Multi-modal learning aims to learn predictive models based on the data from different modalities. However, due to the requirement of data security and privacy protection, real-world multi-modal data are often scattered to different agents and cannot be shared across the agents, which limits the application of existing multi-modal learning methods. To achieve robust multi-modal learning in such a challenging scenario, we propose a novel optimal transport-based mixer (OTM), which works as an effective latent code alignment and augmentation method for unaligned and distributed multi-modal data. In particular, we train a Wasserstein autoencoder (WAE) for each agent, which encodes its single modal samples in a latent space. Through a central server, the proposed OTM computes a stochastic fused Gromov-Wasserstein barycenter (FGWB) to mix different modalities' latent codes, so that each agent applies the barycenter to reconstruct its samples. This method neither requires well-aligned multi-modal data nor assumes the data to share the same latent distribution, and each agent can learn a specific model based on multi-modal data while achieving inference based on its local modality. Experiments on multi-modal clustering and classification demonstrate that the models learned with the OTM method outperform the corresponding baselines.

Protein backbone generation plays a central role in de novo protein design and is significant for many biological and medical applications. Although diffusion and flow-based generative models provide potential solutions to this challenging task, they often generate proteins with undesired designability and suffer computational inefficiency. In this study, we propose a novel rectified quaternion flow (ReQFlow) matching method for fast and high-quality protein backbone generation. In particular, our method generates a local translation and a 3D rotation from random noise for each residue in a protein chain, which represents each 3D rotation as a unit quaternion and constructs its flow by spherical linear interpolation (SLERP) in an exponential format. We train the model by quaternion flow (QFlow) matching with guaranteed numerical stability and rectify the QFlow model to accelerate its inference and improve the designability of generated protein backbones, leading to the proposed ReQFlow model. Experiments show that ReQFlow achieves on-par performance in protein backbone generation while requiring much fewer sampling steps and significantly less inference time (e.g., being 37$\times$ faster than RFDiffusion and 63$\times$ faster than Genie2 when generating a backbone of length 300), demonstrating its effectiveness and efficiency.

Graph neural networks have been widely used to represent 3D molecules, which capture molecular attributes and geometric information through various message-passing mechanisms. This study proposes a novel quaternion message-passing (QMP) module that can be plugged into many existing 3D molecular representation models and enhance their power for distinguishing molecular conformations. In particular, our QMP module represents the 3D rotations between one chemical bond and its neighbor bonds as a quaternion sequence. Then, it aggregates the rotations by the chained Hamilton product of the quaternions. The real part of the output quaternion is invariant to the global 3D rotations of molecules but sensitive to the local torsions caused by twisting bonds, providing discriminative information for training molecular conformation representation models. In theory, we prove that considering these features enables invariant GNNs to distinguish the conformations caused by bond torsions. We encapsulate the QMP module with acceleration, so combining existing models with the QMP requires merely one-line code and little computational cost. Experiments on various molecular datasets show that plugging our QMP module into existing invariant GNNs leads to consistent and significant improvements in molecular conformation representation and downstream tasks.

Temporal action alignment aims at segmenting videos into clips and tagging each clip with a textual description, which is an important task of video semantic analysis. Most existing methods, however, rely on supervised learning to train their alignment models, whose applications are limited because of the common insufficiency issue of labeled videos. To mitigate this issue, we propose a weakly-supervised temporal action alignment method based on a novel computational optimal transport technique called unbalanced spectral fused Gromov-Wasserstein (US-FGW) distance. Instead of using videos with known clips and corresponding textual tags, our method just needs each training video to be associated with a set of (unsorted) texts while does not require the fine-grained correspondence between the frames and the texts. Given such weakly-supervised video-text pairs, our method trains the representation models of the video frames and the texts jointly in a probabilistic or deterministic autoencoding architecture and penalizes the US-FGW distance between the distribution of visual latent codes and that of textual latent codes. We compute the US-FGW distance efficiently by leveraging the Bregman ADMM algorithm. Furthermore, we generalize classic contrastive learning framework and reformulate it based on the proposed US-FGW distance, which provides a new viewpoint of contrastive learning for our problem. Experimental results show that our method and its variants outperform state-of-the-art weakly-supervised temporal action alignment methods, whose results are even comparable to those derived by supervised learning methods on some specific evaluation measurements. The code is available at \urlhttps://github.com/hhhh1138/Temporal-Action-Alignment-USFGW.