SAHC-NS: Structure-Aware and Hardness-Calibrated Negative Sampling for Implicit Collaborative Filtering

Negative sampling is a key component of implicit collaborative filtering (CF), as it enables recommenders to effectively learn user preferences. Existing negative sampling methods mostly follow a two-stage paradigm: they first construct a candidate negative pool for each user and then select negative samples from the pool according to predefined sampling rules. However, these methods usually overlook the hardness variation of candidate negative pools across users, making it difficult to adaptively adjust the hardness and informativeness of negative samples according to candidate-pool conditions. In addition, most existing samplers evaluate candidate negatives mainly through a matching score computed from the final aggregated user and item embeddings, while ignoring the structural differences captured by multi-hop neighborhood aggregation. As a result, the training value of negatives may be insufficiently characterized. To address these issues, we propose SAHC-NS, a Structure-Aware and Hardness-Calibrated Negative Sampling method. Specifically, SAHC-NS uses the mean and standard deviation of layer-wise matching scores to capture the overall matching strength and cross-layer structural discrepancy of candidate negatives, respectively. This enables SAHC-NS to select informative negatives by taking cross-layer structural discrepancy into account, rather than relying solely on final matching scores. Moreover, SAHC-NS introduces a candidate-pool-aware hardness calibration module to dynamically adjust negative augmentation strength according to candidate-pool hardness, producing hardness-controllable negatives. Extensive experiments demonstrate the superiority of SAHC-NS over existing negative sampling methods.

Toward Federated Multimodal Graph Foundation Models: A Topology-Aware Multimodal Alignment Framework

Multimodal-attributed graphs (MAGs), whose nodes carry modalities such as images and text alongside topological structure, now pervade applications including social platforms, e-commerce, and biomedical networks, offering richer semantic signals than single-modality graphs. In practice, such graphs are fragmented across privacy-restricted silos owned by different platforms and institutions, so learning a broadly transferable model over them demands collaborative training that never exposes raw data. This places the task at the intersection of multimodal graph learning and federated learning, yet existing methods cover only one side of it. To address the challenges from these two perspectives, we propose FedGAMMA, casting federated multimodal graph foundation learning as a two-stage semantic-structural alignment problem of federated pre-training and prompt-based fine-tuning. During pre-training, a shared-private semantic enhancer disentangles cross-modal commonality from modality-specific information, aligning it through optimal transport, a topology-aware graph fusion module decouples semantic and structural views via semantic residual graphs and dual positional encodings, and a dual-channel affinity-aware aggregation mechanism estimates client similarity from feature and graph centroids without exposing raw data. During fine-tuning, FedGAMMA adapts the pretrained encoder through lightweight graph-aware prompts, a shared prompt pool with controlled exploration, and channel-wise prompt synchronization. Experiments on twelve multimodal graph datasets show FedGAMMA consistently surpassing a broad range of baselines across downstream tasks, with gains of up to 12.96%. FedGAMMA further outperforms competitive baselines accross multi-domain datasets on multiple tasks with up to 5.71% under few-shot learning scenario.

Towards Modality-imbalanced Federated Graph Learning: A Data Synthesis-based Approach

MultiModal Federated Graph Learning (MM-FGL) offers a natural collaborative training paradigm, but its practical deployment is challenged by two granularities of modality imbalance. Client-level imbalance occurs when certain clients lack entire modalities, while node-level imbalance occurs when individual nodes exhibit missing visual or textual attributes. While several relevant studies exist, our investigation reveals that they predominantly target graph-agnostic or centralized scenarios, rendering them difficult to adapt directly. To address these challenges, we formalize modality-imbalanced MM-FGL as an implicit graph-aware latent semantic representation synthesis problem. This paradigm recovers missing modal semantics directly within the representation space, thereby maximizing alignment with the original data's semantic distribution and mitigating the high variance induced by missing modalities. To this end, we propose FedMGS (Federated Modality-aware Graph Synthesis), which integrates three core components. The availability-aware graph encoder prevents missing modalities from contaminating local structural propagation. The prototype-guided latent semantic synthesizer establishes cross-client semantic anchors for unavailable modalities. The reliability-calibrated semantic fusion mechanism regulates the impact of recovered latent representations prior to predictive readout. Extensive experiments on four tasks show that FedMGS consistently outperforms competitive baselines with gains up to 17.41% with best efficiency-performance tradeoff.

Context-aware Modality-Topology Co-Alignment for Multimodal Attributed Graphs

Multimodal Attributed Graphs (MAGs) model real-world entities by coupling graph topology with heterogeneous attributes such as text and images. They support graph-centric tasks requiring structural and class-discriminative representations, and modality-centric tasks requiring fine-grained cross-modal correspondence. However, existing MAG methods often rely on fixed graph contexts or uniformly fused representations, causing task-agnostic propagation and over-compressed fusion that hinder diverse task requirements and modality-specific evidence preservation. To address this, we propose CoMAG, a unified MAG backbone that learns task-adaptive reliable contexts and modality-preserving alignment within them. CoMAG first conducts Reliable Context Learning by estimating edge reliability from multimodal semantic consistency, complementing raw topology with semantic neighbors, and selecting context components through a task-aware gate. It then performs Modality-preserving Hop-token Alignment by maintaining modality-specific multi-hop trajectories, matching modality-hop tokens across modalities, and decoupling shared and private representations. Thus, CoMAG produces graph and modality representations from one forward pass while retaining modality-specific cues. We further analyze stable propagation, over-smoothing mitigation, and modality-collapse control. Experiments on nine OpenMAG datasets compare CoMAG with feature-only, graph-only, multimodal, and unified MAG baselines across graph-level prediction, modality matching, and graph-conditioned generation. Results show that CoMAG achieves the best reported performance, demonstrating that task-adaptive reliable contexts and modality-preserving alignment improve structural prediction, cross-modal matching, and graph-conditioned generation while retaining sparse edge-linear complexity.

Multimodal Graph Negative Learning

Multimodal attributed graphs (MAGs) integrate graph topology with heterogeneous modality attributes, such as text and images, thereby enabling richer modeling of complex relational systems. However, such expressiveness also makes learning on MAGs depend on multiple semantic sources, including structural topology, textual and visual attributes, each of which can be regarded as a branch for node representation. Node-level branch semantic imbalance arises when these branches differ across nodes in semantic informativeness and reliability: a branch that provides discriminative semantics for one node may mislead another due to bias in modality quality or structural context. Existing methods often mitigate such heterogeneity through cross-branch agreement or alignment, implicitly treating the dominant prediction as reliable supervision. When the dominant branch is biased, forced imitation may propagate its bias to other branches and suppress original semantics that are useful for classification. We propose GraphMNL, a graph-aware multimodal negative learning framework that addresses this issue by using Negative Learning as cross-branch guidance. Instead of forcing inferior branches to imitate a teacher prediction, the model teaches them which classes a node is unlikely to belong to. GraphMNL builds a branch library, identifies dominant and inferior branches via graph-aware reliability arbitration, gates unstable transfer, and applies target-preserving negative learning over non-target classes. This design decouples target supervision from branch guidance so that supervised losses learn the correct class, while Negative Learning suppresses unlikely alternatives when branch agreement is unreliable. Through the comprehensive experimental evaluation, GraphMNL achieves the best performance on Grocery datasets with 72.47% accuracy and 76.60 F1 score on Reddit M datasets.

SMGFM: Spectral Multimodal Graph Pretraining for Multimodal-Attributed Graphs

Multimodal-attributed graphs (MAGs) couple graph topology with node semantics from text, images, and other modalities. Traditional graph learning contextualizes node semantics by coupling topology with node features. However, this coupling design becomes troublesome in MAGs, where structure-induced and modality-intrinsic semantics may contribute differently to downstream tasks. Structure-induced semantics promote relational consistency through smooth topological variation, whereas modality-intrinsic semantics often encode local, fine-grained distinctions that should not be uniformly smoothed or aligned. Therefore, the key challenge is to identify semantic roles before cross-modal fusion. To this end, we leverage graph-frequency variation as a prior, where low-frequency components capture topology-consistent semantics and high-frequency components preserve modality-specific semantics. Based on this intuition, we propose SMGFM, a spectral multimodal graph pretraining framework that decomposes each modality-specific node signal into graph-frequency bands and assigns band-level semantic roles before cross-modal interaction. Concretely, SMGFM constructs frequency-resolved modality tokens with scalable Chebyshev filters, estimates their coupling reliability through topology-conditioned routing, and performs band-modality interaction before fusion. Its frequency-routed objectives align smooth consensus routes while preserving modality-specific routes, mitigating spatial-domain entanglement and uniform cross-modal alignment. Extensive experiments conducted on the MAG datasets demonstrate that SMGFM achieves state-of-the-art performance across graph-level and modality-level tasks.

A Boundary Integral-based Neural Operator for Mesh Deformation

This paper presents an efficient mesh deformation method based on boundary integration and neural operators, formulating the problem as a linear elasticity boundary value problem (BVP). To overcome the high computational cost of traditional finite element methods and the limitations of existing neural operators in handling Dirichlet boundary conditions for vector fields, we introduce a direct boundary integral representation using a Dirichlet-type Green's tensor. This formulation expresses the internal displacement field solely as a function of boundary displacements, eliminating the need to solve for unknown tractions. Building on this, we design a Boundary-Integral-based Neural Operator (BINO) that learns the geometry- and material-aware Green's traction kernel. A key technical advantage of our framework is the mathematical decoupling of the physical integration process from the geometric representation via geometric descriptors. While this study primarily demonstrates robust generalization across diverse boundary conditions, the architecture inherently possesses potential for cross-geometry adaptation. Numerical experiments, including large deformations of flexible beams and rigid-body motions of NACA airfoils, confirm the model's high accuracy and strict adherence to the principles of linearity and superposition. The results demonstrate that the proposed framework ensures mesh quality and computational efficiency, providing a reliable new paradigm for parametric mesh generation and shape optimization in engineering.

TFPS: A Temporal Filtration-enhanced Positive Sample Set Construction Method for Implicit Collaborative Filtering

The negative sampling strategy can effectively train collaborative filtering (CF) recommendation models based on implicit feedback by constructing positive and negative samples. However, existing methods primarily optimize the negative sampling process while neglecting the exploration of positive samples. Some denoising recommendation methods can be applied to denoise positive samples within negative sampling strategies, but they ignore temporal information. Existing work integrates sequential information during model aggregation but neglects time interval information, hindering accurate capture of users' current preferences. To address this problem, from a data perspective, we propose a novel temporal filtration-enhanced approach to construct a high-quality positive sample set. First, we design a time decay model based on interaction time intervals, transforming the original graph into a weighted user-item bipartite graph. Then, based on predefined filtering operations, the weighted user-item bipartite graph is layered. Finally, we design a layer-enhancement strategy to construct a high-quality positive sample set for the layered subgraphs. We provide theoretical insights into why TFPS can improve Recall@k and NDCG@k, and extensive experiments on three real-world datasets demonstrate the effectiveness of the proposed method. Additionally, TFPS can be integrated with various implicit CF recommenders or negative sampling methods to enhance its performance.

LION: A Clifford Neural Paradigm for Multimodal-Attributed Graph Learning

Recently, the rapid advancement of multimodal domains has driven a data-centric paradigm shift in graph ML, transitioning from text-attributed to multimodal-attributed graphs. This advancement significantly enhances data representation and expands the scope of graph downstream tasks, such as modality-oriented tasks, thereby improving the practical utility of graph ML. Despite its promise, limitations exist in the current neural paradigms: (1) Neglect Context in Modality Alignment: Most existing methods adopt topology-constrained or modality-specific operators as tokenizers. These aligners inevitably neglect graph context and inhibit modality interaction, resulting in suboptimal alignment. (2) Lack of Adaptation in Modality Fusion: Most existing methods are simple adaptations for 2-modality graphs and fail to adequately exploit aligned tokens equipped with topology priors during fusion, leading to poor generalizability and performance degradation. To address the above issues, we propose LION (c\underline{LI}ff\underline{O}rd \underline{N}eural paradigm) based on the Clifford algebra and decoupled graph neural paradigm (i.e., propagation-then-aggregation) to implement alignment-then-fusion in multimodal-attributed graphs. Specifically, we first construct a modality-aware geometric manifold grounded in Clifford algebra. This geometric-induced high-order graph propagation efficiently achieves modality interaction, facilitating modality alignment. Then, based on the geometric grade properties of aligned tokens, we propose adaptive holographic aggregation. This module integrates the energy and scale of geometric grades with learnable parameters to improve modality fusion. Extensive experiments on 9 datasets demonstrate that LION significantly outperforms SOTA baselines across 3 graph and 3 modality downstream tasks.

FedBook: A Unified Federated Graph Foundation Codebook with Intra-domain and Inter-domain Knowledge Modeling

Foundation models have shown remarkable cross-domain generalization in language and vision, inspiring the development of graph foundation models (GFMs). However, existing GFMs typically assume centralized access to multi-domain graphs, which is often infeasible due to privacy and institutional constraints. Federated Graph Foundation Models (FedGFMs) address this limitation, but their effectiveness fundamentally hinges on constructing a robust global codebook that achieves intra-domain coherence by consolidating mutually reinforcing semantics within each domain, while also maintaining inter-domain diversity by retaining heterogeneous knowledge across domains. To this end, we propose FedBook, a unified federated graph foundation codebook that systematically aggregates clients' local codebooks during server-side federated pre-training. FedBook follows a two-phase process: (1) Intra-domain Collaboration, where low-frequency tokens are refined by referencing more semantically reliable high-frequency tokens across clients to enhance domain-specific coherence; and (2) Inter-domain Integration, where client contributions are weighted by the semantic distinctiveness of their codebooks during the aggregation of the global GFM, thereby preserving cross-domain diversity. Extensive experiments on 8 benchmarks across multiple domains and tasks demonstrate that FedBook consistently outperforms 21 baselines, including isolated supervised learning, FL/FGL, federated adaptations of centralized GFMs, and FedGFM techniques.