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StrWAEs to Invariant Representations
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Shows Wasserstein autoencoders can automatically derive structured encoders (with conditional-independence penalties) from a factorized decoder, yielding StrWAEs for semi-supervised classification, conditional generation, and invariant representation learning.
Problem
Imposing conditional-independence structure on latent variables to make them invariant to nuisance variables in autoencoders usually relies on ad hoc, heuristic penalties added to VAE objectives, with no principled way to determine the matching encoder structure.
Approach
Starting from a Wasserstein distance between data and a structured (chain-model) decoder distribution, the optimal encoder is shown to be constrained to mirror the decoder's factorization, so the encoder structure and penalties (distribution matching plus HSIC-type independence) follow from the WAE framework rather than being hand-designed.
Key results
- On MNIST with 100 labels, StrWAE reached 98.69% classification accuracy, the highest among compared semi-supervised models.
- On Extended Yale B, StrWAE achieved 0.98 identity accuracy (random forest) versus 0.72 for HCV, and FID 55.7 versus 232 for HCV.
- On MNIST conditional generation with true labels, StrWAE achieved 96.06% versus 36.69% for AAE and 16.03% for CCVAE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use StrWAE instead of AAE | Semi-supervised classification · MNIST (100 labeled) | classification accuracy: 98.10 (±0.35) -> 98.69 (±0.04) | Helped |
| Use StrWAE instead of GMVAE | Conditional generation · MNIST (100 labeled) | conditional generation accuracy (Y): 87.44 (±1.45) -> 96.06 (±0.57) | Helped |
| Use StrWAE instead of CCVAE | Semi-supervised classification · SVHN (1000 labeled) | classification accuracy: 90.02 (±0.07) -> 85.59 (±0.22) | Hurt |
| Use StrWAE instead of AAE | Conditional generation · SVHN (1000 labeled) | conditional generation accuracy (Y): 82.99 (±3.17) -> 98.80 (±0.44) | Helped |
| Use StrWAE instead of HCV | Invariant representation learning · Extended Yale B | identity accuracy: 0.72 -> 0.98 | Helped |
| Use StrWAE instead of HCV | Invariant representation learning · Extended Yale B | lighting group accuracy (RF): 0.51 -> 0.23 | Helped |
| Use StrWAE instead of HCV | Image generation · Extended Yale B | FID: 232 -> 55.7 | Helped |
| Use StrWAE instead of AAE | Speech recognition · Mini Speech Recognition | classification accuracy (Y): 24.03 -> 60.88 | Helped |
| remove the HSIC penalty (ablation) | StrWAE invariant representation model · Extended Yale B | identity accuracy | Hurt |
Surprising findings
- The authors report that the M1+M2 classification accuracy from Kingma et al. (2014) could not be reproduced, so they excerpt the reported number.
- Smooth-ELBO had high SVHN classification accuracy but poor generation quality, where generated images did not retain the input class.
Limitations
- Penalty parameters are finite in practice, so the choice of divergence D and independence criterion H affects performance; exotic divergences were not explored.
- Results on the Extended Yale B and VGGFace2 generation are evaluated with FID on small test sets, which the authors caution should be interpreted carefully.
- Requires the decoder to be injective (ensured via leaky ReLU and random convolution kernels), a restriction on architecture.
Experimental setup
Datasets: MNIST SVHN VGGFace2 Extended Yale B Mini Speech Recognition dataset
Benchmarks: MNIST SVHN VGGFace2 Extended Yale B Mini Speech Recognition
Metrics: classification accuracy conditional generation accuracy FID sharpness MSE
Baselines: GMVAE M1+M2 AAE CCVAE Smooth-ELBO HCV VAE Fader Networks
Builds on: Wasserstein autoencoder semi-supervised VAE (M1+M2) HSIC-constrained VAE adversarial autoencoder Fader Networks
Closest papers by meaning
- A Statistical Analysis of Wasserstein Autoencoders for Intrinsically Low-dimensional Data (ICLR 2024 · similarity 0.89)
- Statistical Regeneration Guarantees of the Wasserstein Autoencoder with Latent Space Consistency (NeurIPS 2021 · similarity 0.89)
- Gromov-Wasserstein Autoencoders (ICLR 2023 · similarity 0.89)
- Wasserstein Auto-Encoders (ICLR 2018 · similarity 0.87)
- Embrace the Gap: VAEs Perform Independent Mechanism Analysis (NeurIPS 2022 · similarity 0.87)
- Trading Information between Latents in Hierarchical Variational Autoencoders (ICLR 2023 · similarity 0.87)
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