The Earth mover's distance (EMD) is a useful metric for image recognition and classification, but its usual implementations are not differentiable or too slow to be used as a loss function for training other algorithms via gradient descent. In this paper, we train a convolutional neural network (CNN) to learn a differentiable, fast approximation of the EMD and demonstrate that it can be used as a substitute for computing-intensive EMD implementations. We apply this differentiable approximation in the training of an autoencoder-inspired neural network (encoder NN) for data compression at the high-luminosity LHC at CERN. The goal of this encoder NN is to compress the data while preserving the information related to the distribution of energy deposits in particle detectors. We demonstrate that the performance of our encoder NN trained using the differentiable EMD CNN surpasses that of training with loss functions based on mean squared error.

翻译：推土机距离（EMD）是图像识别与分类中一种有效的度量标准，但其常规实现方式非可微或速度过慢，难以作为损失函数通过梯度下降法训练其他算法。本文中，我们训练了一个卷积神经网络（CNN），用于学习EMD的可微快速近似，并证明其可作为计算密集型EMD实现的替代方案。我们将这一可微近似应用于类自编码器神经网络（编码器NN）的训练中，用于CERN高亮度LHC的数据压缩。该编码器NN的目标是在压缩数据的同时，保留与粒子探测器能量沉积分布相关的信息。实验表明，采用可微EMD CNN训练的编码器NN的性能，超越了基于均方误差损失函数的训练方案。