利用耦合自由能弯曲几何优化的变分推断
Variational Inference Optimized Using the Curved Geometry of Coupled Free Energy
AI总结：
提出基于耦合自由能及其弯曲几何的变分推断框架，并用于设计 CVAE，通过重尾潜变量和耦合概率采样提升离群值鲁棒性与训练稳定性，CelebA 上5轮后较 VAE 改善3%。
摘要：
我们提出了一种基于耦合自由能的变分推断优化框架，扩展了变分推断技术，以考虑耦合指数族的弯曲几何。该分布族包含广义 Pareto 分布和 Student's t 分布等重要的重尾分布。通过利用耦合自由能（它等于逆概率的耦合证据下界（ELBO）），我们提升了所学模型的准确性和鲁棒性。文中给出了 Fisher 信息度量和仿射联络的耦合推广。该方法被应用于耦合变分自编码器（CVAE）的设计。通过在分布和代价函数中同时使用耦合，重构度量被推导为仍为均方平均损失，但常数经过修改。创新之处在于利用相关联的耦合概率对重尾潜分布进行采样，该耦合概率具有更快衰减的尾部。其结果是能够训练出对严重离群值具有鲁棒性的模型，同时确保训练过程稳定。重构 CelebA 图像的 Wasserstein-2 或 Fréchet Inception Distance 表明，经过 5 个 epoch 的训练后，CVAE 相比 VAE 有 3% 的提升。
英文摘要：
We introduce an optimization framework for variational inference based on the coupled free energy, extending variational inference techniques to account for the curved geometry of the coupled exponential family. This family includes important heavy-tailed distributions such as the generalized Pareto and the Student's t. By leveraging the coupled free energy, which is equal to the coupled evidence lower bound (ELBO) of the inverted probabilities, we improve the accuracy and robustness of the learned model. The coupled generalization of Fisher Information metric and the affine connection. The method is applied to the design of a coupled variational autoencoder (CVAE). By using the coupling for both the distributions and cost functions, the reconstruction metric is derived to still be the mean-square average loss with modified constants. The novelty comes from sampling the heavy-tailed latent distribution with its associated coupled probability, which has faster decaying tails. The result is the ability to train a model robust against severe outliers, while assuring that the training process is stable. The Wasserstein-2 or Fréchet Inception Distance of the reconstructed CelebA images shows the CVAE has a 3\% improvement over the VAE after 5 epochs of training.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
