are not necessarily desirable for an autoencoder because they might lead to less semantically meaningful and discriminative representation for downstream tasks.

### Qualitative results

Here, we assess the representational power of our models by the common practice of testing their ability to perform linear algebra in their latent spaces.

**Interpolation** Fig \[fig:interpolation\]: We choose two sufficiently different samples $\mathbf{x_1}$ and $\mathbf{x_2}$ from our test set, encode them in their latent representations $\mathbf{z_1}$ and $\mathbf{z_2}$ and then produce intermediate encodings by sampling the line that connects them $\mathbf{z} = a\mathbf{z_1}+(1-a)\mathbf{z_2}$, where $a\in(0,1)$.

**Extrapolation** Fig \[fig:extrapolation\]: Similarly, we decode latent representations that reside on the line defined by $\mathbf{z_1}$ and $\mathbf{z_2}$, but outside the respective line segment, $\mathbf{z} = a*\mathbf{z_1}+(1-a)*\mathbf{z_2}$, where $a\in(-\infty,0)\cup(1,+\infty)$. We choose $\mathbf{z_1}$ to be our neutral expression for COMA and neutral pose for DFAUST, in order to showcase the exaggeration of a specific characteristic on the shape.

![Extrapolation. Left: neutral expression/pose[]{data-label="fig:extrapolation"}](extrapolation_final.png){width="0.6\linewidth"}

**Shape Analogies** Fig \[fig:analogies\]: We choose three meshes $A$, $B$, $C$, and construct a $D$ such that it satisfies $A$:$B$::$C$:$D$ using linear algebra in the latent space as in [@mikolov]: $e(B)-e(A)=e(D)-e(C)$ ($e(*)$ the encoding), where we then solve for $e(D)$ and decode it. This way we transfer a 