Uniformity plays an important role in evaluating learned representations, providing insights into self-supervised learning. In our quest for effective uniformity metrics, we pinpoint four principled properties that such metrics should possess. Namely, an effective uniformity metric should remain invariant to instance permutations and sample replications while accurately capturing feature redundancy and dimensional collapse. Surprisingly, we find that the uniformity metric proposed by \citet{Wang2020UnderstandingCR} fails to satisfy the majority of these properties. Specifically, their metric is sensitive to sample replications, and can not account for feature redundancy and dimensional collapse correctly. To overcome these limitations, we introduce a new uniformity metric based on the Wasserstein distance, which satisfies all the aforementioned properties. Integrating this new metric in existing self-supervised learning methods effectively mitigates dimensional collapse and consistently improves their performance on downstream tasks involving CIFAR-10 and CIFAR-100 datasets. Code is available at \url{https://github.com/statsle/WassersteinSSL}.

Variational autoencoders (VAEs) have been widely applied for text modeling. In practice, however, they are troubled by two challenges: information underrepresentation and posterior collapse. The former arises as only the last hidden state of LSTM encoder is transformed into the latent space, which is generally insufficient to summarize the data. The latter is a longstanding problem during the training of VAEs as the optimization is trapped to a disastrous local optimum. In this paper, we propose Discrete Auto-regressive Variational Attention Model (DAVAM) to address the challenges. Specifically, we introduce an auto-regressive variational attention approach to enrich the latent space by effectively capturing the semantic dependency from the input. We further design discrete latent space for the variational attention and mathematically show that our model is free from posterior collapse. Extensive experiments on language modeling tasks demonstrate the superiority of DAVAM against several VAE counterparts. Code will be released.

We consider a different setting from regular multitask learning, where data from different tasks share no common instances and no common feature dictionary, while the features can be semantically correlated and all tasks share the same class space. For example, in the two tasks of identifying terrorism information from English news and Arabic news respectively, one associated dataset could be news from Cable News Network (CNN), and the other be news crawled from websites of Arabic countries. Intuitively, these two tasks could help each other, although they share no common feature space. This new setting has brought obstacles to traditional multi-task learning algorithms and multi-view learning algorithms. We argue that these different data sources can be co-trained together by exploring the latent semantics among them. To this end, we propose a new graphical model based on sparse Gaussian Conditional Random Fields (GCRF) and Hilbert-Schmidt Independence Criterion (HSIC). In additional to output the prediction accuracy for each single task, it can also model (1) the dependency between the latent feature spaces of different tasks, (2) the dependency of the category spaces, and (3) the dependency between the latent feature space and the category space in each task. To make the model inference effective, we have provided an efficient variational EM algorithm. Experiments on both synthetic data sets and real-world data sets have indicated the feasibility and effectiveness of the proposed framework.