Research map / Probabilistic and scientific modeling / Variational and generative sampling
Towards Scalable Topological Regularizers
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes PPM-Reg, a GPU-parallelized topological regularizer built from principal persistence measures of small subsamples compared via MMD, and shows gains in shape matching, GAN image generation, and semi-supervised learning.
Problem
Persistent homology is too costly to compute at scale and its gradients are discontinuous, causing unstable training when used as a topological regularizer in latent space matching for GANs and adversarial tasks.
Approach
Replace full persistent homology with principal persistence measures (PH of many 2q+2-point subsamples), parallelized on GPU, and compare these measures with an MMD using a persistence-weighted RBF kernel, which is proven to induce the Wasserstein topology and to have continuous gradients for smooth densities.
Key results
- On 32x32 image generation, Cramer + PPM-Reg reduces CMMD on AnimeFace from 0.73 to 0.56 and on CelebA from 0.72 to 0.58 versus Cramer alone.
- On semi-supervised learning with 200 labels, Cramer + PPM-Reg reaches 75.78% on Kuzushiji-MNIST versus 48.40% for the baseline, and 96.62% on MNIST versus 80.52%.
- PPM-Reg running time for 100 gradient steps stays around 0.55-1.00 s across 128-1024 points with s=512-2048, while PD-Reg takes 655.58 s at 1024 points.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add PPM-Reg to Cramer | Cramer GAN · AnimeFace 32×32 | CMMD: 0.73 -> 0.56 | Helped |
| Add PPM-Reg to Cramer | Cramer GAN · CelebA 32×32 | CMMD: 0.72 -> 0.58 | Helped |
| Add PPM-Reg to Cramer | Cramer GAN · AnimeFace 32×32 | FD_Dinov2: 953.99 -> 780.68 | Helped |
| Add PPM-Reg to Cramer | Cramer GAN · CelebA 32×32 | FD_Dinov2: 722.86 -> 700.73 | Helped |
| Add PPM-Reg to Cramer | Cramer GAN · AnimeFace 32×32 | WD_latent: 0.6294 -> 0.6080 | Helped |
| Add PPM-Reg to Cramer | Cramer GAN · CelebA 32×32 | WD_latent: 0.6795 -> 0.6666 | Helped |
| Add PPM-Reg to Cramer GAN representation learning | Semi-supervised classifier using frozen GAN discriminator features · Fashion-MNIST, 200 labels | test accuracy: $62.70\pm1.25$ -> $76.84\pm1.23$ | Helped |
| Add PPM-Reg to Cramer GAN representation learning | Semi-supervised classifier using frozen GAN discriminator features · Fashion-MNIST, 400 labels | test accuracy: $68.58\pm1.08$ -> $80.59\pm0.69$ | Helped |
| Add PPM-Reg to Cramer GAN representation learning | Semi-supervised classifier using frozen GAN discriminator features · Kuzushiji-MNIST, 200 labels | test accuracy: $47.77\pm1.40$ -> $75.78\pm1.99$ | Helped |
| Add PPM-Reg to Cramer GAN representation learning | Semi-supervised classifier using frozen GAN discriminator features · Kuzushiji-MNIST, 400 labels | test accuracy: $56.06\pm1.88$ -> $79.33\pm1.69$ | Helped |
| Add PPM-Reg to Cramer GAN representation learning | Semi-supervised classifier using frozen GAN discriminator features · MNIST, 200 labels | test accuracy: $71.10\pm 1.52$ -> $96.62\pm\textbf{0.39}$ | Helped |
| Add PPM-Reg to Cramer GAN representation learning | Semi-supervised classifier using frozen GAN discriminator features · MNIST, 400 labels | test accuracy: $78.26\pm1.30$ -> $97.33\pm\textbf{0.21}$ | Helped |
Surprising findings
- Improved Cramer loss does not always translate into better evaluation metrics during GAN training, so the reported results use CMMD for early stopping.
- Cramer GAN alone does not improve semi-supervised classification over the baseline on several datasets (e.g., Fashion-MNIST at 200 labels: 62.70% vs 67.18%).
Limitations
- MMD metrics on PPMs are not guaranteed to be stable with respect to Wasserstein perturbations, unlike the PPM stability result.
- Reported image generation results rely on CMMD-based early stopping that is expensive to compute in practice.
- Experiments are limited to small image resolutions (32x32, with 64x64 in appendix) and small GANs.
Experimental setup
Datasets: CelebA AnimeFace Fashion-MNIST Kuzushiji-MNIST MNIST SVHN LSUN Kitchen
Benchmarks: CelebA AnimeFace Fashion-MNIST Kuzushiji-MNIST MNIST
Metrics: CMMD FD_Dinov2 WD_latent classification accuracy 2-Wasserstein distance between persistence diagrams running time
Baselines: Cramer GAN PD-Reg W-PPM-Reg MMD
Builds on: Cramer GAN principal persistence measures persistence weighted kernels torch-topological
Closest papers by meaning
- Diffeomorphic interpolation for efficient persistence-based topological optimization (NeurIPS 2024 · similarity 0.87)
- Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithms (NeurIPS 2024 · similarity 0.87)
- Compositional PAC-Bayes: Generalization of GNNs with persistence and beyond (NeurIPS 2024 · similarity 0.87)
- Enhancing Implicit Shape Generators Using Topological Regularizations (ICML 2024 · similarity 0.87)
- Point-Level Topological Representation Learning on Point Clouds (ICML 2025 · similarity 0.86)
- The Flood Complex: Large-Scale Persistent Homology on Millions of Points (NeurIPS 2025 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.