Max-Affine Spline深入剖析深度生成网络
Max-Affine Spline Insights into Deep Generative Networks
摘要：
我们将一大类生成深度网络（GDN）与样条算子连接起来，以获得它们的属性，限制和新的机会。通过对生成流形的特征空间划分、维数和棱角性的刻画，将流形维数和逼近误差与样本量联系起来。每个区域的流形仿射子空间定义了一个局部坐标基，我们提供了必要和充分的条件，这些基向量与解纠缠。我们还推导出映射到生成的流形上的输出概率密度的潜在空间密度，这使得计算关键的统计数据，如香农熵。这一发现也使计算的GDN的可能性，这提供了一个新的机制，模型比较，以及提供一个质量测量（生成）的样本下学习的分布。我们证明了低熵和/或多峰分布如何不自然地由DGN建模，并且是训练不稳定性的原因。
英文摘要：
We connect a large class of Generative Deep Networks (GDNs) with spline operators in order to derive their properties, limitations, and new opportunities. By characterizing the latent space partition, dimension and angularity of the generated manifold, we relate the manifold dimension and approximation error to the sample size. The manifold-per-region affine subspace defines a local coordinate basis; we provide necessary and sufficient conditions relating those basis vectors with disentanglement. We also derive the output probability density mapped onto the generated manifold in terms of the latent space density, which enables the computation of key statistics such as its Shannon entropy. This finding also enables the computation of the GDN likelihood, which provides a new mechanism for model comparison as well as providing a quality measure for (generated) samples under the learned distribution. We demonstrate how low entropy and/or multimodal distributions are not naturally modeled by DGNs and are a cause of training instabilities.
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。
