Missing modality issues are common in real-world applications, arising from factors such as equipment failures and privacy concerns. When fine-tuning pre-trained models on downstream datasets with missing modalities, performance can degrade significantly. Current methods often aggregate various missing cases to train recovery modules or align multimodal features, resulting in suboptimal performance, high computational costs, and the risk of catastrophic forgetting in continual environments where data arrives sequentially. In this paper, we formulate the dynamic missing modality problem as a continual learning task and introduce the continual multimodal missing modality task. To address this challenge efficiently, we introduce three types of prompts: modality-specific, task-aware, and task-specific prompts. These prompts enable the model to learn intra-modality, inter-modality, intra-task, and inter-task features. Furthermore, we propose a contrastive task interaction strategy to explicitly learn prompts correlating different modalities. We conduct extensive experiments on three public datasets, where our method consistently outperforms state-of-the-art approaches.

--Recent research in the domain of multimodal unified representations predominantly employs codebook as representation forms, utilizing V ector Quantization(VQ) for quantization, yet there has been insufficient exploration of other quantization representation forms. Our work explores more precise quantization methods and introduces a new framework, Semantic Residual Cross-modal Information Disentanglement (SRCID), inspired by the numerical residual concept inherent to Residual V ector Quantization (RVQ). SRCID employs semantic residual-based information disentanglement for multimodal data to better handle the inherent discrepancies between different modalities. Our method enhances the capabilities of unified multimodal representations and demonstrates exceptional performance in cross-modal generalization and cross-modal zero-shot retrieval. Its average results significantly surpass existing state-of-the-art models, as well as previous attempts with RVQ and Finite Scalar Quantization (FSQ) based on these modals. Different modalities contain distinctly different information; for example, sounds present in audio may not have corresponding visual sources in video.

Recent advances in representation learning have demonstrated the significance of multimodal alignment. The Dual Cross-modal Information Disentanglement (DCID) model, utilizing a unified codebook, shows promising results in achieving fine-grained representation and cross-modal generalization. However, it is still hindered by equal treatment of all channels and neglect of minor event information, resulting in interference from irrelevant channels and limited performance in fine-grained tasks. Thus, in this work, We propose a Training-free Optimization of Codebook (TOC) method to enhance model performance by selecting important channels in the unified space without retraining. Additionally, we introduce the Hierarchical Dual Cross-modal Information Disentanglement (H-DCID) approach to extend information separation and alignment to two levels, capturing more cross-modal details. The experiment results demonstrate significant improvements across various downstream tasks, with TOC contributing to an average improvement of 1.70% for DCID on four tasks, and H-DCID surpassing DCID by an average of 3.64%. The combination of TOC and H-DCID further enhances performance, exceeding DCID by 4.43%. These findings highlight the effectiveness of our methods in facilitating robust and nuanced cross-modal learning, opening avenues for future enhancements. The source code and pre-trained models can be accessed at https://github.com/haihuangcode/TOC_H-DCID.

Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve various downstream analyses and achieve state-of-the-art performance in many applications. Despite the empirical effectiveness, most existing methods lack theoretical understanding under a general nonlinear setting. To fill this gap, we develop a statistical framework on a low-dimension product manifold to model the data augmentation transformation. Under this framework, we introduce a new representation learning method called augmentation invariant manifold learning and design a computationally efficient algorithm by reformulating it as a stochastic optimization problem. Compared with existing self-supervised methods, the new method simultaneously exploits the manifold's geometric structure and invariant property of augmented data and has an explicit theoretical guarantee. Our theoretical investigation characterizes the role of data augmentation in the proposed method and reveals why and how the data representation learned from augmented data can improve the $k$-nearest neighbor classifier in the downstream analysis, showing that a more complex data augmentation leads to more improvement in downstream analysis. Finally, numerical experiments on simulated and real datasets are presented to demonstrate the merit of the proposed method.

Recent advances in self-supervised learning have highlighted the efficacy of data augmentation in learning data representation from unlabeled data. Training a linear model atop these enhanced representations can yield an adept classifier. Despite the remarkable empirical performance, the underlying mechanisms that enable data augmentation to unravel nonlinear data structures into linearly separable representations remain elusive. This paper seeks to bridge this gap by investigating under what conditions learned representations can linearly separate manifolds when data is drawn from a multi-manifold model. Our investigation reveals that data augmentation offers additional information beyond observed data and can thus improve the information-theoretic optimal rate of linear separation capacity. In particular, we show that self-supervised learning can linearly separate manifolds with a smaller distance than unsupervised learning, underscoring the additional benefits of data augmentation. Our theoretical analysis further underscores that the performance of downstream linear classifiers primarily hinges on the linear separability of data representations rather than the size of the labeled data set, reaffirming the viability of constructing efficient classifiers with limited labeled data amid an expansive unlabeled data set.

Self-supervised metric learning has been a successful approach for learning a distance from an unlabeled dataset. The resulting distance is broadly useful for improving various distance-based downstream tasks, even when no information from downstream tasks is utilized in the metric learning stage. To gain insights into this approach, we develop a statistical framework to theoretically study how self-supervised metric learning can benefit downstream tasks in the context of multi-view data. Under this framework, we show that the target distance of metric learning satisfies several desired properties for the downstream tasks. On the other hand, our investigation suggests the target distance can be further improved by moderating each direction's weights. In addition, our analysis precisely characterizes the improvement by self-supervised metric learning on four commonly used downstream tasks: sample identification, two-sample testing, $k$-means clustering, and $k$-nearest neighbor classification. As a by-product, we propose a simple spectral method for self-supervised metric learning, which is computationally efficient and minimax optimal for estimating target distance. Finally, numerical experiments are presented to support the theoretical results in the paper.

Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing group-level differences, i.e., in identifying if trends of estimated objects (e.g., covariance or precision matrices) are different across disparate conditions (e.g., gender or disease). Often, poor effect sizes make detecting the differential signal over the full set of features difficult: for example, dependencies between only a subset of features may manifest differently across groups. In this work, we first give a parametric model for estimating trends in the space of SPD matrices as a function of one or more covariates. We then generalize scan statistics to graph structures, to search over distinct subsets of features (graph partitions) whose temporal dependency structure may show statistically significant group-wise differences. We theoretically analyze the Family Wise Error Rate (FWER) and bounds on Type 1 and Type 2 error. On a cohort of individuals with risk factors for Alzheimer's disease (but otherwise cognitively healthy), we find scientifically interesting group differences where the default analysis, i.e., models estimated on the full graph, do not survive reasonable significance thresholds.