Source
Karras et al. (2021), LIT-559 — StyleGAN3. Read as NOTE-300.
Filed for #163’s “equivariant representation”.
The practice
If the generated image will be transformed or animated (latent walks, video, anything where detail should move with the surface it belongs to), design the generator so that absolute pixel position cannot leak into it:
- Filter around nonlinearities: upsample 2×, apply the pointwise nonlinearity, low-pass filter, downsample. Use radially symmetric filters for rotation equivariance
- Treat each layer’s cutoff as the budget for new detail at that layer
- Start from a Fourier-feature input (LIT-550), not a learned constant, and drop per-pixel noise inputs, which are tied to pixel positions
The recommendation originates with StyleGAN3, LIT-559, which traced texture sticking to aliasing in the generator and built this design to remove it. Its Figure 3 ablation on FFHQ-U at 256² is the evidence: both alias-free configurations reach high measured equivariance while matching or slightly improving on StyleGAN2’s FID.
| FFHQ-U 256² | FID | EQ-T (dB) | EQ-R (dB) |
|---|---|---|---|
| StyleGAN2 | 5.14 | – | – |
| StyleGAN3-T | 4.62 | 63.0 | 13.1 |
| StyleGAN3-R | 4.50 | 66.7 | 40.5 |
Conditions
- For still images, this buys nothing measurable in FID. The case for it is motion
- It costs compute. Larger filters and upsampling factors raise equivariance at up to 2.3× the time
- Equivariance is measured on synthetic transforms of generated images, not on real video