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Disentanglement Learning via Topology
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Proposes TopDis, a differentiable multi-scale topological loss (RTD between reconstructions of a batch and of its Gaussian-preserving latent shift) added to VAE-family models to improve unsupervised disentanglement.
Problem
Unsupervised learning of disentangled representations in VAE-type models, which typically rely on statistical independence assumptions that fail for correlated factors of variation.
Approach
Adds a representation topology divergence (RTD) loss between a batch reconstructed from original latents and one reconstructed from latents shifted along a single latent axis via a Gaussian-CDF-preserving shift, plus gradient orthogonalization to protect reconstruction quality.
Key results
- FactorVAE + TopDis reaches MIG 0.356 vs 0.295 on dSprites and SAP 0.238 vs 0.179 on MPI 3D (FactorVAE baseline).
- beta-VAE + TopDis reaches FactorVAE score 1.0 and DCI 0.998 on 3D Shapes vs 0.965 and 0.913 for beta-VAE.
- Models with TopDis are the best variant for a dataset/metric in 94% of cases, per the authors.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add TopDis loss to FactorVAE | FactorVAE · dSprites | MIG: 0.295 ± 0.049 -> 0.356 ± 0.025 | Helped |
| Add TopDis loss to FactorVAE | FactorVAE · dSprites | DCI disentanglement: 0.534 ± 0.029 -> 0.521 ± 0.044 | Hurt |
| Add TopDis loss to FactorVAE | FactorVAE · 3D Shapes | MIG: 0.698 ± 0.151 -> 0.779 ± 0.036 | Helped |
| Add TopDis loss to FactorVAE | FactorVAE · 3D Faces | MIG: 0.593 ± 0.058 -> 0.626 ± 0.026 | Helped |
| Add TopDis loss to FactorVAE | FactorVAE · MPI 3D | SAP: 0.179 ± 0.052 -> 0.238 ± 0.040 | Helped |
| Add TopDis loss to VAE | VAE · dSprites reconstruction | reconstruction error: 8.67 ± 0.29 -> 9.54 ± 0.19 | Hurt |
| Add TopDis loss to VAE | VAE · 3D Shapes reconstruction | reconstruction error: 3494.10 ± 3.27 -> 3489.53 ± 1.50 | Helped |
| Add TopDis loss to FactorVAE | FactorVAE · 3D Faces reconstruction | reconstruction error: 1488.26 ± 4.47 -> 1377.93 ± 3.47 | Helped |
| Add TopDis loss to β-TCVAE | β-TCVAE · dSprites reconstruction | reconstruction error: 17.87 ± 0.56 -> 17.32 ± 0.31 | Helped |
| Add TopDis loss to DAVA | DAVA · MPI 3D reconstruction | reconstruction error: 3890.42 ± 2.15 -> 3893.41 ± 3.48 | Hurt |
Surprising findings
- DAVA reconstruction error on dSprites drops from 36.41 to 26.03 with TopDis loss.
- On 3D Faces, TopDis does not improve MIG or DCI for beta-VAE, and FactorVAE scores saturate at 1.0 across variants.
Limitations
- Evaluation restricted to image domain and mostly synthetic datasets with known factors.
- Disentanglement metrics show high variance across initialization seeds; some improvements are within error bars.
- Computational cost of RTD and the gradient orthogonalization details are only briefly discussed.
Experimental setup
Datasets: dSprites 3D Shapes 3D Faces MPI 3D CelebA FFHQ
Benchmarks: dSprites 3D Shapes 3D Faces MPI 3D
Metrics: MIG FactorVAE score SAP score DCI disentanglement score reconstruction error
Baselines: beta-VAE FactorVAE beta-TCVAE ControlVAE DAVA TCWAE HFS
Builds on: beta-VAE FactorVAE beta-TCVAE ControlVAE DAVA Representation Topology Divergence
Closest papers by meaning
- Evaluating the Disentanglement of Deep Generative Models through Manifold Topology (ICLR 2021 · similarity 0.90)
- Disentangled Representation Learning with the Gromov-Monge Gap (ICLR 2025 · similarity 0.87)
- When Is Unsupervised Disentanglement Possible? (NeurIPS 2021 · similarity 0.86)
- $\alpha$TC-VAE: On the relationship between Disentanglement and Diversity (ICLR 2024 · similarity 0.86)
- Learning disentangled representations via product manifold projection (ICML 2021 · similarity 0.86)
- Disentanglement via Latent Quantization (NeurIPS 2023 · similarity 0.86)
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