论文标题
Markov-Lipschitz深度学习
Markov-Lipschitz Deep Learning
论文作者
论文摘要
我们提出了一个名为Markov-Lipschitz深度学习（MLDL）的新型框架，以应对基于媒介的神经网络转换引起的几何劣化，以基于媒介的神经网络变换，以基于流形的表示和流形数据生成。先前的约束，称为局部等距平滑度（LIS），被施加在跨层中，并编码为Markov随机场（MRF） - GIBBS分布。通过局部几何变形和局部Bi-Lipschitz的连续性测量，这导致了最佳的局部几何保存和鲁棒性的解决方案。因此，层的矢量变换被增强为行为良好的，受限的指标同构。广泛的实验，比较和消融研究表明，MLDL在流形学习和流动数据生成方面具有显着优势。 MLDL足够通用，可以增强基于向量转换的任何网络。该代码可从https://github.com/westlake-cairi/markov-lipschitz-deep-learning获得。
We propose a novel framework, called Markov-Lipschitz deep learning (MLDL), to tackle geometric deterioration caused by collapse, twisting, or crossing in vector-based neural network transformations for manifold-based representation learning and manifold data generation. A prior constraint, called locally isometric smoothness (LIS), is imposed across-layers and encoded into a Markov random field (MRF)-Gibbs distribution. This leads to the best possible solutions for local geometry preservation and robustness as measured by locally geometric distortion and locally bi-Lipschitz continuity. Consequently, the layer-wise vector transformations are enhanced into well-behaved, LIS-constrained metric homeomorphisms. Extensive experiments, comparisons, and ablation study demonstrate significant advantages of MLDL for manifold learning and manifold data generation. MLDL is general enough to enhance any vector transformation-based networks. The code is available at https://github.com/westlake-cairi/Markov-Lipschitz-Deep-Learning.
