# [Style Intervention: How to Achieve Spatial Disentanglement with Style-based Generators?](https://arxiv.org/pdf/2011.09699.pdf)
The authors analyse the latent space of StyleGAN and propose a manipulation method on the Stylespace termed as *S* using interpolation and specific loss function for task of face attribute editing.

**Latent Space Analysis:**
- Unsupervised approaches use classical ML techniquies like PCA to solve latent directions and interpret semantic meanings for generation.
- Supervised methods solve for the manipulated latent vector with the supervision of semantic labels.

**Face Atrribute Editing(FAE):**
- FAE ams at manipulating target attribute of input image wile keeping irrelevant content intact.
- Most methods use new networks or lss functions.
- To reduce computation required the paper proposes to control their behaviour by manipulating the latent codes.

### Style Space Translation:
- The translation done here uses feature maps and components required are marked as c and not required as c'
- To edit precisely semantic of c the author states to use a separating hyperplane with normal vector n_α, with displacemrnt vector of style channel(s) following certain conditions.

- This means interpolating along deltas would yield in desired output.
- ∆S^ is approximated using ∆s_n a normal vector on S,which classifies style codes according to labels of the translated attribute α.
- Sparsity regularization us imposed on this to meet the specifed conditions.
### Style Intervention:
- ∆s_n contains minimum information to translate the input thus as we translate Z(z → z'), it is plausible to the same for corresponding displacement vector.
- ∆s_z = f(z)-f(z')
- To combine translation in Z which produces realistic semantic changes but with entanglement and S which exerts precise modifications but not photo-realistic a intervention coefficient lambda is used which various losses.

**Pixel-level Loss:**
- Λ is penalised for modifying image other than c using a binary mask.

**Attribute Loss:**
- To ensure image shows target change atrribute loss is take between Sn and Sm as cosine loss.

**L2 Loss:**
- To make sure image does not deviate from generation manifold L2 loss is used on lamda.

The overall loss function is:

### Separability of stylespace
- The model is trainedon Face++ and it is found that most of facial attributes are linearly separable.
- This indicates stylecodes contain semantic information of image attributes

### Spatially Disentangled Image Translation
- The authors fix the lamda*(optimal lambda) and change coefficients of ∆s_n to check of translation could be interpolated for only a target area.
- The output shows translating in ∆s_n only affects thetargeted content.
- The intermediate generation is also visualised and it is observed changes between succesive layers is discrete and monotonous.
- This implies that facial component is treated as a whole and embedded in neigbouring feature map instead of collection of texture patches in successive layers.