Multimodal Structure Learning: Disentangling Shared and Specific Topology via Cross-Modal Graphical Lasso

Estimating interpretable conditional-dependence structures from multimodal visual-linguistic features remains largely unexplored. We propose CM-GLasso (Cross-Modal Graphical Lasso), a framework that bridges vision-language representation learning and sparse Gaussian Graphical Models. CM-GLasso introduces three key components: (i) a text visualization strategy that renders class-attribute descriptions as images and processes them through the same SigLIP-2 vision encoder as natural images, yielding prototype-indexed patch-level attention footprints in a shared feature coordinate system; (ii) a cross-attention distillation mechanism that condenses high-dimensional patches into a small set of semantic graph nodes, whose attention-footprint similarities yield cross-modal structural priors for non-uniform L1 penalization; (iii) a joint ADMM formulation that estimates shared and class-specific precision components within a single convex objective, avoiding the need to first estimate and then decompose separate class-wise graphs. The learned sparse graph topologies directly support a parameter-free, precision-based classification rule and a lightweight topology-aware segmentation head. Extensive experiments on eight benchmarks demonstrate that CM-GLasso achieves competitive or superior performance compared with strong feature-based and task-specific baselines. Under the matched controlled protocol, it attains the highest average classification accuracy (91.97%) and the highest segmentation mIoU among the controlled baselines on VOC (74.75%) and ADE20K (64.01%), while also yielding explicit sparse conditional-dependence graphs with common-specific decomposition.

Recent advances in large language models (LLMs) have opened new avenues for multimodal reasoning. Yet, most existing methods still rely on pretrained vision-language models (VLMs) to encode image-text pairs in isolation, ignoring the relational structure that real-world multimodal data naturally form. This motivates reasoning on multimodal graphs (MMGs), where each node has textual and visual attributes and edges provide structural cues. Enabling LLM-based reasoning on such heterogeneous multimodal signals while preserving graph topology introduces two key challenges: resolving weak cross-modal consistency and handling heterogeneous modality preference. To address this, we propose Mario, a unified framework that simultaneously resolves the two above challenges and enables effective LLM-based reasoning over MMGs. Mario consists of two innovative stages. Firstly, a graph-conditioned VLM design that jointly refines textual and visual features through fine-grained cross-modal contrastive learning guided by graph topology. Secondly, a modality-adaptive graph instruction tuning mechanism that organizes aligned multimodal features into graph-aware instruction views and employs a learnable router to surface, for each node and its neighborhood, the most informative modality configuration to the LLM. Extensive experiments across diverse MMG benchmarks demonstrate that Mario consistently outperforms state-of-the-art graph models in both supervised and zero-shot scenarios for node classification and link prediction. The code will be made available at https://github.com/sunyuanfu/Mario.

Vision-language models have shown strong performance, but they often generalize poorly to specialized domains. While semi-supervised vision-language learning mitigates this limitation by leveraging a small set of labeled image-text pairs together with abundant unlabeled images, existing methods remain fundamentally pairwise and fail to model the global structure of multimodal representation manifolds. Most existing topology-based alignment methods rely on persistence diagram matching, which neither guarantees geometric alignment nor uses the image-text pairing information central to vision-language learning. We propose Topology-Aware Representation Alignment for Semi-Supervised Vision-Language Learning (ToMA), a framework that uses persistent homology to decompose pairwise relations into $H_0$-death and $H_1$-birth relations and aligns them across modalities through available cross-modal correspondences. This lightweight decomposition captures both connectivity and cycle-closing structure without constructing 2-simplices. Experiments show clear improvements on remote sensing, while fashion results reveal strong gains in classification and particularly strong retrieval improvements for difficult queries. Additional analysis shows that ToMA provides more consistent gains than alternative topology-based objectives and that lightweight $H_1$-birth edges provide useful higher-order structural signals.