3D generative modeling is accelerating as the technology allowing the capture
of geometric data is developing. However, the acquired data is often
inconsistent, resulting in unregistered meshes or point clouds. Many generative
learning algorithms require correspondence between each point when comparing
the predicted shape and the target shape. We propose an architecture able to
cope with different parameterizations, even during the training phase. In
particular, our loss function is built upon a kernel-based metric over a
representation of meshes using geometric measures such as currents and
varifolds. The latter allows to implement an efficient dissimilarity measure
with many desirable properties such as robustness to resampling of the mesh or
point cloud. We demonstrate the efficiency and resilience of our model with a
generative learning task of human faces.

该论文提出了一种可以处理不同参数化的、基于核的计量的网络架构，可以用于人脸的生成学习任务。

利用几何度量实现网格不变的三维生成深度学习

Toward Mesh-Invariant 3D Generative Deep Learning with Geometric  Measures

Several interesting generative learning algorithms involve a complex
probability distribution over many random variables, involving intractable
normalization constants or latent variable normalization. Some of them may even
not have an analytic expression for the unnormalized probability function and
no tractable approximation. This makes it difficult to estimate the quality of
these models, once they have been trained, or to monitor their quality (e.g.
for early stopping) while training. A previously proposed method is based on
constructing a non-parametric density estimator of the model's probability
function from samples generated by the model. We revisit this idea, propose a
more efficient estimator, and prove that it provides a lower bound on the true
test log-likelihood, and an unbiased estimator as the number of generated
samples goes to infinity, although one that incorporates the effect of poor
mixing. We further propose a biased variant of the estimator that can be used
reliably with a finite number of samples for the purpose of model comparison.

研究提出了一种更高效的密度估计方法，从而解决了一些复杂的生成学习算法中难以估计模型质量的问题，并证明其提供了真实测试对数似然的下界和无偏估计，同时还提出了一种偏差估计的变体，可以在有限的样本数下可靠地用于模型比较。