论文标题
神经网络最佳地压缩锯布里奇
Neural Networks Optimally Compress the Sawbridge
论文作者
论文摘要
事实证明，基于神经网络的压缩机在压缩源（例如图像）方面具有非常有效的效果，这些图像具有很高的二维，但被认为集中在低维歧管上。我们考虑了一个连续的随机过程，该过程模拟了这种源的极端版本，其中实现沿着具有无限维线性跨度的函数空间中的一维“曲线”。我们精确地表征了该来源的最佳熵依赖权权衡，并以数值的方式表明它是通过通过随机梯度下降训练的基于神经网络的压缩机来实现的。相比之下，我们在分析和实验上都表明，基于经典的Karhunen-Loève变换的压缩机以高速率高度优化。
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-Loève transform are highly suboptimal at high rates.
