360 +0.416
Qwen2.5-VL + 2M 0.500 0.648 0.353 +0.295
Qwen3-VL-235B-A22B 0.908 0.948 0.880 +0.068

Even after vertical position and depth are decoupled in the synthetic images, every model still scores higher on the consistent group, so the bias cannot be explained by evaluation-set skew. Base Qwen2.5-VL-3B-Instruct shows the largest Δ of all (+0.416, with v_cons = 0.776 against v_ctr = 0.360); base NVILA-Lite-2B has a small Δ (+0.033) but a near-chance overall v = 0.488, so its small gap reflects a model that cannot do the task either way rather than a clean representation. Scaling clearly mitigates the bias: RoboRefer, trained on more than 20M samples, has the smallest Δ (+0.046) among models performing above chance, and Qwen3-VL-235B attains the highest mean accuracy (0.908) with an equally small Δ (+0.068), indicating that very large-scale pretraining can substantially weaken the bias without targeted spatial fine-tuning. The 16 × 16 heatmaps for Molmo make the same point at cell level: if predictions were insensitive to 2D placement, accuracy would be roughly uniform across the grid, whereas it in fact shows a sharp contrast between consistent and counter regions.

The second analysis experiment collapses the delta vectors into two scalar metrics (CohH / CohV / CohD are the axis coherence of the horizontal, vertical, and distance axes; VD-EI is the entanglement index):

Model CohH CohV CohD VD-EI
Molmo-7B-O-0924 0.143 0.228 0.075 0.279
Molmo + 2M 0.239 0.574 0.112 0.474
NVILA-Lite-2B 0.323 0.289 0.052 0.539
NVILA + 2M 0.241 0.553 0.104 0.550
RoboRefer-2B-SFT 0.649 0.830 0.182 0.362
Qwen2.5-VL-3B-Instruct 0.367 0.293 0.043 0.457
Qwen2.5-VL + 2M 0.485 0.586 0.052 0.472

Three findings stand out. The distance axis is the weakest: CohD is the lowest of the three axes for every model and every training scale, and while fine-tuning lifts vertical coherence substantially (Molmo 0.228 → 0.574, Qwen2.5-VL 0.293 → 0.586), the distance axis barely moves (Qwen2.5-VL stays at 0.043 → 0.052 throughout). Distance coherence tracks counter accuracy: on EmbSpatial-Bench — the same data the coherence is computed from — the two rise together once a model reaches a sufficient scale, for NVILA from 80k onward and for Molmo from 400k onward, whereas Qwen2.5-VL's CohD stays flat and its counter accuracy declines, widening Δ. The signal transfers across domains: CohD measured on SpatialTunnel correlates with counter accuracy on other benchmarks (ρ = 0.759 with EmbSpatial-Bench and 0.804 with CV-Bench-3D, both p < 10⁻³), so it is not an artifact of in-domain computation. The PCA in Figure 7 gives the visual counterpart: base NVILA's distance delta vectors collapse near the origin without forming a direction; after 2M fine-tuning they begin to spread but the vertical and distance clusters still overlap; RoboRefer shows three cleanly separated clusters each aligned with a distinct principal component (CohD 0.182, VD-EI 0.362, corresponding to 59.7% counter accuracy on EmbSpatial-Bench versus 41.1% for NVILA 2M). Qwen3-VL-235B has no numeric entry in the metric table and is shown only in the PCA figure, where it exhibits the same clean three-cluster structure as RoboRefer.

Key Findings

  • Vertical-distance entanglement is universal across model families, scales, and evaluation modalities: the consistent group beats the counter group on real benchmarks and still does so on the synthetic one, so the gap is contributed by the model rather than by the evaluation set.
  • More spatial fine-tuning data does not automatically resolve the entanglement, and can even move it the wrong way: Qwen2.5-VL widens its EmbSpatial gap from −22.1 at base to −36.9 at 2M because the consistent score rises while the counter score falls from 32.6 to 24.0, whereas Molmo and NVILA each rise and fall without monotone convergence.
  • A high benchmark score does not imply a structured representation: NVILA (2M) scores 93.8% on CV-3D Depth but 62.9% on BLINK Spatial Relation, while Qwen2.5-VL (2M) does the opposite (78.3% versus 52.2%), whereas the two models with the most structured representations, RoboRefer and Qwen3-VL-235B, are uniformly strong.
  • Of the three axes, distance is the hardest: CohD comes last everywhere, and only CohD shows a stable cross-benchmark correlation with counter-example accuracy (ρ = 0.759 / 0.804), making "is the distance axis encoded as a stable direction" a more predictive diagnostic than the average score.
  • The two metrics are best read together: a model can have high CohD and still score high on VD-EI if the two axes remain glued, and RoboRefer's value lies in achieving the highest CohD together with the lowest VD-EI.

Highlights & Insights

  • Turning "is it taking a shortcut" into a measurable quantity: the consistent / counter partition uses only annotations and pixel coordinates and no model information, so it doubles as a data audit — counter examples make up only about 10% of existing benchmarks, a number every spatial reasoning evaluation should probably report.
  • Swapping object order to build a minimal contrastive pair is the cleverest step: the visual input is identical and only the ground-truth relation flips, so subtracting the two hidden states cancels objects, scenes, and wording, leaving a displacement that carries approximately only the direction of the relation. That recipe — minimal edit → representation difference → aggregate by category — transfers directly to any question of the form "is concept X encoded along its own direction", including color, material, count, or causal direction.
  • The spatial weakness looks more like an encoding problem than a readout problem: entanglement shows up in intermediate-layer representations (collapsed distance delta vectors, persistently low CohD), and representational structure co-varies with counter-heuristic robustness across models and benchmarks, which points to concepts not being separated at encoding time rather than to a decoder failing to use structure that exists. ⚠️ This reading is still correlational; the authors run no causal intervention to separate the two explanations.
  • The metric works as a training-time diagnostic: CohD needs no extra annotation, only contrastive question pairs, and it transfers across benchmarks, so it can be plugged into data-mixing or curriculum iterations to test whether a batch of data actually improved the distance representation.

Limitations & Future Work

  • The evidence chain is correlational rather than causal: the paper shows CohD and counter accuracy moving together and representational structure tracking robustness, but performs no directional ablation, activation patching, or causal intervention, so it cannot claim that raising CohD raises accuracy, or vice versa.
  • The absolute scale of the metrics is small: even the best model, RoboRefer, reaches only CohD = 0.182, while most others sit between 0.04 and 0.11. The paper gives no interpretable threshold for "this axis is effectively not encoded" or "this is good enough."
  • Layer choice is preset: L* is fixed per model family based on prior layer-selection work, and neither the main text nor the cached version reports whether other layers would yield different entanglement conclusions or whether entanglement eases with depth.
  • SpatialTunnel has a single single-point-perspective corridor, two objects, and fixed depth separations; appearances are randomized but the domain gap remains substantial, and the tunnel geometry is itself a new distribution that could interact with uncontrolled factors.
  • RoboRefer changes data scale (20M+), modality (RGB-D), and supervision form at the same time; the authors themselves treat it as an illustrative reference rather than attributing the gains to any single factor. Qwen3-VL-235B has the same confound and, additionally, no numeric CohD / VD-EI values.
  • Concrete next steps: move the probe from correlation to causation by ablating or substituting activations along the delta-vector direction and checking whether counter-example accuracy moves; and try optimizing CohD directly as an auxiliary objective during fine-tuning to see whether it buys counter-heuristic robustness.
  • vs What's Up / COMFORT and other controlled behavioral evaluations: they rewrite questions and check frame-of-reference consistency to expose positional failures, measuring whether a model errs; this paper measures where inside the model the error lives, and further separates model bias from evaluation-set skew with a synthetic environment.
  • vs attention-based analyses such as ADAPTVIS: those explain why spatial reasoning is hard by looking at where attention focuses, a local mechanism; this paper looks at the geometric relation among the three spatial axes in representation space, which surfaces axis-to-axis entanglement that single-mechanism probes cannot see.
  • vs DepthCues and linear-mechanism probes: those establish that depth cues exist in vision encoders and that geometric coordinates are bound to object activations in early layers; this paper does not test whether a primitive exists but how it is oriented relative to other primitives, and can therefore flag the subtler case where a depth cue exists but shares its direction with the vertical axis.
  • vs representation-alignment methods such as Spatial Forcing: those explicitly align intermediate layers to 3D structure and are training-time interventions; this paper contributes a diagnostic, and CohD's cross-benchmark transferability makes it suitable as an observable for checking whether such alignment actually happened during training.

Rating

  • Novelty: ⭐⭐⭐⭐ It converts "shortcut versus structure" from a qualitative claim into representation-level quantities (axis coherence, an entanglement index, and a decoupled synthetic benchmark); the combination is new for spatial-reasoning analysis.
  • Experimental Thoroughness: ⭐⭐⭐⭐ Three model families across four data scales plus two reference models, five benchmarks plus a purpose-built synthetic one — broad coverage; it loses a point for stopping at correlational probing, deferring layer selection and hyper-parameters to the appendix, and running no causal intervention.
  • Writing Quality: ⭐⭐⭐⭐ The argument chain is clear and the metric definitions are complete, with restrained attribution for confounded references such as RoboRefer; a few equations are corrupted in the cached text and must be checked against the original.
  • Value: ⭐⭐⭐⭐ CohD is a cheap, cross-domain-transferable diagnostic of spatial representation that can be embedded in training iterations, directly useful for spatial data mixing and for VLM representation analysis.