发表机构
Tufts University; East Tennessee State University; Boston University（塔夫茨大学; 东田纳西州立大学; 波士顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对逆最优传输对比学习忽略负样本导致维度坍缩的问题，提出多边际逆最优传输对比学习方法Neg-MMIOT-CL，通过显式锚点-正样本-负样本耦合缓解坍缩，并证明其等角性质，同时提出高效变体Neg-IOT-CL-PushPull，在合成与真实数据上显著优于现有方法。
AI 中文摘要
基于逆最优传输（IOT）的表示学习方法旨在学习表示，使得表示空间中一对数据边际之间的全局最优传输（OT）耦合集中于正样本对。这与以往主要关注成对匹配的方法形成对比。然而，这些方法不使用负样本对，因此其方法并非真正的对比式。我们表明，这会导致维度坍缩问题，从而降低下游性能。为解决此问题，我们开发了一种新颖的多边际（MM）逆最优传输（IOT）对比学习（CL）方法，称为Neg-MMIOT-CL，该方法学习表示，使得表示空间中三个数据边际之间的全局多边际最优传输（MMOT）耦合，相对于精心设计的三元组数据点之间的基础代价，集中于锚点-正样本-负样本三元组。对于潜在类别模型，我们经验性地表明Neg-MMIOT-CL缓解了维度坍缩。此外，对于表示空间中所有三元组的基础代价的特定选择，我们证明了Neg-MMIOT-CL的最优表示配置在类内和类间表示上表现出等角性质，当表示维度大于类别数减一时，这转化为神经坍缩——这一结果先前仅针对成对对比学习方法建立。最后，我们提出了Neg-IOT-CL-PushPull，它是Neg-MMIOT-CL的一种计算高效替代方案，缓解了实现过程中计算MMOT计划的高成本。我们将这些方法应用于合成和真实世界数据集，并展示了相对于现有基于OT的对比学习方法的显著改进。
英文摘要
Inverse Optimal Transport (OT) based methods for representation learning learn representations such that the global OT coupling between a pair of data marginals in the representation space, concentrates on the positive pairs. This is in contrast to previous methods that primarily focused on pairwise matching. However, these methods $\textit{DO NOT}$ utilize negative pairs and hence are not truly contrastive in their approach. We show that this leads to issues of dimensional collapse and hence degraded downstream performance. To alleviate this, we develop a novel multi-marginal (MM) inverse OT (IOT) contrastive learning (CL) approach called Neg-MMIOT-CL, which learns representations such that the global multi-marginal OT (MMOT) coupling between a triple of data marginals, with respect to a carefully designed ground-cost between triplets of data points in the representation space, concentrates on the anchor-positive-negative $\textit{triplets}$. For a latent class model, we empirically show that Neg-MMIOT-CL alleviates dimensional collapse. Furthermore, for a specific choice of ground cost for all triplets in representation space, we prove that the optimal representation configuration for Neg-MMIOT-CL exhibits equiangular property for within-class and across-class representations, which translates to Neural-Collapse when the representation dimension is larger than the number of classes minus one -- a result that is $\textit{previously established only}$ for pairwise contrastive learning methods. Finally, we propose Neg-IOT-CL-PushPull, that is a computationally efficient alternative to Neg-MMIOT-CL, alleviating the high cost of computing MMOT plans needed during implementation. We apply these methods on both synthetic and real-world datasets and show significant improvements over existing OT-based contrastive learning methods.
