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Function-space regularized Rényi divergences
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the rescaled IC-Γ-R divergence at alpha=inf (IC-Γ-WCR) instead of smaller alpha (ablation) | AUC rare sub-population detection on single-cell data · Single-cell mass cytometry, 100K samples | AUC: 0.89 vs 0.55 (alpha=2) and 0.70 (alpha=5) at 0.2% rarity | Helped |
| Use IC-Γ-WCR (alpha=inf) instead of Wasserstein distance | AUC rare sub-population detection · Single-cell mass cytometry, 20K and 100K samples | AUC: e.g., 0.89 vs 0.58 at 0.2% (100K); 0.91 vs 0.40 at 1.0% (20K) | Helped |
| Replace DV-Rényi variational formula with convex-conjugate Rényi formula (no risk-sensitive terms) | Estimation of classical Rényi divergence between Gaussians · 1000-dim Gaussians, alpha large or distributions far apart | variance and MSE | Helped |
| Use poly-softplus final layer instead of -abs for CC-Rényi discriminator (ablation) | CC-Rényi estimator · 1000-dim Gaussians | failed runs (NaN outputs) | Helped |
| Add symmetry-preserving equivariant generator and invariant discriminator (C8 group) to IC-Γ-R GAN (ablation) | RotMNIST GAN · RotMNIST 1%-10% training data | median FID (lower is better): 114 vs 357 at 1% data; 62 vs 298 at 10% data | Helped |
| Replace plain CNN generator/discriminator with equivariant generator and invariant discriminator at C4 group (partial symmetry) (ablation) | RotMNIST GAN · RotMNIST 1% training data | median FID (lower is better): Eqv G+CNN D 464 and CNN G+Inv D 366 vs CNN 357 at 1%; Eqv G+Inv D C4 151 at 1% | Mixed |
| Rescaled IC-Γ-R (D_alpha) with large alpha instead of unscaled R_alpha^{Γ,IC} GAN (ablation) | CIFAR-10 GAN with 1-Lipschitz Γ · CIFAR-10 inception score / FID | inception score | Helped |
| Use IC-Γ regularized divergence GAN instead of unregularized Rényi-DV GAN with alpha>1 | CIFAR-10 GAN · CIFAR-10 | training stability | Helped |
| Use IC-Γ-R GANs with alpha<=... (rather than WGAN-GP) on CIFAR-10 | CIFAR-10 GAN · CIFAR-10 inception score | inception score | Helped |
| Use Γ-Rényi-DV regularization (instead of IC) for alpha>1 | Rényi divergence regularization via function space · Theory counterexample (Dirac distributions) | bound R_alpha <= W^Γ | Hurt |
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