建造望远镜以观察高维图像空间
Building a Telescope to Look Into High-Dimensional Image Spaces
摘要：
图像模式可以由其密度集中在高维图像空间中的不同低维子空间上的概率分布来表示。这样的概率密度有天文数字的本地模式对应于典型的模式外观。相关的模式组可以结合起来，形成代表模式概念的宏观图像盆地。最近的工作使用神经网络，捕捉高阶图像统计学习吉布斯模型能够合成许多模式的现实图像。然而，表征学习的概率密度来揭示由局部模式的结构编码的模型的Hopfield记忆，仍然是一个开放的挑战。在这项工作中，我们提出了新的计算实验，映射和可视化吉布斯密度的局部模式结构。有效的测绘需要确定全球流域，而不需要列举无数的模式。受Grenander跳跃扩散方法的启发，我们提出了一种新的MCMC工具，称为吸引扩散（AD），可以通过测量局部模式的亚稳性来捕获高度非凸密度的宏观结构。AD涉及改变目标密度，其中磁化电势惩罚与已知模式的距离，并运行改变的密度的MCMC样本以测量初始链状态的稳定性。使用低维生成器网络来促进探索，我们映射了多达12，288维的图像空间（RGB中的64 $\times$ 64像素）。我们的工作表明：（1）AD可以有效地映射高度非凸的概率密度，（2）模式概率密度的亚稳区域包含相干的图像组，以及（3）训练图像之间的差异的可感知性影响图像盆的亚稳性。
英文摘要：
An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join to form macroscopic image basins that represent pattern concepts. Recent works use neural networks that capture high-order image statistics to learn Gibbs models capable of synthesizing realistic images of many patterns. However, characterizing a learned probability density to uncover the Hopfield memories of the model, encoded by the structure of the local modes, remains an open challenge. In this work, we present novel computational experiments that map and visualize the local mode structure of Gibbs densities. Efficient mapping requires identifying the global basins without enumerating the countless modes. Inspired by Grenander's jump-diffusion method, we propose a new MCMC tool called Attraction-Diffusion (AD) that can capture the macroscopic structure of highly non-convex densities by measuring metastability of local modes. AD involves altering the target density with a magnetization potential penalizing distance from a known mode and running an MCMC sample of the altered density to measure the stability of the initial chain state. Using a low-dimensional generator network to facilitate exploration, we map image spaces with up to 12,288 dimensions (64 $\times$ 64 pixels in RGB). Our work shows: (1) AD can efficiently map highly non-convex probability densities, (2) metastable regions of pattern probability densities contain coherent groups of images, and (3) the perceptibility of differences between training images influences the metastability of image basins.
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