In this section, we analyze the impact of the encoder/decoder architecture on the generation quality of considered models. The generation quality experiment of section 5 is repeated on the fMNIST and MNIST data set, where the architecture and hyperparameters are adapted from Dupont (2018). From Table 5 and Figure 9, we see that the overall FID scores and generation quality have improved; however, the relative scores among the models did not change significantly.

Table 5:

. | St-RKM . | VAE . | $\beta $-VAE . | FactorVAE . | InfoGAN . |
---|---|---|---|---|---|

MNIST | 24.63 (0.22) | 36.11 (1.01) | 42.81 (2.01) | 35.48 (0.07) | 45.74 (2.93) |

fMNIST | 61.44 (1.02) | 73.47 (0.73) | 75.21 (1.11) | 69.73 (1.54) | 84.11 (2.58) |

. | St-RKM . | VAE . | $\beta $-VAE . | FactorVAE . | InfoGAN . |
---|---|---|---|---|---|

MNIST | 24.63 (0.22) | 36.11 (1.01) | 42.81 (2.01) | 35.48 (0.07) | 45.74 (2.93) |

fMNIST | 61.44 (1.02) | 73.47 (0.73) | 75.21 (1.11) | 69.73 (1.54) | 84.11 (2.58) |

Notes: Lower is better with standard deviations. Adapted from Dupont (2018).

Table 6:

Models . | dSprites . | 3DShapes . | 3D cars
. |
---|---|---|---|

St-RKM-sl ($\sigma =10-3$, $U\u2605$) | 0.17 (0.05) | 0.23 (0.03) | 0.21 (0.04) |

St-RKM ($\sigma =10-3$, $U\u2605$) | 0.26 (0.05) | 0.30 (0.10) | 0.31 (0.09) |

St-RKM ($\sigma =10-3$, random $U$) | 0.61 (0.02) | 0.72 (0.01) | 0.69 (0.03) |

Models . | dSprites . | 3DShapes . | 3D cars
. |
---|---|---|---|

St-RKM-sl ($\sigma =10-3$, $U\u2605$) | 0.17 (0.05) | 0.23 (0.03) | 0.21 (0.04) |

St-RKM ($\sigma =10-3$, $U\u2605$) | 0.26 (0.05) | 0.30 (0.10) | 0.31 (0.09) |

St-RKM ($\sigma =10-3$, random $U$) | 0.61 (0.02) | 0.72 (0.01) | 0.69 (0.03) |

Notes: Denote $M=1|C|\u2211i\u2208CU\u2605\u22a4\u2207\psi (yi)\u2207\psi (yi)\u22a4U\u2605,withyi=PU\varphi \theta (xi)$ (cf. equation 3.6). Then we compute the score as $M-diag(M)F/MF$, where $diag:Rm\xd7m\u21a6Rm\xd7m$ sets the off-diagonal elements of matrix to zero. The scores are computed for each model over 10 random seeds and show the mean (standard deviation). Lower scores indicate better diagonalization.

Figure 8:

Figure 9:

Figure 10:

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