Neural-network-based compressors have proven to be remarkably effective at
compressing sources, such as images, that are nominally high-dimensional but
presumed to be concentrated on a low-dimensional manifold. We consider a
continuous-time random process that models an extreme version of such a source,
wherein the realizations fall along a one-dimensional "curve" in function space
that has infinite-dimensional linear span. We precisely characterize the
optimal entropy-distortion tradeoff for this source and show numerically that
it is achieved by neural-network-based compressors trained via stochastic
gradient descent. In contrast, we show both analytically and experimentally
that compressors based on the classical Karhunen-Lo\`{e}ve transform are highly
suboptimal at high rates.

本文研究了基于神经网络的压缩器在处理集中于低维流形上的高维数据（如图像）方面的有效性，同时研究了一个连续时间随机过程的最优熵 - 失真权衡并对比了经典的 Karhunen-Loève 变换的压缩器，结果表明基于神经网络的压缩器在训练采用随机梯度下降的情况下可实现最佳性能。