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Weakly Supervised Disentangled Generative Causal Representation Learning

Xinwei Shen, Furui Liu, Hanze Dong, Qing Lian, Zhitang Chen, Tong Zhang

arXiv:2010.02637v3cs.LGcs.AIstat.ML

TL;DR

Disentanglement methods that assume independent latent factors do not address settings where factors are causally related, and the paper shows such priors can fail even under supervision. DEAR uses an SCM prior in a supervised bidirectional generative model. Experiments demonstrate causal controllable generation and downstream benefits, while its identifiability result is scoped to population-level supervision.

  • Problem

    Many disentanglement methods assume independent factors, although factors of interest may be causally related, and independent priors can fail even under supervision.

    Source: §1 · p. 2, §3.3 · p. 8

  • Method

    DEAR jointly learns an SCM latent prior, generator, and encoder in a supervised bidirectional generative model using annotated factors and causal-structure information.

    Source: §1 · p. 2, §3.2 · p. 7

  • Results

    Experiments demonstrate DEAR’s effectiveness in causal controllable generation and downstream tasks, including sample efficiency and distributional robustness.

    Source: §1 · p. 3

  • Takeaways & Limitations

    The learned causal representations support generation under desired latent-factor interventions and are beneficial for downstream prediction tasks.

    Source: §1 · p. 3, §5.1 · p. 16

    The identifiability result is at the population level under expectations over data and true-factor labels, not a general guarantee under weaker supervision.

    Source: §4.2 · p. 12

Abstract

from arXiv · show

This paper proposes a Disentangled gEnerative cAusal Representation (DEAR) learning method under appropriate supervised information. Unlike existing disentanglement methods that enforce independence of the latent variables, we consider the general case where the underlying factors of interests can be causally related. We show that previous methods with independent priors fail to disentangle causally related factors even under supervision. Motivated by this finding, we propose a new disentangled learning method called DEAR that enables causal controllable generation and causal representation learning. The key ingredient of this new formulation is to use a structural causal model (SCM) as the prior distribution for a bidirectional generative model. The prior is then trained jointly with a generator and an encoder using a suitable GAN algorithm incorporated with supervised information on the ground-truth factors and their underlying causal structure. We provide theoretical justification on the identifiability and asymptotic convergence of the proposed method. We conduct extensive experiments on both synthesized and real data sets to demonstrate the effectiveness of DEAR in causal controllable generation, and the benefits of the learned representations for downstream tasks in terms of sample efficiency and distributional robustness.

1. Introduction

Disentanglement can support both learning useful representations and controlling semantic generation, but many methods assume independent factors even though meaningful factors may be causally related. DEAR uses an SCM prior in a bidirectional generative model and provides theoretical guarantees, with experiments demonstrating benefits for generation and downstream tasks.

Motivation and contributions

  • Disentanglement means that each latent dimension measures a distinct factor of variation, supporting both downstream representation learning and semantic control of generation.The introduction relates these goals to disentangled latent variables, citing Bengio et al. (2013) and StyleGAN (Karras et al., 2019).Source: §1 · p. 2
  • DEAR places an SCM prior on latent variables and jointly learns it with a generator and encoder using a suitable GAN algorithm.The method assumes a known super-graph of the underlying causal graph, ranging from causal ordering to the true structure.Source: §1 · pp. 2–3
  • Independent-prior methods fail to disentangle causally related factors, even with supervision, motivating DEAR’s causal formulation.The paper also establishes theoretical guarantees for identifiability and asymptotic convergence.Source: §1 · pp. 2–3
  • Experiments on synthesized and real data demonstrate causal controllable generation and downstream representation benefits in sample efficiency and distributional robustness.The paper frames causal controllable generation as producing data from desired interventional distributions of latent factors.Source: §1 · p. 3

2. Related work

Prior work often promotes disentanglement through independent latent priors, while this paper addresses causal relationships among factors. The related work distinguishes DEAR from approaches with narrower causal assumptions, different objectives, or fully supervised and unidirectional designs.

VAE-based disentanglement methods

  • Unlike methods enforcing independent latents, DEAR targets more general causal relationships than conditionally independent mechanisms or pairwise-correlated factors.Suter et al. (2019) consider conditional independence given a common confounder, while Träub­le et al. (2021) study pairwise correlation.Source: §2 · pp. 4–5

Identifiability and supervision

  • Khemakhem et al. (2020) provide conditional-prior identifiability under suitable conditions, while DEAR targets causal-factor disentanglement with annotated true-factor labels and does not claim general identifiability.The paper describes the two approaches as complementary; their supervision requirements differ.Source: §2 · pp. 4–5

GAN-based and causal generative methods

  • InfoGAN and InfoGAN-CR retain independent latent priors, while CausalGAN-style models are unidirectional, require full attribute supervision, and do not learn representations.CausalGAN and related methods also leave latent variables as independent Gaussian noises and consider binary factors.Source: §2 · p. 5

Generative modeling with causal latent spaces

  • GraphVAE uses an SCM to improve VAE expressive capacity, whereas DEAR targets disentanglement and permits reparameterizable SCMs without requiring an explicit prior density.The paper notes GraphVAE’s Gaussian additive-noise choice and lack of guaranteed factor disentanglement.Source: §2 · pp. 5–6

3. Problem setting

The problem setting combines bidirectional generation and inference with supervision on ground-truth factors and their graph structure. It formalizes why an independent latent prior can favor entangled representations when the factors are causally related.

3. Problem setting

  • The problem setting studies supervised bidirectional generative models and formalizes the unidentifiability problem of prior methods.The framework considers ground-truth factors of interest and supervision on both their labels and graph structure.Source: §3 · p. 6, §3.2 · p. 7

3.1 Generative model

  • A bidirectional generative model pairs a generator’s joint distribution with an encoder’s joint distribution, and expressive implicit distributions motivate adversarial training.The generator models pG(x,z)=pz(z)pG(x|z), while the encoder models qE(x,z)=qx(x)qE(z|x); implicit distributions are favored for complex data such as images.Source: §3.1 · p. 7

3.2 Supervised regularizer

  • Supervision aligns encoder dimensions with annotated ground-truth factors, using labels that may be discrete or continuous.The supervised and generative losses take separate expectations, allowing different sample sizes and making the formulation applicable when labeled samples are limited.Source: §3.2 · pp. 7–8, §3.3 · p. 8

3.3 Unidentifiability with an independent prior

  • With causally connected factors and a factorized latent prior, Proposition 4 gives conditions under which an entangled solution has lower total loss than a disentangled one.The paper says the threshold on the supervised-loss weight is impossible to estimate in real applications, while too large a weight makes learning the bidirectional model difficult.Source: §3.3 · pp. 8–9

4. Causal disentanglement learning

Section 4 develops DEAR, a bidirectional generative model with an SCM prior over latent factors, and establishes its formulation, learning procedure, and theoretical guarantees. It also describes interventional generation and a composite prior for handling an unknown latent dimension.

4.1 Generative model with a causal prior

  • DEAR combines a bidirectional generator–encoder with a nonlinear SCM latent prior and learns the prior’s weighted adjacency matrix.The prior is incorporated into the model alongside the encoder and generator.Source: §4.1 · p. 9, §4.1.1 · pp. 9–10

4.1.1 SCM prior

  • The SCM prior represents a DAG over latent factors through weighted adjacency A and exogenous Gaussian noise; invertibility of f supports latent interventions.After transformation by f, the factors satisfy a linear SCM.Source: §4.1.1 · pp. 9–10

4.1.2 Learning of A

  • DEAR learns edge weights within a supplied super-graph, which may range from the true graph to causal ordering alone; this constraint ensures acyclicity and removes a separate acyclicity constraint.The paper leaves causal discovery from scratch to future work.Source: §4.1.2 · pp. 10–11

4.1.3 Generation from interventional distributions

  • For an intervention, DEAR modifies the SCM equations, ancestrally samples the resulting latent factors, and decodes them into generated data.The intervention mechanism requires f to be invertible; exogenous noise can be fixed or resampled.Source: §4.1.3 · p. 11

4.1.4 Latent dimension and composite prior

  • To handle unknown total factor count M, DEAR sets k sufficiently large and composes a causal prior for m target dimensions with another distribution for the remaining k−m dimensions.Only the factors of interest need annotated labels for the supervised regularizer.Source: §4.1.4 · p. 11

4.2 DEAR formulation

  • The DEAR objective adds a supervised encoder loss to the generative loss, and under infinite E and G capacity and Assumption 1 its solution is identifiable as disentangled.This population-level result evaluates expectations over data and true-factor labels, rather than establishing a guarantee for weaker supervision.Source: §4.2 · p. 12

4.3 Algorithm

  • Algorithm 1 jointly learns the encoder, generator, and SCM prior using discriminator-estimated adversarial gradients together with the supervised loss.The generative loss uses unlabeled data, while the supervised loss uses labeled examples, whose sample size can be much smaller.Source: §4.3 · pp. 12–13

4.4 Consistency

  • Under the stated regularity assumptions, smooth objective, and Polyak–Łojasiewicz condition, increasing sample sizes yield approximate loss minimization with high probability and the desired disentangled model.The paper describes the PL condition as weaker than assumptions such as strong convexity.Source: §4.4 · pp. 14–15

5. Experiments

The experiments evaluate DEAR on Pendulum and CelebA through causal interventions, downstream prediction and structure learning, and tests of accuracy and sample efficiency across supervision and regularization settings.

5.1 Causal controllable generation

  • DEAR traversals vary only the selected factor where S-β-VAE changes multiple factors, while intervening on a cause changes its effects and intervening on an effect does not influence its cause.The examples include pendulum angle affecting shadow length and position, and smile affecting mouth open; without an SCM prior, S-β-VAE cannot generate general interventional distributions.Source: Figure 3 · p. 17, Figure 4 · p. 17, §5.1 · pp. 17–18

5.2.1 Sample efficiency

  • DEAR has the highest sample efficiency and test accuracy on both data sets; with 10% of labels, its efficiency remains comparable to full supervision while accuracy sacrifices remain competitive with more-supervised baselines.DEAR-SG performs comparably to DEAR with the true graph, while DEAR-O is slightly worse but still competitive; S-GraphVAE is inferior to DEAR and performs especially poorly on CelebA.Source: §5.2.1 · pp. 19–20, Table 1 · p. 20

5.2.2 Distributional robustness

  • DEAR representations significantly outperform the baselines in average and worst-case test accuracy, with a smaller robustness decline on CelebA than the roughly 80-to-60 drop for other methods.Worst-case accuracy is measured on the least accurate of four test groups formed by target and spurious labels; training data deliberately correlates spurious attributes with targets, unlike the test sets.Source: §5.2.2 · pp. 20–21, Table 2 · p. 21

5.3 Learning of the structure A

  • With the true graph, DEAR learns meaningful edge weights; given a super-graph, it can prune redundant edges and recover the true structure, whereas with only an ordering it can retain a spurious young-to-gender edge.The paper concludes that absent hidden confounders or spurious correlations, DEAR can recover the true graph from an ordering; under such biases, it may need a proper super-graph, and it outperforms GraphVAE in structure learning.Source: §5.3 · pp. 22, 24, Figure 8 · p. 23, Figure 9 · p. 24

5.4 Ablation study

  • Across λ values from 0.1 to 10, DEAR remains significantly superior to baseline methods, while performance generally decreases as λ approaches 0.At population level any positive λ suffices for the stated theoretical guarantees, but finite-sample estimation error motivates treating λ as a hyperparameter.Source: §5.4 · p. 25, Figure 10 · p. 25
  • As annotated labels decrease, all methods generally worsen, but DEAR continues to outperform VAEs; with 0.1%-1% CelebA labels, S-β-VAE and S-TCVAE fail in the worst-case group.At lower supervision, those VAEs can show higher sample-efficiency scores despite poor performance on both small and large samples, making the score misleading.Source: §5.4 · p. 25
  • Figure 11 evaluates worst-case and average test accuracy across λ choices on Pendulum and CelebA.The tested λ values are 0.1, 1, 5, and 10 on Pendulum, and 0.01, 0.1, 1, 5, and 10 on CelebA.Source: Figure 11 · p. 26
  • Figure 12 evaluates test accuracy with small training samples and sample efficiency across labeled-sample proportions on CelebA and Pendulum.The proportions are 0.001, 0.01, 0.1, and 1 on CelebA, and 0.01, 0.1, and 1 on Pendulum.Source: Figure 12 · p. 26

6. Conclusion

DEAR addresses the failure of independent-prior methods to disentangle causally related factors, and experiments support its use for causal generation, structure learning, and downstream tasks. The conclusion identifies more flexible supervision and structure discovery as directions for broader application.

6. Conclusion

  • Experiments support DEAR for causal controllable generation and structure learning, with learned representations benefiting downstream tasks.The paper also reports theoretical guarantees for identifiability and asymptotic consistency.Source: §6 · p. 26
  • Broader adoption may require more flexible factor supervision and causal-structure supervision, including structure discovery without prior graph information.The conclusion also suggests auxiliary observed variables or restricted labels, and causal discovery within DEAR, as future directions.Source: §6 · pp. 26–27
  • The current approach assumes IID observational data; extending it to non-IID settings, including data collected through interventions, remains future work.The conclusion points to interactive reinforcement-learning environments as one possible source of mixed interventional distributions.Source: §6 · p. 27

A.1 Preliminaries

  • The appendix preliminaries introduce notions and lemmas used in the proofs, including the Hellinger distance between distributions.The supplied bracketing covering number definition and uniform continuous mapping lemma are among the preliminary technical tools.Source: §A.1 · p. 28

A.2 Proof of Proposition 4

  • Independent-prior methods fail to disentangle causally related factors; the appendix proof shows the factorized prior cannot match the non-factorized encoded distribution.The proof concludes that the generative loss has a positive minimum for a disentangled encoder, and compares this with the supervised objective under stated conditions.Source: §A.2 · p. 29

Discussion on Tr¨auble et al. (2021, Proposition 1)

  • The paper’s Proposition 4 studies the formulation used by disentanglement methods directly, whereas Tr¨auble et al. (2021) Proposition 1 frames the issue through maximum likelihood estimation.The paper notes that the formulation’s first term upper-bounds negative log-likelihood.Source: Discussion on Tr¨auble et al. (2021,… · p. 29

A.3 Proof of Proposition 5

The Proposition 5 proof establishes recovery of a disentangled encoder and the true causal structure under capacity and identifiability assumptions. The encoder’s target transformation depends on the supervised loss.

A.3 Proof of Proposition 5

  • With infinite-capacity encoder and generator and Assumptions 1 and 2, DEAR learns a disentangled encoder and the true causal structure.Assumption 2 requires any matching prior parameterization to identify the true adjacency matrix; the proof also invokes causal ordering under Markov and causal-minimality conditions.Source: §A.3 · p. 30
  • The proof assumes the true factor distribution is represented by a parameterized prior, enabling the generative loss to match the encoded joint distribution.The proof’s matching argument yields a zero generative loss at the target encoder and generator.Source: §A.3 · p. 30
  • The recovered encoder applies σ^-1 to each factor with cross-entropy supervision and the identity transformation with L2 supervision.For stochastic encoders, the proof establishes disentanglement for the deterministic part.Source: §A.3 · pp. 30–31

A.4 Proof of Lemma 7

The Lemma 7 proof establishes consistency of the discriminator and its approximate gradient in the generative-model analysis. It combines likelihood-based estimation with compactness, smoothness, and tightness arguments.

A.4 Proof of Lemma 7

  • The discriminator is fit as a logistic classifier distinguishing encoded data pairs from generator-prior pairs, with equal class priors.The empirical loss is based on IID samples from the resulting joint distribution over data, latent variables, and class labels.Source: §A.4 · p. 31
  • The proof establishes consistency of the discriminator estimate and then of its gradient as the discriminator sample size grows.It identifies the target discriminator as the log density ratio between the encoded joint and generator-prior joint distributions.Source: §A.4 · pp. 31–32
  • Uniform boundedness and regularity on compact sets, together with tightness, extend the consistency argument beyond compact regions.The proof bounds the tail contribution using bounded functions, gradients, and Hessians, then lets the tail probability shrink.Source: §A.4 · p. 33
  • The proof next establishes consistency of the approximate gradient and combines it with convergence of the target gradient to the loss gradient.The conditional event argument yields convergence in probability as discriminator and sample counts grow.Source: §A.4 · p. 34

A.5 Proof of Theorem 8

The appendix proves an asymptotic convergence result and develops a causal disentanglement metric. It then relates that metric to downstream-task performance and discusses its scope.

A.5 Proof of Theorem 8

  • With a sufficiently small learning rate, the proof bounds the squared approximate-gradient norm by O(1/T) at some iterate.The step-size condition is η < 1/4ℓ0.Source: §A.5 · p. 35

A.6 Proof of Lemma 6

  • To prove Lemma 6, the authors use a lemma specifying dynamics of the generator and encoder joint distributions; separately, the proof of Lemma 13 establishes only (21), identified as distinct from Shen et al. (2020).Source: §A.6 · p. 36

B. Causal disentanglement and downstream tasks

  • The downstream analysis compares methods using the same encoder and decoder architectures and label amounts, with GraphVAE and DEAR given the same graph information.It investigates whether causal disentanglement scores correlate with sample efficiency and distributional robustness.Source: B. Causal disentanglement and… · p. 37

B.1 Metric for causal disentanglement

  • The authors explain that MIG can score a disentangled representation poorly when correlated factors each carry information about separate representation coordinates.In that case, the mutual-information gap between the top two coordinates may be small despite one-to-one mappings from each factor to its coordinate.Source: §B.1 · p. 38
  • The proposed causal disentanglement metric adapts the FactorVAE metric to causally related factors by sampling according to the true SCM.Its evaluation requires ground-truth factors and the ground-truth SCM, so the authors limit its use to evaluating this relationship and leave a broadly applicable metric for future work.Source: §B.1 · pp. 38–39

B.2 Experimental results

Across seven supervised disentanglement models, causal disentanglement scores positively correlate with downstream performance. Small-sample accuracy and worst-case accuracy show the strongest reported association.

B.2 Experimental results

  • Higher causal disentanglement scores positively correlate with downstream-task performance across the evaluated models.The scatter plots compare seven models, trained with the same architectures and labels; GraphVAE and DEAR receive the true graph structure.Source: §B.2 · p. 39, Figure 14 · p. 39
  • Small-sample accuracy and worst-case accuracy show the strongest reported association with causal disentanglement.The corresponding fitted lines have the largest slope, as reported by the authors.Source: §B.2 · p. 39, Figure 14 · p. 39
  • The comparison includes S-β-VAE, S-TCVAE, S-GraphVAE, and four DEAR-LIN models with λ values 0.1, 1, 5, and 10.All models use fully supervised labels; GraphVAE and DEAR are given the true graph structure.Source: §B.2 · p. 39

C. Discussion: supervision for disentanglement learning

The discussion distinguishes direct factor labels from auxiliary information and treats the two supervision forms as complementary. It argues that causal-graph settings challenge existing methods based on independent or conditionally independent priors.

C. Discussion: supervision for disentanglement learning

  • Auxiliary-variable supervision avoids direct factor annotations but requires variability and correlation assumptions, and current identifiability theory also imposes relatively strong structure assumptions.The cited example assumes conditional independence of the true factors.Source: C. Discussion: supervision for… · p. 40
  • Direct labels are a feasible setting when conceptual knowledge of the true factors is available, but existing independent- or conditionally-independent-prior methods generally cannot identify causal disentanglement.The paper states this holds even with Form 1 supervision and cites its Proposition 4.Source: C. Discussion: supervision for… · p. 40
  • DEAR addresses this causal-graph setting with a bidirectional generative model using an SCM prior, trained with a GAN-type algorithm under stated assumptions.The discussion contrasts this approach with existing formulations that may not reach the optimum of the supervised loss.Source: C. Discussion: supervision for… · p. 40

D. Discussion: generalization to unseen interventions

DEAR is trained on observational data, while its estimated SCM supports sampling from interventional distributions. Experiments show generated samples for interventions absent from training, though systematic encoder generalization analysis remains future work.

D. Discussion: generalization to unseen interventions

  • DEAR’s observational training data do not include a mixture of interventional distributions, motivating the question of generalization to unseen interventions.The discussion considers an interventional latent distribution whose induced data distribution differs from the observational one.Source: D. Discussion: generalization to… · p. 41
  • Given the causal graph, the authors describe estimating SCM assignments from observational data and using the estimated SCM to sample interventional distributions.Interventions modify assignments, for example by changing exogenous noise or setting an assignment to a constant.Source: D. Discussion: generalization to… · p. 41
  • DEAR generates examples for unseen interventions, including bald female faces, female faces with beards, and intermediate glasses states absent from training.The examples also include changing factors while holding others fixed, including cases that do not satisfy the projection law.Source: D. Discussion: generalization to… · p. 41, Figure 15 · p. 42
  • Systematic analysis of the encoder’s out-of-distribution generalizability is left for future work.The authors suggest using the generator’s generalization to unseen interventions as one possible direction for improving encoder OOD performance.Source: D. Discussion: generalization to… · p. 41

E. Experiments in the independent case

The independent-factor benchmarks test DEAR with an independent prior and sparse labels. DEAR outperforms weakly-supervised TCVAE on disentanglement, while both methods lose performance under cross-dataset transfer.

E. Experiments in the independent case

  • MPI3D-real and MPI3D-simu each contain 1,036,800 images at 64 × 64 × 3 resolution, with labels for about 0.01% of samples and independent ground-truth factors.The experiments use a simplified DEAR with a standard Gaussian prior and require no graph-structure information.Source: E. Experiments in the independent case · p. 42
  • The evaluation uses weakly-supervised TCVAE as the representative baseline and FactorVAE score, skipping the majority-vote classifier because supervision aligns representations with factors.The experiments also examine transfer between real and simulated data.Source: E. Experiments in the independent case · pp. 42–43
  • DEAR significantly outperforms weakly-supervised TCVAE on disentanglement, especially within-dataset; both decline under transfer, and the section reports state-of-the-art performance on independent-factor data.Table 3 presents the MPI3D results, but the supplied passages do not report its cell values.Source: E. Experiments in the independent case · p. 43, Table 3 · p. 43

F. Implementation details

The appendix specifies the data processing, network architectures, SCM prior implementation, and training settings used across experiments.

F. Implementation details

  • CelebA images are center-cropped and CelebA and Pendulum images resized to 64 × 64; adversarial training uses Adam and the stated supervised-loss settings.The supervised regularizer coefficient is set to 5 unless otherwise indicated; the cited passage also notes full supervision for the reported controllable-generation results.Source: F. Implementation details · p. 43
  • Downstream classifiers are two-level MLPs with 100 hidden nodes, trained for about 150 CelebA, 600 Pendulum, and 50 MPI3D epochs.The classifier uses Adam with a learning rate of 1 × 10^-2 and batch size 128.Source: F. Implementation details · p. 44
  • Pendulum’s factors are pendulum angle and light angle, which determine shadow length and position under the simulator’s projection law.The paper assumes parallel light and specifies uniform distributions for the noise variables.Source: F. Implementation details · p. 44, Figure 16 · p. 44
  • The SCM prior uses Gaussian unexplained noise with identity mapping, while its invertible elementwise transformation is implemented as diagonal linear or piecewise-linear functions.The piecewise-linear family is described as expressive enough to model general elementwise nonlinear invertible transformations.Source: F. Implementation details · pp. 44–45
  • For realistic data, the discriminator and generator use SAGAN architectures, and the encoder uses ResNet50 followed by a four-layer MLP.The architecture details are referenced in Figure 17 and Table 4.Source: F. Implementation details · p. 45, Table 4 · p. 45, Figure 17 · p. 46
  • The reproduced S-VAEs share DEAR’s encoder and generator architectures and optimizer; GraphVAE uses matching encoder-decoder architectures and precision-weighted fusion with 32 latent dimensions.The independence-regularizer coefficient for the S-VAEs is set to 4.Source: F. Implementation details · pp. 45–46

G. Additional results in causal controllable generation

The additional traversals evaluate causal controllable generation on Pendulum and CelebA under three structures. DEAR’s interventions show cause-effect changes, while baseline methods exhibit limitations in smoothness, disentanglement, or generation quality.

G. Additional results in causal controllable generation

  • Intervening on a DEAR cause variable changes its effect variables, while intervening on effect variables leaves causes unchanged.The figure contrasts these causal interventions with traditional latent traversals used to show disentanglement.Source: Figure 18 · p. 48
  • Baseline traversals show entanglement and uncaptured factors, while VAE-generated images are blurry.Some latent dimensions produce no change in decoded images when traversed.Source: Figure 19 · p. 49
  • CausalGAN’s binary-factor traversals show sudden changes, whereas manipulating continuous logits produces smoother traversals; its controllability remains limited by entanglement.The comparisons cover Pendulum and CelebA under the structures described for the traversal results.Source: G. Additional results in causal… · pp. 46–47, Figure 20 · p. 50
  • S-GraphVAE traversals look better than S-VAEs on Pendulum’s first two factors, but its CelebA performance and generation quality are poor.The baseline traversal results also report entanglement and factors not captured by some models.Source: Figure 19 · p. 49, Figure 20 · p. 50
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