Optimal Transport (OT) has emerged as a fundamental tool in machine learning for comparing probability distributions in a geometrically meaningful manner. However, a key limitation of classical OT is its requirement that the source and target distributions have equal total mass, limiting its use in real-world settings involving imbalanced data, noise, outliers, or structural inconsistencies. Partial Transport (PT) addresses this limitation by allowing only a fraction of the mass to be transported, offering greater flexibility and robustness. Nonetheless, similar to OT, PT remains computationally expensive, as it typically involves solving large-scale linear programs-especially in high-dimensional spaces. To alleviate this computational burden, several emerging works have introduced the TreeSliced Wasserstein (TSW) distance, which projects distributions onto tree-metric spaces where OT problems admit closed-form solutions. Building on this line of research, we propose a novel framework that extends the tree-sliced approach to the PT setting, introducing the Partial Tree-Sliced Wasserstein (PartialTSW) distance. Our method is based on the key observation that, within tree-metric space, the PT problem can be equivalently reformulated as a standard balanced OT problem between suitably modified measures. This reformulation enables efficient computation while preserving the adaptability and robustness of partial transport. Our method proves effective across challenging tasks such as outlier removal and addressing class imbalance in image-to-image translation.

Self-supervised learning (SSL) excels at finding general-purpose latent representations from complex data, yet lacks a unifying theoretical framework that explains the diverse existing methods and guides the design of new ones. We cast SSL as latent distribution matching (LDM): learning representations that maximize their log-probability under an assumed latent model (alignment), while maximizing latent entropy to prevent collapse (uniformity). This view unifies independent component analysis with contrastive, non-contrastive, and predictive SSL methods, including stop gradient approaches. Leveraging LDM, we derive a nonlinear, sampling-free Bayesian filtering model with a Kalman-based predictor for high-dimensional timeseries. We further prove that predictive LDM yields identifiable latent representations under mild assumptions, even with nonlinear predictors. Overall, LDM clarifies the assumptions behind established SSL methods and provides principled guidance for developing new approaches.

Deep neural networks suffer from over-fitting and catastrophic forgetting when trained with small data. One natural remedy for this problem is data augmentation, which has been recently shown to be effective. However, previous works either assume that intra-class variances can always be generalized to new classes, or employ naive generation methods to hallucinate finite examples without modeling their latent distributions. In this work, we propose Covariance-Preserving Adversarial Augmentation Networks to overcome existing limits of low-shot learning. Specifically, a novel Generative Adversarial Network is designed to model the latent distribution of each novel class given its related base counterparts. Since direct estimation on novel classes can be inductively biased, we explicitly preserve covariance information as the ``variability'' of base examples during the generation process. Empirical results show that our model can generate realistic yet diverse examples, leading to substantial improvements on the ImageNet benchmark over the state of the art.

Itcomeswiththeadvantages ofVAEs, such asstable training, largesample diversity and aprincipled inference network, while having the flexibility to model a combination of continuous and discrete generative factors.

Specifically, a novel Generative Adversarial Network is designed to model thelatent distribution of each novel class given its related base counterparts.

Our investigation starts with the classic generative adversarial networks (GANs). Inspired by the GAN training objective, we propose a novel "distance" between the latent and data distributions, whose minimization

Neural Information Processing Systems http://nips.cc/

InfoGAN [10] in particular, learns an unsupervised disentangled representation by maximizing the mutual information between the discrete or continuous latent variables and the corresponding generated samples.