An Empirical Study of Simplicial Representation Learning with Wasserstein Distance
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: Wasserstein diistance, Self-supervised Learning
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
Abstract: In this paper, we delve into the problem of simplicial representation learning utilizing the 1-Wasserstein distance on a tree structure (a.k.a., Tree-Wasserstein distance (TWD)), where TWD is defined as the L1 distance between two tree-embedded vectors. Specifically, we consider a framework for simplicial representation estimation employing a self-supervised learning approach based on SimCLR with a negative TWD as a similarity measure. In SimCLR, the cosine similarity with real-vector embeddings is often utilized; however, it has not
been well studied utilizing L1-based measures with simplicial embeddings. A key challenge is that training the L1 distance is numerically challenging and often yields unsatisfactory outcomes, and there are numerous choices for probability models. Thus, this study empirically investigates a strategy for optimizing self-supervised learning with TWD and find a stable training procedure. More specifically, we evaluate the combination of two types of TWD (total variation and ClusterTree) and several simplicial models including the softmax function, the ArcFace probability model, and simplicial embedding. Moreover, we propose a simple yet effective Jeffrey divergence-based regularization method to stabilize the optimization. Through empirical experiments on STL10, CIFAR10, CIFAR100, and SVHN, we first found that the simple combination of softmax function and TWD can obtain significantly lower results than the standard SimCLR (non-simplicial model and cosine similarity). We found that the model performance depends on the combination of TWD and the simplicial model, and the Jeffrey divergence regularization usually helps model training. Finally, we inferred that the appropriate choice of combination of TWD and simplicial models outperformed cosine similarity based representation learning.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 2265
Loading