Research map / Label-efficient and robust learning / Recognition and long-tail
Manifold Topology Divergence: a Framework for Comparing Data Manifolds.
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MTop-Div to evaluate controllable CIFAR10 disturbances instead of Geometry Score | GAN evaluation · CIFAR10 synthetic modifications | Kendall-tau rank correlation with disturbance level: 0.36 to 0.89 | Helped |
| Use relative point-cloud positions in MTop-Div rather than Geometry Score's RLT comparison | Evaluation of flipped MNIST digits · MNIST vertically flipped 5s | Sensitivity to the flip | Helped |
| Use MTop-Div to assess mode coverage rather than Geometry Score | GAN evaluation · 2D mixture of Gaussians | Detection of mode dropping | Helped |
| Apply truncation ψ=0.7 instead of ψ=1.0 | StyleGAN and StyleGAN2 · FFHQ | MTop-Div(M,D): 234.33 to 712.57; 162.08 to 1011.53 | Hurt |
| Use MTop-Div to track training dynamics alongside conventional distribution metrics | GAN trained on ShapeNet chairs · ShapeNet chairs | Sensitivity to generated-manifold expansion at epoch 50 | Helped |
| Use MTop-Div alongside discriminative score to track training | TimeGAN · Market stock time-series | Sensitivity to manifold convergence around epoch 2000 | Helped |
| Use MTop-Div rather than FID to compare real COVID-positive and COVID-negative images | GAN evaluation · Chest X-ray images | Consistency with the expected real-data comparison | Helped |
Closest papers by meaning
- Topology Distance: A Topology-Based Approach for Evaluating Generative Adversarial Networks (AAAI 2021 · similarity 0.89)
- The Data Manifold under the Microscope (ICML 2026 · similarity 0.88)
- Verifying the Union of Manifolds Hypothesis for Image Data (ICLR 2023 · similarity 0.87)
- What Secrets Do Your Manifolds Hold? Understanding the Local Geometry of Generative Models (ICLR 2025 · similarity 0.86)
- The Geometric Wall: Manifold Structure Predicts Layerwise Sparse Autoencoder Scaling Laws (NeurIPS 2026 · similarity 0.86)
- MANTRA: The Manifold Triangulations Assemblage (ICLR 2025 · similarity 0.85)
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