Deep multi-modal clustering generally focuses on improving clustering accuracy by leveraging information from different modalities. However, existing methods are designed around the finest-grained points as input, neglecting the relationships and information integration across different granularity levels, which negatively affects the clustering results. To this end, we propose a novel granular information bottleneck (GIB) for deep multi-modal clustering, which embeds a dual-tiered information bottleneck constraint mechanism that operates synergistically at both granular and sample levels, thereby learning discriminative feature representations with enhanced inter-cluster separability. Specifically, GIB adaptively represents and covers the sample points through granular balls of different granularity levels, which effectively captures the feature distribution within each cluster. Simultaneously, information compression and preservation are used to exploit the independence and complementarity of modalities while optimizing cluster assignments alignment. Finally, the objectives of GIB are formulated as a target function based on mutual information, and we propose a variational optimization method to ensure its convergence. Extensive experimental results validate the effectiveness of the proposed GIB model in accuracy and reliability.

In this work, we propose a novel high-order state space model embedded within an interpretable unfolding algorithm for MRI reconstruction, marking the first adaptation of the Mamba framework to this domain. Traditional methods often rely on stacking second-order interactions through transformer architectures to capture high-order global information. However, these approaches exhibit inherent quadratic complexity, resulting in significant computational overhead and limiting their efficiency in practical environments. Through a reexamination of the intrinsic properties of Mamba, we observe that it is fundamentally a first-order function and leveraging this insight, we introduce a high-order variant of Mamba, wherein the linear complexity attention mechanism within the initial Mamba is shared across successive Mamba calculations, achieving the same functionality while mitigating the computational cost of stacked methods. This adaptation allows our model to retain the benefits of cascaded modeling while significantly improving computational efficiency. By capturing high-order interactions more efficiently, our approach strikes a balance between performance and resource usage, providing a practical solution for accelerated MRI reconstruction. Furthermore, extensive experiments on multiple MRI benchmark datasets demonstrate that our approach delivers competitive performance compared to other state-of-the-arts.