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Verifying the Union of Manifolds Hypothesis for Image Data
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| weight cross entropy terms per class proportionally to class intrinsic dimension | ResNet-18 on CIFAR-100 · CIFAR-100 | test accuracy (%): +0.39 points (61.38% to 61.77%) | Helped |
| train disconnected WAE per class label instead of single WAE | WAE · MNIST, FMNIST, CIFAR-10 (FID) | FID: MNIST 19.1 to 13.5; FMNIST 51.2 to 36.8; CIFAR-10 146.7 to 133.3 | Helped |
| train disconnected WAE per class label instead of single WAE | WAE on CIFAR-100 · CIFAR-100 | FID: 145.0 to 209.9 (worse) | Hurt |
| random labels instead of class labels for disconnected WAE (ablation) | WAE on MNIST · MNIST | FID: D-WAE (random) 23.7 vs D-WAE (classes) 13.5; also worse than WAE 19.1 | Hurt |
| unsupervised clustering (agglomerative, Ward) instead of class labels for disconnected WAE | WAE · CIFAR-100 | FID: 145.0 to 134.3 | Helped |
| disconnected two-step VAE+NF with clusters vs non-disconnected VAE+NF | VAE+NF · MNIST | FID: 119.7 to 73.0 | Helped |
| per-class disconnected two-step VAE+NF with constant latent dimension vs VAE+NF | VAE+NF · CIFAR-100 | FID: 204.0 to 188.1 | Helped |
| setting per-cluster latent dimensions to estimated intrinsic dimension instead of constant dimension in disconnected VAE+NF (ablation) | D-VAE+NF · MNIST, FMNIST, SVHN, CIFAR-10, CIFAR-100 | FID: mixed differences, not significant per paper (e.g. MNIST 73.0 vs 75.1; CIFAR-100 207.8 vs 207.2) | No clear effect |
| per-class disconnected WAE+NF with latent dims set to class intrinsic dimension estimates vs constant dimension on synthetic golden retriever-based data (ablation) | D-WAE+NF · synthetic BigGAN golden retriever data | FID: large improvement, gap shrinks as true dimension difference decreases | Helped |
| WAE with GMM prior instead of Gaussian prior | WAE · MNIST | FID: 152.7 vs 19.1 | Hurt |
| per-class disconnected VAE trained on class labels | VAE · MNIST | FID: 110.7 to 81.5 | Helped |
| per-class disconnected VAE trained on class labels | VAE on CIFAR-100 · CIFAR-100 | FID: 198.4 to 203.3 | Hurt |
Closest papers by meaning
- CW Complex Hypothesis for Image Data (ICML 2024 · similarity 0.91)
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- Hardness of Learning Neural Networks under the Manifold Hypothesis (NeurIPS 2024 · similarity 0.87)
- Geometric Analysis of Nonlinear Manifold Clustering (NeurIPS 2024 · similarity 0.87)
- Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations (ICLR 2025 · similarity 0.86)
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