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REVIEW 4 major objections 5 minor 43 references

Revisiting Marr in Face: The Building of 2D--2.5D--3D Representations in Deep Neural Networks

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Deep face networks construct representations in the order Marr's theory predicts: flat 2D, low-relief 2.5D, then full 3D.

desk verdict A clever and reusable graphics-probe tool, but the headline 2D–2.5D–3D result is confounded by the probe's growing receptive field and by training the network to reconstruct through the probes. read the letter →

arxiv 2411.16148 v1 pith:NG5YZ54N submitted 2024-11-25 cs.CV

Xiangyu Zhu , Chang Yu , Jiankuo Zhao , Zhaoxiang Zhang , Stan Z. Li , Zhen Lei This is my paper · ORCID
classification cs.CV
keywords Marr'stheoryofvision2Dsketch2.5D3Dmodelgraphicsprobedeepneuralnetworkinterpretabilityfaceperceptionanalysis-by-synthesis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that deep neural networks trained to reconstruct or perceive faces organize their internal representations according to the classic 2D–2.5D–3D construction theory of vision. The authors insert a graphics probe into intermediate layers; the probe reads out what a layer encodes by rendering the input image from the layer's features using depth, albedo, camera view, and lighting. Readouts show flat geometry with no depth variation in low-level layers, shallow depth with rich surface-normal variation in middle layers, and full 3D shape at high layers. The same probing reveals mid-level features are tuned to viewpoints while high-level features are tuned to facial parts, and training on single-view faces prevents the 3D stage from appearing. If correct, the paper gives empirical support for a much-debated stage theory inside deep learning models, and a tool for seeing what those models actually compute.

What carries the argument

The graphics probe is the object that carries the argument: a probe token is inserted into each window of a transformer or appended to a CNN block, gathers information from the layer's tokens through self-attention, and is decoded into four computer-graphics elements—a depth map, an albedo map, a 6DoF camera view, and lighting. The probe is trained unsupervised, by analysis-by-synthesis, to reconstruct the input image from those elements. Because the probe can produce either flat or sculpted depth and either viewer-centered or object-centered views, the choices it settles on expose the layer's preferred representation; multiple probes compete through a Z-buffer, revealing which probe is tuned to which image or face part. The depth map and its statistics, depth variation and normal variation, are the direct evidence for classifying a layer as 2D, 2.5D, or 3D.

What would settle it

Train the same Window Transformer with a classification head instead of the reconstruction loss and re-run the graphics probes; if the 2D–2.5D–3D depth pattern vanishes, the sequence is a product of the reconstruction objective rather than of deep perception itself.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a vision-oriented deep network spontaneously develops the three representational stages proposed in classical computational vision. Low-level layers encode a genuinely 2D representation, as shown by decoded depth maps that are flat planes with normals pointing straight at the viewer. Middle layers build a 2.5D representation: depth remains shallow but surface normals vary enough to create shading, like a low-relief sculpture. High layers construct a full 3D model, with depth variations large enough to represent three-dimensional shape from any viewpoint. The same three-stage pattern appears across several architectures, and the final 3D stage only emerges when training data contain viewpoint variation.

Load-bearing premise

The paper treats the decoded depth maps as faithful readouts of what each layer actually encodes, rather than as artifacts of the probe's receptive-field size or its reconstruction objective.

Editorial extensions

If this is right

  • Low-level layers of trained face networks should be read as flat 2D sketches: probing them yields no depth variation and no normal variation.
  • Middle layers should be read as 2.5D low-relief representations: they produce shading through surface normals while keeping depth nearly constant.
  • High-level layers should be read as full 3D object-centered models, with depth variation large enough to render profile views of the face.
  • Viewpoint variation in the training data is a prerequisite for the 3D stage; networks trained on a single yaw angle stay in the 2.5D regime.
  • The 2D–2.5D–3D ordering generalizes across VGG16, ResNet18, ViT, SwinT, and the proposed Window Transformer.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the flat low-level readout is a true representation rather than an artifact of the probe's receptive field, then removing the reconstruction objective should preserve flatness; this is a testable ablation the paper does not run.
  • The sudden jump in high-level depth variance around epoch 15 suggests a phase-transition-like moment in training; probing per epoch could reveal whether the 3D stage appears abruptly or gradually.
  • The same graphics-probe method could be applied to non-face object categories to test whether the 2D–2.5D–3D ladder is a general property of deep visual representation or specific to faces with strong pose variation.
  • Because training on single-view faces still yields a 2.5D shading representation, the 2.5D stage may be a minimal requirement for any reconstruction-based network, while full 3D is an extra adaptation to viewpoint diversity.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper introduces a "graphics probe," a sub-network inserted into intermediate layers of a window-based transformer, that decodes the layer's features into depth, albedo, camera viewpoint, and lighting, and then re-renders the input image via a differentiable renderer. The authors train the network and probes jointly with a reconstruction loss and report that low-level layers decode flat depth maps (2D), middle layers decode shallow depth with strong normal variation (2.5D), and high layers decode full 3D geometry. They also report that middle-level probes are view-tuned while high-level probes are part-tuned, and that a single-view training set prevents 3D emergence. The paper interprets these observations as evidence that deep neural networks implement Marr's 2D-2.5D-3D sequence.

Significance. If the central claim is established, the paper would provide a concrete empirical bridge between DNN internal representations and Marr's classical framework, with implications for interpretability, face perception, and the conditions under which 3D representations emerge. The graphics probe is an original and potentially useful tool, and the paper includes several positive features: quantitative depth/normal variance distributions, a controlled single-view training experiment (Section 4.6), and cross-architecture replication (Section 4.7). However, the central claim is not yet supported because of two confounds: the probed levels have different receptive-field sizes, and the probes are trained jointly with the network rather than applied as readouts of a frozen representation. The paper would need additional controls to substantiate the strong Marr-alignment conclusion.

major comments (4)
  1. [Section 3.1, Section 4.2, Figure 3] The central 2D-2.5D-3D claim is confounded by receptive-field size. The probed stages use window sizes of 1/4, 1/2, and the full image, as stated in Section 3.1 and Table 1 of the supplement. A probe seeing only 1/4 of the image cannot estimate global 3D structure, and a flat depth map plus albedo/texture is the most parsimonious way to reconstruct a local patch. The observed monotonic increase in depth variance with level is therefore exactly what the architecture predicts, independent of whether the layer itself stores a 3D representation. To support the claim, the authors should provide a control that applies the same graphics probe to raw pixels at the same three receptive-field sizes, or that probes features at all layers with a fixed full-image receptive field. Without such a control, the low-level '2D' result cannot be attributed to the representation rather than to limited context.
  2. [Section 4.1, Eq. (5), Section 4.6] The network and the graphics probes are trained jointly with the reconstruction loss in Eq. (5). The decoded depth, albedo, and viewpoint are optimized parameters of the same learning process, not independent readouts of a pre-existing representation. The observation that high-level layers 'build 3D' may reflect the probe's role in explaining viewpoint variation, and Section 4.6 itself shows that 3D depth emerges only when training data contain pose variation. This makes the finding task-dependent rather than a general property of DNNs. The authors should probe a pretrained, fixed network (for example, a face-recognition backbone) or train a linear probe on frozen features, and compare against the joint-training result.
  3. [Section 4.6, Figure 8] The 3D threshold of 15x10^-3 in Figure 8 is introduced post hoc and without justification or sensitivity analysis. The claim that the single-view model 'does not reach the threshold necessary for 3D geometry' is not quantitative evidence unless the threshold is derived independently from the data or from a principled criterion. The authors should report the full distributions of depth variance for both models, include a statistical comparison, and either justify the threshold or replace it with a continuous measure that does not rely on a hand-set cutoff.
  4. [Section 4.7, Table 1, Supplementary Section 3] The cross-architecture results in Table 1 are not accompanied by error bars or significance tests, and the low-level VGG16 and ResNet18 depth variances (0.21 and 0.26 x10^-3) are nonzero. The supplementary text acknowledges these maps are 'not entirely flat' and reclassifies them as 2D because they lack semantic structure. This reclassification makes the 2D/2.5D/3D taxonomy difficult to falsify. The authors should formalize the criteria for each stage and apply them consistently, or report the classification as a categorical judgment rather than a quantitative finding.
minor comments (5)
  1. [Abstract and Conclusion] The abstract contains the typo 's sur normals' and the conclusion contains 'phenomenons'; both should be corrected.
  2. [Eq. (3)] In Eq. (3), the concatenation list repeats 'theta_v_k' twice; the second entry should be 'theta_l_k'. Also, 'theta_b_k' is used for the albedo component but the symbol 'b' is not defined.
  3. [Section 4.2 vs. Section 3.1] Section 4.2 states that lower layers with 1/8 image receptive fields were investigated, while Section 3.1 and the supplementary Table 1 state that the bottom stage is not probed. Please clarify which stages were actually probed.
  4. [Figure 4] Figure 4 shows distributions and mean variations without confidence intervals or sample sizes; adding error bars or box plots would strengthen the quantitative comparison.
  5. [Eq. (2)] The hardmax operation in Eq. (2) is not defined; please specify whether it is a one-hot argmax over each row and discuss its effect on gradient flow.

Circularity Check

2 steps flagged · score 6.0 of 10

The 2D→2.5D→3D progression is read off the graphics probe's fitted depth maps, whose receptive field grows in parallel with the claimed stages; the central claim reduces to the probe's architecture and reconstruction objective.

  1. self definitional [Section 3.2 (Eqs. 3–5) and Section 4.2, Figure 3]
    "The probing and reconstruction process is carried out at three levels: low, middle, and high, with the receptive fields corresponding to 1/4×, 1/2×, and 1× of the image size. ... At the low level with a receptive field of 1/4× image size, we observe that the depth map resembles a 2D plane."

    The depth map D is not an independent measurement of the network's internal geometry; it is a free parameter of the graphics probe, optimized by Eq. 5 to reconstruct the input image. Because the low-level probe token attends only within a 1/4-image window, it lacks the global context needed to infer depth, so a flat depth map plus albedo is the natural solution of the same reconstruction objective. The paper then labels this fitted flatness a '2D representation' and, as the receptive field grows to 1/2 and full image, observes '2.5D' and '3D' depth. The claimed Marr-like progression is therefore built into the probe's increasing receptive field; no control with the same probe on raw pixels or on a network with full-image receptive fields at all layers is provided.

  2. fitted input called prediction [Section 4.3, Figure 4, and Section 4.6, Figure 8]
    "We calculate the variations of the depth values and the x,y,z of the normal vectors for each sample and then calculate the distribution of these variations within the test dataset. ... In summary, 2D representations exhibit low variances in both depth and normal, 2.5D representations show low depth variance but high normal variance, and 3D representations demonstrate high variance in both depth and normal. ... The threshold necessary for 3D geometry is set at 15×10−3."

    The depth and normal variances reported in Figure 4 are statistics of the probe outputs that were fitted by the same reconstruction loss used to train the network. The paper's taxonomy (2D = low depth and low normal variance; 2.5D = low depth and high normal variance; 3D = high depth and high normal variance) is imposed on these fitted numbers rather than derived from an independent ground truth about the network's representation. The 3D threshold of 15×10−3 in Figure 8 is set after the fact without prior justification, so the 'emergence of 3D' conclusion is a restatement of the fitted depth variance relative to a chosen cutoff, not an independent prediction.

full rationale

The paper does not rely on a load-bearing self-citation chain or an imported uniqueness theorem; the cited IGC-Net work by the same authors appears only as related work. The central problem is that the central claim—DNNs build 2D, then 2.5D, then 3D representations—is read directly from the depth maps produced by the graphics probe, and those depth maps are free variables fitted by the reconstruction objective (Eq. 5). The probe's receptive field is co-designed with the claimed stages (1/4, 1/2, full image), which makes flat-to-deep depth progression a predictable consequence of the probe architecture rather than an independent discovery about the network. The paper provides no raw-pixel or full-receptive-field control, and the depth-variance classification uses post hoc thresholds. The cross-architecture results use the same probe methodology, so they do not break the circularity. These issues are substantial, but the paper is transparent about its training objective and does not invoke authority or self-citation to force the conclusion, so the circularity is partial rather than total.

Assumptions & free parameters 3 free parameters · 3 assumptions · 1 invented entities

The central claim rests on the graphics probe's decoded depth, which is a fitted output of a learned decoder. The categorization into 2D/2.5D/3D uses a hand-set threshold and assumes the probe faithfully reads out the layer. The network is trained for reconstruction, which is a strong prior for 3D emergence. The free parameters (threshold, probe counts, insertion layers) are chosen to support the narrative.

free parameters (3)
  • 3D geometry threshold = 15e-3
    Used in Section 4.6 to separate 2.5D from 3D after observing the depth variance distributions; chosen post hoc to match the narrative that single-view training does not reach 3D.
  • Number of graphics probes (templates) per level = 16 at low, 4 at middle, 6 at high
    Architecture choices that determine the granularity of the probe readout; no ablation or principled justification is provided.
  • Probe insertion layers = 3rd, 5th, 11th
    Selected to represent the low, middle, and high levels; the bottom stage is excluded with the rationale that the network has not yet comprehended images, a decision that shapes the observed progression.
assumptions (3)
  • domain assumption The 2D/2.5D/3D categorization operationalized by depth and normal variances is a valid test of Marr's theory.
    The paper equates flat depth with the 2D sketch, shallow depth with 2.5D, and full depth with 3D. This mapping is assumed, not validated against Marr's original definitions or against ground-truth 3D shapes.
  • domain assumption Probe tokens can read out the information encoded in a layer via self-attention.
    The method assumes the probe token's interaction with visual tokens gives direct access to the layer's encoded content. No verification is provided that the probe cannot miss information that is present in the features.
  • domain assumption Training the network with an image reconstruction loss is a valid way to study face perception representations.
    The network is trained from scratch with a reconstruction objective, so the representations are shaped by that task. The paper generalizes to DNN-based face perception without testing recognition-trained networks.
invented entities (1)
  • Graphics probe
    purpose: A sub-network that decodes intermediate DNN features into CG elements (depth, albedo, view, lighting) to reconstruct the input image.
    The probe is introduced in this paper as the measurement tool. It has no independent validation outside the paper, such as matching recovered depth against ground-truth 3D scans.

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Cite this review

Pith. "Pith review of Revisiting Marr in Face: The Building of 2D--2.5D--3D Representations in Deep Neural Networks." pith.science (2026). https://pith.science/paper/NG5YZ54N

@misc{pith2026241116148,
  author       = {Pith},
  title        = {Pith review of: Revisiting Marr in Face: The Building of 2D--2.5D--3D Representations in Deep Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NG5YZ54N}},
  note         = {Machine review of arXiv:2411.16148}
}
read the original abstract

David Marr's seminal theory of vision proposes that the human visual system operates through a sequence of three stages, known as the 2D sketch, the 2.5D sketch, and the 3D model. In recent years, Deep Neural Networks (DNN) have been widely thought to have reached a level comparable to human vision. However, the mechanisms by which DNNs accomplish this and whether they adhere to Marr's 2D--2.5D--3D construction theory remain unexplored. In this paper, we delve into the perception task to explore these questions and find evidence supporting Marr's theory. We introduce a graphics probe, a sub-network crafted to reconstruct the original image from the network's intermediate layers. The key to the graphics probe is its flexible architecture that supports image in both 2D and 3D formats, as well as in a transitional state between them. By injecting graphics probes into neural networks, and analyzing their behavior in reconstructing images, we find that DNNs initially encode images as 2D representations in low-level layers, and finally construct 3D representations in high-level layers. Intriguingly, in mid-level layers, DNNs exhibit a hybrid state, building a geometric representation that s sur normals within a narrow depth range, akin to the appearance of a low-relief sculpture. This stage resembles the 2.5D representations, providing a view of how DNNs evolve from 2D to 3D in the perception process. The graphics probe therefore serves as a tool for peering into the mechanisms of DNN, providing empirical support for Marr's theory.

Figures

Figures reproduced from arXiv: 2411.16148 by the authors.

Figure 1
Figure 1. The building of 2D–2.5D–3D representations in DNN. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Schematic of Graphics Probe. (a) During the probing process, a probe token interacts with the original tokens and generates multiple graphics probes to reconstruct the input image in a CG manner. (b) The architecture of the probed network. (c) The visualization of probed representations across different levels: 2D at the low level, 2.5D at the middle level, and 3D at the high level. similarity to those observed in i… view at source ↗
Figure 3
Figure 3. Visualization of intermediate representations. The geometry of representations at the low, middle, and high levels with receptive field (RF) corresponding to 1 4×, 1 2×, and the full image size, respectively. At the low level, the geometry is flat, lacking any depth or normal variations. At the middle level, variations in normal begin to appear, yet the depth remains shallow, similar to a low-relief sculpture. At th… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Distribution of depth and normal variations. The distributions of variations for individual samples across the testing dataset for (a) depth, (b) x-axis of normal, (c) y-axis of normal, and (d) z-axis of normal. The mean variations for (e) depth and (f) normal througho…
Figure 5
Figure 5. Figure 5: The distribution of yaw angles across different [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: The view tuning at the middle level. The y-axis is the [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Tuning of the graphics probes. The samples that activate specific graphics probes, with the activated regions highlighted. At the low level, the activated samples reveal no clear semantic meanings. At the middle level, the probes exhibit a view-tuning behavior, with ce…
Figure 8
Figure 8. Figure 8: Depth variations distribution when trained on the dataset [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 1
Figure 1. Figure 1: The datasets used in the experiments. (a) The Celeb-A dataset, which is collected in the unconstrained scenarios. (b) The BP4D [PITH_FULL_IMAGE:figures/full_fig_p011_1.png]
Figure 2
Figure 2. Figure 2: Visualization of intermediate representations.We show the reconstructed depth maps in canonical and profile views, the albedo maps, and the reconstructed results. end of each block. This branch performs average pooling on the final feature map and aggregates it into a …
Figure 3
Figure 3. Figure 3: Visualization of intermediate representations on more architectures, including (a) VGG16, (b) Resnet18, (c) Swin-tiny, (d) ViT [PITH_FULL_IMAGE:figures/full_fig_p014_3.png]
Figure 4
Figure 4. Figure 4: Visualization of the intermediate representations within a network trained on faces in a single viewpoint. (a) The probing results [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.