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REVIEW 3 major objections 5 minor 76 references

Symbolic Disentangled Representations for Images

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read ArSyD stores each image property as a full-size hypervector so editing an object is a vector swap.

desk verdict ArSyD is a promising HDC-based disentanglement architecture with real novelty, but the DCM metric is misimplemented and the 'by construction' claim overreaches. read the letter →

arxiv 2412.19847 v1 pith:TPIJX6E7 submitted 2024-12-25 cs.CV cs.AIcs.LG

Alexandr Korchemnyi , Alexey K. Kovalev , Aleksandr I. Panov This is my paper · ORCID
classification cs.CVcs.AIcs.LG
keywords disentangledrepresentationshyperdimensionalcomputingvectorsymbolicarchitecturesweaklysupervisedlearningimageeditingslotattentiondisentanglementmetricscompositionalgeneralization
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

ArSyD aims to make image generation factors separately editable by representing each generative factor (shape, color, size, position, and so on) as its own full-dimensional hypervector, rather than as one coordinate of a latent vector. The representation of an object is the superposition of these factor-value hypervectors, so changing a property means exchanging one hypervector for another. The paper claims this disentanglement is achieved by construction: the encoder and attention modules are trained only to reconstruct images from weakly supervised pairs that differ in one factor, with no extra assumptions about latent distributions. If the claim holds, controlled image editing becomes a simple, interpretable vector swap, and the same representation can be used in scenes with several objects by combining it with slot-based object discovery.

What carries the argument

The load-bearing mechanism is attention over a frozen random codebook (item memory), used as a bridge between the encoder's localist feature vector and a distributed hypervector representation. For each generative factor $i$, a projection of the encoder output is matched by softmax attention against fixed seed hypervectors from the codebook, and the weighted sum of those seeds becomes the factor's value vector $V_i^*$. These value vectors are bound to factor hypervectors and bundled into the object representation, following Holographic Reduced Representation operations. The same encoder runs on donor and target images, and the feature-exchange module swaps one value vector before decoding.

What would settle it

On the dSprites dataset, take two images that differ only in orientation, swap only the orientation value vector in the latent representation, decode both edited images, and classify their shape with a pretrained shape classifier. If the shape prediction changes when only orientation is exchanged, the orientation vector carries shape information and the factor-level disentanglement claim fails; the paper's own Figure 7 already shows such a shape distortion for orientation.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a disentangled representation can be built as a sum of learned value hypervectors, one per generative factor, instead of a vector whose individual coordinates each encode a factor. Each value vector $V_i^*$ is produced by an attention mechanism that selects a weighted combination of fixed random seed vectors from an item memory, and the object representation is $O = \sum_i G_i \circledast V_i^*$. The model is trained by swapping the value vector of one factor between two images that differ only in that factor and reconstructing both images with an MSE loss. The authors argue that because each generative factor has its own vector and the value vectors are grounded in the image through attention, disentanglement holds by construction, and editing reduces to exchanging the corresponding vector.

Load-bearing premise

The paper's claim depends on the assumption that training only the attention weights, with nothing but reconstruction error on image pairs that differ in one factor, forces each selected hypervector to align with exactly one true generative factor and to stay independent of the others.

Editorial extensions

If this is right

  • Editing an image property becomes a vector substitution, so the same edit operation is well-defined regardless of where in the latent space a factor lives.
  • The model can be combined with Slot Attention to edit a single object inside a multi-object scene, not just isolated objects.
  • Because disentanglement is claimed by construction, the approach avoids distributional assumptions and the loss-tuning typical of beta-VAE-style methods.
  • The proposed DMM and DCM metrics allow comparisons between localist and distributed representations by measuring changes in pixel-space classifications.
  • Reconstruction from a single factor vector shows that individual value vectors carry property-specific information, which supports interpretable editing.

Reading between the lines

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

  • Editorial inference: if the value hypervectors are truly independent symbols, then latent vector arithmetic (for instance, adding the vector for one object property and subtracting another) should produce coherent composite edits, a test the paper does not run.
  • Editorial inference: the entanglement of orientation with shape visible in the paper's Figure 7 suggests that adding a sparsity or orthogonality penalty on the attention weights would make the factor vectors cleaner; the paper itself does not propose such a penalty.
  • Editorial inference: because DMM and DCM measure disentanglement through classifiers on reconstructed images, better decoders or stronger classifiers could change the measured scores even if the latent representation is unchanged, so the metrics should be read as bounded by the reconstruction and classification pipeline.
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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

3 major / 5 minor

Summary. The paper proposes ArSyD, an architecture that learns 'symbolic disentangled representations' in which each generative factor is represented by a full hypervector, and the object representation is a superposition of factor-value vectors obtained by attention over a fixed random codebook. The model is trained with weak supervision: image pairs differ in exactly one factor, and the feature-exchange reconstruction loss (Eq. 5) is the only training signal. The paper also introduces two classifier-based metrics, DMM and DCM, intended to evaluate disentanglement and compactness for distributed latent representations. Experiments on dSprites, CLEVR1, CLEVR5 (with Slot Attention), and a CelebA proof-of-concept show qualitative controlled edits and quantitative comparisons against BetaVAE and FactorVAE on FID/IoU, DMM, and DCM.

Significance. If the central claims held, this would be a valuable contribution: it offers a genuinely different, VSA-based route to disentangled representations that supports interpretable vector-level editing and proposes model-agnostic metrics that do not assume localist coordinates. The paper is also carefully structured around explicit research questions, and the qualitative exchange results on dSprites and CLEVR are compelling proof-of-concept. However, the evaluation instrument DCM is implemented inconsistently with its definition, and the 'disentanglement by construction' claim is stronger than the training objective and the paper's own qualitative results support. The significance of the contribution therefore depends on the extent to which these issues can be resolved.

major comments (3)
  1. [Section 3.4, Eq. (8), Figure 4] Eq. (8) defines DCM as (1/|C|) Σ_{c∈C} | Σ_{Gi∈G} [Cl(Ŝ'_c) ≠ ŷ]_{Gi} − 1 |, which is a per-unit row sum over generative factors. However, the text and Figure 4 state that DCM should use a per-factor column sum, counting how many latent units affect each generative factor. The metric's stated definition, 'whether each generative factor is encoded by a single latent unit,' requires a column sum. As written, DCM measures the average number of factors changed by a unit, not compactness across units for a factor. Consequently, the DCM values in Tables 3 and 4, including the conclusions that ArSyD is more compact than BetaVAE and FactorVAE, do not support the claims. Please correct Eq. (8) to aggregate over units for each factor, recompute the affected tables, and state clearly which operationalization is used.
  2. [Abstract; Section 3.1, Eqs. (3)–(4); Section 3.2–3.3, Eq. (5); Section 4, Figure 7] The abstract and Section 3.1 claim that 'disentanglement is achieved by construction,' but this is not established by the training procedure. In each weakly supervised pair, all factors except the exchanged one are identical between target and donor, so the exchange loss in Eq. (5) only requires V*_p to carry enough information to transfer factor p; it never penalizes V*_p for also encoding other factors, because those factors are constant in the pair and the decoder can ignore redundant information. The HDC binding in Eq. (1) makes the bound terms quasi-orthogonal, but it does not constrain V*_i itself to be independent of the other factors. The paper's own Figure 7 and accompanying text say that the 'Orientation' feature is 'strongly related' to the 'Shape' feature, which is direct evidence that the factor-alignment assumption can fail. The claim should be weakened to 'encouraged by the weak supervision objective,' or the authors should provide a direct analysis (e.g., probing or decoding each V*_i in isolation, or a full pairwise intervention matrix) demonstrating that each V*_i is factor-pure.
  3. [Section 4, RQ8, Figures 13–14] RQ8 concludes that the value vectors V*_i represent separate properties because decoding a single vector bound to a placeholder does not reconstruct a complete image. This conclusion does not follow from the evidence: a vector that encodes a mixture of several factors, but is alone insufficient to generate a full image, would produce qualitatively the same incomplete reconstructions. To support the factor-purity interpretation, the authors should test interventions directly, e.g., by modifying V*_i and measuring which downstream factor classifications change, or by training linear probes on V*_i to see whether they predict only the intended factor.
minor comments (5)
  1. [Figure 4] The caption says 'DCN metric' in the last sentence; this should be 'DCM metric.'
  2. [Eq. (5)] The text after Eq. (5) says '˜Od – a reconstructed target object'; this should be '˜Ot – a reconstructed target object,' and the donor terms should be labeled consistently.
  3. [Section 3.7 and Table 3] Section 3.7 states that dSprites paired was trained for 600 epochs, whereas the caption of Table 3 says 200 epochs for dSprites paired; please reconcile these numbers.
  4. [Section 3.8] The metric classifiers are described as six ResNet-34 models fine-tuned on the CLEVR1 paired dataset, but the paper also reports DMM and DCM for dSprites paired; please specify which classifiers are used for dSprites and CelebA, and report their per-factor accuracies on the reconstruction sets.
  5. [Section 3.4] The term 'unit' is introduced in the metrics section, but Figure 4 and the surrounding text use 'DCN' and 'DCM' inconsistently; please unify the notation.

Circularity Check

1 steps flagged · score 4.0 of 10

The headline 'disentanglement by construction' is partly definitional: the decomposition is named a 'symbolic disentangled representation' without an equation or loss term forcing each V*_i to be factor-pure; the empirical evaluations themselves are not fitted to the metrics.

  1. self definitional [Abstract; Section 3.1, paragraph after Eq. (4) and text defining the representation]
    "Disentanglement is achieved by construction, no additional assumptions about the underlying distributions are made during training... The resulting value vectors V ∗ i are multiplied by the corresponding generative factor vectors Gi and summed to produce the vector O, which is a symbolic disentangled representation of an object."

    The 'achieved by construction' claim reads the disentanglement property off the notation 'generative factor vector' and the name 'symbolic disentangled representation'. Equation (4) only defines V*_i as an attention mixture over the codebook of factor i; Equation (5) only requires MSE reconstruction after exchanging one index. Nothing in Eqs. (3)-(5) constrains V*_i to exclude information about other generative factors, and the paper itself reports in Figure 7 that on dSprites 'the Orientation feature is strongly related to the Shape feature'. Thus the asserted guarantee is not derived from the architecture or loss; it is equivalent to the paper's own definitional label for a sum of bound hypervectors.

full rationale

I examined the claimed derivation chain: HDC composition (Eq. 1-2), grounding through attention over a frozen codebook (Eq. 3-4), weak-supervision exchange with reconstruction-only loss (Eq. 5-6), and the DMM/DCM evaluation (Eq. 7-8). The only load-bearing step that reduces to its own input is the abstract's 'disentanglement is achieved by construction': the representation is called a 'symbolic disentangled representation' because it is written as a sum of vectors named after generative factors, but the learned V*_i are not proven factor-pure, and the paper's own qualitative results show orientation/shape entanglement. That is a terminological/definitional circularity in the central claim. The remaining machinery is not circular in the same way: DMM and DCM are not part of the training losses, the classifier-based metrics use external ResNet classifiers and are not fitted to ArSyD, and the comparisons also include IoU/FID against BetaVAE and FactorVAE. Self-citations in the paper ([21,22,29-32]) are contextual and not load-bearing. The Limitations section candidly acknowledges classifier dependence and the need to know generative factors beforehand; those are validity caveats, not circularity. Overall the central guarantee is overstated by definitional naming, but the empirical core retains independent content, so a moderate score is appropriate.

Assumptions & free parameters 5 free parameters · 6 assumptions · 2 invented entities

The central contribution is built on a frozen random codebook, an assumed known factor structure, paired training data, and two new metrics. Since no code, data, or pre-trained models are released, all support comes from the paper's own reported experiments, and one of the metrics, DCM, appears to be misformulated relative to its definition.

free parameters (5)
  • Latent dimension D = 1024 in main runs; swept from 16 to 2048
    Manual hyperparameter controlling hypervector dimension; larger D improves IoU and classifier accuracy in Tables 4-6.
  • Number of generative factors N = 5 for dSprites, 6 for CLEVR, 7 for CelebA
    Must be specified a priori; the paper lists this as a limitation in Section 5.
  • Value codebook sizes per factor = dSprites: 3 shapes, 6 scales, 40 orientations, 32 x-values, 32 y-values; CLEVR: per-dataset factor value lists…
    Defines the item memory and the softmax scope in the attention module; chosen from dataset metadata.
  • Attention K/Q projection size = 1024
    Architecture choice for the GF representation modules; not systematically ablated.
  • Number of slots K for CLEVR5 = 6
    One more than the maximum number of objects in the scene, following Slot Attention defaults.
assumptions (6)
  • standard math Random Gaussian hypervectors of dimension D are mutually quasi-orthogonal and circular convolution binding and unbinding behave as in HRR.
    Section 3.1 relies on concentration of measure and HRR properties for the frozen codebook.
  • domain assumption Each image contains one object with a known finite set of generative factors, or in CLEVR5 a known maximum number of objects and reliable slot decomposition.
    Section 3.1 and 3.5; required to construct codebooks and paired training sets.
  • domain assumption Training pairs differ in exactly one known generative factor and the feature exchange vector e is available.
    Section 3.2; this weak supervision signal is the only learning signal that aligns each attention output with a factor.
  • domain assumption MSE reconstruction is a sufficient training signal for the attention outputs to become factor-aligned.
    Section 3.3; no explicit orthogonality, sparsity, or factor-alignment loss is imposed.
  • domain assumption Classifiers trained on original images give reliable factor predictions on reconstructed images for DMM and DCM.
    Section 3.4; acknowledged as a limitation, and Tables 5-6 show low accuracies for some factors.
  • domain assumption Slot Attention discovers object masks that are accurate enough for edited objects to be re-inserted into scenes.
    Section 3.3 and Figure 10; the authors note that restored slot masks often take up more space than the object.
invented entities (2)
  • Symbolic disentangled representation (superposition of bound hypervectors as a latent image code)
    purpose: Central representation that enables controlled factor editing by vector exchange.
    Introduced by this paper; its disentanglement is demonstrated only through the paper's own metrics and qualitative figures, with no external benchmark or downstream task validation.
  • DMM and DCM disentanglement metrics
    purpose: Evaluate disentanglement across localist and distributed latent representations using classification of reconstructed images.
    New metrics proposed here; DCM as written appears inconsistent with its stated definition, and the metrics depend on external labeled classifiers whose accuracy is limited for several factors.

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Pith. "Pith review of Symbolic Disentangled Representations for Images." pith.science (2026). https://pith.science/paper/TPIJX6E7

@misc{pith2026241219847,
  author       = {Pith},
  title        = {Pith review of: Symbolic Disentangled Representations for Images},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TPIJX6E7}},
  note         = {Machine review of arXiv:2412.19847}
}
read the original abstract

The idea of disentangled representations is to reduce the data to a set of generative factors that produce it. Typically, such representations are vectors in latent space, where each coordinate corresponds to one of the generative factors. The object can then be modified by changing the value of a particular coordinate, but it is necessary to determine which coordinate corresponds to the desired generative factor -- a difficult task if the vector representation has a high dimension. In this article, we propose ArSyD (Architecture for Symbolic Disentanglement), which represents each generative factor as a vector of the same dimension as the resulting representation. In ArSyD, the object representation is obtained as a superposition of the generative factor vector representations. We call such a representation a \textit{symbolic disentangled representation}. We use the principles of Hyperdimensional Computing (also known as Vector Symbolic Architectures), where symbols are represented as hypervectors, allowing vector operations on them. Disentanglement is achieved by construction, no additional assumptions about the underlying distributions are made during training, and the model is only trained to reconstruct images in a weakly supervised manner. We study ArSyD on the dSprites and CLEVR datasets and provide a comprehensive analysis of the learned symbolic disentangled representations. We also propose new disentanglement metrics that allow comparison of methods using latent representations of different dimensions. ArSyD allows to edit the object properties in a controlled and interpretable way, and the dimensionality of the object property representation coincides with the dimensionality of the object representation itself.

Figures

Figures reproduced from arXiv: 2412.19847 by the authors.

Figure 1
Figure 1. The Architecture for Symbolic Disentanglement (ArSyD) uses an encoder network and a Generative Factor (GF) projection to represent the target and donor images as sets of HVs. These HVs correspond to the values of the underlying generative factors in the data. The same encoder is used for both target and donor objects. While most of the values for the generative fac￾tors are the same between the donor and target imag… view at source ↗
Figure 2
Figure 2. The process of obtaining a symbolic disentangled representation of an object: a) usual approach in HDC – a symbolic description is used without grounding in the raw data; b) approach in ArSyD – the symbolic description of an object is grounded in the raw data to obtain its symbolic disentangled representation. object and the donor object and get the representations Oˆ1 and Oˆ2, respectively. If we reconstruct the or… view at source ↗
Figure 3
Figure 3. An ArSyD architecture for the case of multiple objects in the scene. We use Slot Attention to discover objects in the scene and represent it as a collection of individual objects. The Feature Exchange module is then used to replace the value of the desired generative factor. The model is trained end-to-end with a loss LScene (Equation 6). where S – an original scene, S˜ – a reconstructed original scene, S ′ – a scen… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: The Disentanglement Modularity Metric refers to evaluating whether each latent unit is responsible for encoding only one gen￾0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 2 2 1 3 2 4 2 1 0 F1 F2 F3 F4 F5 DMM DCM DCM DCM . . . . ℎ Decoder 𝑆" Classifier…
Figure 5
Figure 5. Figure 5: Examples of image pairs from the training sample of datasets: a) dSprites paired; b) CLEVR1 paired; c) CLEVR5 paired. 3.5.3 CelebA paired The CelebA dataset consists of 200k celebrity images and is la￾beled with 40 binary features describing appearance. Since ArSyD is …
Figure 6
Figure 6. Figure 6: Image reconstruction of the CLEVR1 paired and dSprites paired objects from HDC representations without grounding to the images [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Image reconstruction of objects with modified generative factor values (yellow frame) for the dSprites paired dataset. The target object (red frame) differs from the donor object (blue frame) in all factor values. D DMM↓ DCM↓ IoU ↑ 16 1.46 ± 0.12 1.74 ± 0.02 0.948 ± 0.…
Figure 8
Figure 8. Figure 8: Image reconstruction of objects with modified generative factor values (yellow frame) for the CLEVR1 paired dataset. The target object (red frame) differs from the donor object (blue frame) in all factor values. Original BetaVAE FactorVAE Our dSprites CLEVR Original Be…
Figure 9
Figure 9. Figure 9: Examples of image reconstruction for all models from the dSprites paired (left) and CLEVR paired (right) datasets. D Shape Scale Orientation Pos X Pos Y 16 0.36±0.08 0.23±0.31 0.09±0.06 0.04±0.03 0.01±0.01 32 0.61±0.01 0.18±0.18 0.11±0.02 0.03±0.02 0.03±0.02 64 0.41±0.…
Figure 10
Figure 10. Figure 10: Image reconstruction of scenes with multiple objects from a test sample with modified values of generative factors of one object for the CLEVR5 paired dataset. D Shape Size Material Color Pos X Pos Y 16 0.52 ± 0.33 0.51 ± 0.06 0.42 ± 0.41 0.27 ± 0.26 0.04 ± 0.02 0.04 …
Figure 12
Figure 12. Figure 12: Examples of image reconstruction from the CelebA paired dataset. feature reconstruction of a pre-trained DINO model [73]. We consider extending our approach to the unlabeled data, where the selection of generative factors to exchange during training is based on a crit…
Figure 11
Figure 11. Figure 11: Examples of image reconstruction of objects from the dSprites paired dataset with modified values of the generative factors. The target object (red frame) differs from the donor object (blue frame) in all factor values. trained neural networks, which are good feature …
Figure 14
Figure 14. Figure 14: Visualization of image reconstruction from a single feature vec￾tor from an item memory (bound to a placeholder value) for the CLEVR dataset. It shows that a complete image is not reconstructed from a single vector. This indicates that the vector represents a separate…
Figure 13
Figure 13. Figure 13: Visualization of image reconstruction from a single feature vec￾tor from an item memory (bound to a placeholder value) for the dSprites dataset. It shows that a complete image is not reconstructed from a single vector. This indicates that the vector represents a separ…

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Pith tools

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