Abstract
Feature space topology refers to the organization of samples within the feature space. Modifying this topology can be beneficial in machine learning applications, including dimensionality reduction, generative modeling, transfer learning, and robustness to adversarial attacks. This paper introduces a novel loss function, Hopkins loss, which leverages the Hopkins statistic to enforce a desired feature space topology, which is in contrast to existing topology-related methods that aim to preserve input feature topology. We evaluate the effectiveness of Hopkins loss on speech, text, and image data in two scenarios: classification and dimensionality reduction using nonlinear bottleneck autoencoders. Our experiments show that integrating Hopkins loss into classification or dimensionality reduction has only a small impact on classification performance while providing the benefit of modifying feature topology.
Abstract (translated)
特征空间拓扑指的是在特征空间中样本的组织方式。修改这种拓扑结构对于机器学习应用是有益的，包括维度缩减、生成模型、迁移学习以及对抗性攻击的鲁棒性等方面。本文介绍了一种新颖的损失函数——霍普金斯（Hopkins）损失，该函数利用霍普金斯统计量来强制执行所需的特征空间拓扑结构，这与现有的旨在保持输入特征拓扑的方法形成了对比。我们在分类和使用非线性瓶颈自编码器进行维度缩减这两种场景下，评估了霍普金斯损失在语音、文本及图像数据上的有效性。实验结果显示，在将霍普金斯损失集成到分类或维度缩减应用中时，对分类性能仅有很小的影响，但同时带来了修改特征拓扑的好处。
URL
https://arxiv.org/abs/2509.11154
