Contribution
An account of texture sticking as aliasing, and a generator that removes it by construction. Equivariance becomes a measured property (EQ-T, EQ-R) instead of a visual impression.
Key insight
A pointwise nonlinearity is where new frequencies come from, so it is where to filter. In continuous terms a nonlinearity commutes with geometric transforms. Discretely it aliases unless the signal is briefly represented at higher resolution and band-limited afterward.
Assumptions
- Features are samples of bandlimited continuous signals. Every operation is judged by what it does to that signal
- Infinite spatial extent, approximated by a 10-pixel margin cropped after each layer, because border padding leaks absolute position
- The discriminator is unchanged from StyleGAN2
Method
- Input: fixed Fourier features, with frequencies sampled in a disc at the 4×4 band, replacing the learned constant
- Per-pixel noise removed. Mixing and path-length regularization disabled. Output skips removed and replaced by dividing features by an EMA of their RMS
- Resampling: Kaiser-windowed sinc filters (n = 6), which need far stronger stopband attenuation (the paper says over 100 dB) than common filters give
- Nonlinearity: upsample m = 2, leaky ReLU, low-pass, downsample, fused into a custom kernel. For rotation, radially symmetric (jinc) filters and 1×1 convolutions
- Per-layer cutoffs follow a geometric progression, which sets how much new frequency each layer may add
Key results
- Figure 3: StyleGAN2 FID 5.14. StyleGAN3-T 4.62 with EQ-T 63.0 dB. StyleGAN3-R 4.50 with EQ-T 66.7 and EQ-R 40.5
- Intermediate configurations lose FID (6.35 at filtered nonlinearities) before non-critical sampling recovers it. The changes interact, and the path is not monotone
Recommendations
- R1 — For content that must move with the scene, build the generator alias-free. Filed as SOTA-335
Bearing on the record
- SOTA-336 (no progressive growing, output skips): StyleGAN3 keeps the fixed topology but drops the output skips, which it believes were mainly fixing gradient-magnitude dynamics
- SOTA-335 is filed from this paper
Limitations
- FFHQ-U at 256² for the main ablation
- Equivariance is measured under synthetic transforms of one image, not on video