用新损失函数调控特征空间拓扑，提升模型鲁棒性与可解释性。
Feature Space Topology Control via Hopkins Loss
- 引入霍普金斯统计量设计新损失，主动控制特征空间结构
- 在分类与降维任务中保持性能，同时改变特征分布拓扑
- 适用于需要稳定特征结构的场景，如对抗攻击防御
特征空间拓扑指样本在特征空间中的组织方式。改变这一拓扑结构有助于降维、生成建模、迁移学习及增强对对抗攻击的鲁棒性。本文提出一种新损失函数——霍普金斯损失（Hopkins loss），利用霍普金斯统计量来强制实现期望的特征空间拓扑，与现有方法侧重保留输入特征拓扑不同。我们在语音、文本和图像数据上，通过非线性瓶颈自编码器在分类与降维两个场景中评估了该方法的有效性。实验表明，将霍普金斯损失融入分类或降维任务时，分类性能仅略有下降，但能有效改变特征空间拓扑结构。
原文摘要 · Abstract (English)
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.
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