modified the COMA architecture for our simple Neural3DMM by adding an extra convolution and an extra downsampling/upsampling layer in the encoder and the decoder respectively (encoder filter sizes: \[8,16,16,32,32\], decoder: mirror of the encoder). The larger Neural3DMM follows the above architecture, but with an increased parameter space. For COMA, the convolutional filters of the encoder had sizes \[64,64,64,128\] and for Mein3D the sizes were \[8,16,32,64,128\], while the decoder is a mirror of the encoder. For DFAUST, the sizes were \[16,32,64,128\] and \[128,64,32,32,16\] and dilated convolutions with $h=2$ hops and dilation ratio $r=2$ were used for the first and the last two layers of the encoder and the decoder respectively. We observed that by adding an additional convolution at the very end (of size equal to the size of the input feature space), training was accelerated. All of our activation functions were ELUs [@ELU]. Our learning rate was $10^{-3}$ with a decay of $0.99$ after each epoch, and our weight decay was $5\times 10^{-5}$. All models were trained for 300 epochs.

![Spiral vs ChebNet (spectral) filters[]{data-label="fig:spectral_spiral_comparison"}](coma_isotropic_anisotropic.png "fig:"){width="0.6\linewidth"} \[fig:coma\_tropic\_comparison\]

![Spiral vs ChebNet (spectral) filters[]{data-label="fig:spectral_spiral_comparison"}](dfaust_isotropic_anisotropic.png "fig:"){width="0.6\linewidth"} \[fig:dfaust\_tropic\_comparison\]

Ablation Studies {#ablation}
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### Isotropic vs Anisotropic Convolutions {#iso_comaparison}

For the purposes of this experiment 