In the era of big data, the sheer volume and complexity of datasets pose
significant challenges in machine learning, particularly in image processing
tasks. This paper introduces an innovative Autoencoder-based Dataset
Condensation Model backed by Koopman operator theory that effectively packs
large datasets into compact, information-rich representations. Inspired by the
predictive coding mechanisms of the human brain, our model leverages a novel
approach to encode and reconstruct data, maintaining essential features and
label distributions. The condensation process utilizes an autoencoder neural
network architecture, coupled with Optimal Transport theory and Wasserstein
distance, to minimize the distributional discrepancies between the original and
synthesized datasets. We present a two-stage implementation strategy: first,
condensing the large dataset into a smaller synthesized subset; second,
evaluating the synthesized data by training a classifier and comparing its
performance with a classifier trained on an equivalent subset of the original
data. Our experimental results demonstrate that the classifiers trained on
condensed data exhibit comparable performance to those trained on the original
datasets, thus affirming the efficacy of our condensation model. This work not
only contributes to the reduction of computational resources but also paves the
way for efficient data handling in constrained environments, marking a
significant step forward in data-efficient machine learning.

在大数据时代，数据集的体量和复杂性给机器学习，特别是图像处理任务带来了重大挑战。本文介绍了一种基于自编码器的数据集压缩模型，支持库普曼算子理论，有效地将大规模数据集压缩成紧凑、信息丰富的表示。该模型受人脑预测编码机制的启发，采用一种新颖的编码和重构数据方法，保持了关键特征和标签分布。压缩过程利用自编码器神经网络结构、最优输运理论和瓦瑟斯坦距离，以最小化原始数据集和合成数据集之间的分布差异。我们提出了一个两阶段的实施策略：首先将大型数据集压缩成一个较小的合成子集；其次，通过训练一个分类器并将其性能与在等价原始数据子集上训练的分类器进行比较，来评估合成数据。我们的实验结果表明，使用压缩的数据训练的分类器表现与在原始数据集上训练的分类器相当，从而证明了我们压缩模型的有效性。这项工作不仅有助于减少计算资源的使用，还为受限环境下的高效数据处理铺平了道路，是数据高效机器学习的重要进展。