In typical graph neural networks (GNNs), feature representation learning naturally evolves through iteratively updating node features and exchanging information based on graph topology. In this context, we conceptualize that the learning process in GNNs is a mean-field game (MFG), where each graph node is an agent, interacting with its topologically connected neighbors. However, current GNNs often employ the identical MFG strategy across different graph datasets, regardless of whether the graph exhibits homophilic or heterophilic characteristics. To address this challenge, we propose to formulate the learning mechanism into a variational framework of the MFG inverse problem, introducing an in-context selective message passing paradigm for each agent, which promotes the best overall outcome for the graph. Specifically, we seek for the application-adaptive transportation function (controlling information exchange throughout the graph) and reaction function (controlling feature representation learning on each agent), on the fly, which allows us to uncover the most suitable selective mechanism of message passing by solving an MFG variational problem through the lens of Hamiltonian flows. Taken together, our variational framework unifies existing GNN models into various mean-field games with distinct equilibrium states, each characterized by the learned in-context message passing operators. Furthermore, we present an agnostic end-to-end deep model, coined Game-of-GNN, to jointly identify the message passing mechanism and fine-tune the GNN hyper-parameters on top of the elucidated message passing operators. Game-of-GNN has achieved SOTA performance on diverse graph data, including popular benchmark datasets and human connectomes. More importantly, the mathematical insight of MFG framework provides a new window to understand the foundational principles of graph learning as an interactive dynamical system, which allows us to reshape the idea of designing next-generation GNN models.

Model-Heterogeneous Federated Learning (Hetero-FL) has attracted growing attention for its ability to aggregate knowledge from heterogeneous models while keeping private data locally. To better aggregate knowledge from clients, ensemble distillation, as a widely used and effective technique, is often employed after global aggregation to enhance the performance of the global model. However, simply combining Hetero-FL and ensemble distillation does not always yield promising results and can make the training process unstable. The reason is that existing methods primarily focus on logit distillation, which, while being model-agnostic with softmax predictions, fails to compensate for the knowledge bias arising from heterogeneous models. To tackle this challenge, we propose a stable and efficient Feature Distillation for model-heterogeneous Federated learning, dubbed FedFD, that can incorporate aligned feature information via orthogonal projection to integrate knowledge from heterogeneous models better. Specifically, a new feature-based ensemble federated knowledge distillation paradigm is proposed. The global model on the server needs to maintain a projection layer for each clientside model architecture to align the features separately. Orthogonal techniques are employed to re-parameterize the projection layer to mitigate knowledge bias from heterogeneous models and thus maximize the distilled knowledge. Extensive experiments show that FedFD achieves superior performance compared to state-of-the-art methods.

This paper studies the problem of class-incremental learning (CIL), a core setting within continual learning where a model learns a sequence of tasks, each containing a distinct set of classes. Traditional CIL methods, which do not leverage pretrained models (PTMs), suffer from catastrophic forgetting (CF) due to the need to incrementally learn both feature representations and the classifier. The integration of PTMs into CIL has recently led to efficient approaches that treat the PTM as a fixed feature extractor combined with analytic classifiers, achieving state-ofthe-art performance. However, they still face a major limitation: the inability to continually adapt feature representations to best suit the CIL tasks, leading to suboptimal performance. To address this, we propose AnaCP (Analytic Contrastive Projection), a novel method that preserves the efficiency of analytic classifiers while enabling incremental feature adaptation without gradient-based training, thereby eliminating the CF caused by gradient updates. Our experiments show that AnaCP not only outperforms existing baselines but also achieves the accuracy level of joint training, which is regarded as the upper bound of CIL.

Robust feature representations are essential for learning-based Multi-View Stereo (MVS), which relies on accurate feature matching. Recent MVS methods leverage Transformers to capture long-range dependencies based on local features extracted by conventional feature pyramid networks. However, the quadratic complexity of Transformer-based MVS methods poses challenges to balance performance and efficiency. Motivated by the global modeling capability and linear complexity of the Mamba architecture, we propose MVSMamba, the first Mamba-based MVS network. MVSMamba enables efficient global feature aggregation with minimal computational overhead. To fully exploit Mamba's potential in MVS, we propose a Dynamic Mamba module (DM-module) based on a novel reference-centered dynamic scanning strategy, which enables: (1) Efficient intra-and inter-view feature interaction from the reference to source views, (2) Omnidirectional multi-view feature representations, and (3) Multi-scale global feature aggregation. Extensive experimental results demonstrate MVSMamba outperforms state-of-the-art MVS methods on the DTU dataset and the Tanks-and-Temples benchmark with both superior performance and efficiency.

In typical graph neural networks (GNNs), feature representation learning naturally evolves through iteratively updating node features and exchanging information based on graph topology. In this context, we conceptualize that the learning process in GNNs is a mean-field game (MFG), where each graph node is an agent, interacting with its topologically connected neighbors. However, current GNNs often employ the identical MFG strategy across different graph datasets, regardless of whether the graph exhibits homophilic or heterophilic characteristics. To address this challenge, we propose to formulate the learning mechanism into a variational framework of the MFG inverse problem, introducing an in-context selective message passing paradigm for each agent, which promotes the best overall outcome for the graph. Specifically, we seek for the application-adaptive transportation function (controlling information exchange throughout the graph) and reaction function (controlling feature representation learning on each agent), \textit{on the fly}, which allows us to uncover the most suitable selective mechanism of message passing by solving an MFG variational problem through the lens of Hamiltonian flows. Taken together, our variational framework unifies existing GNN models into various mean-field games with distinct equilibrium states, each characterized by the learned in-context message passing operators. Furthermore, we present an agnostic end-to-end deep model, coined \textit{Game-of-GNN}, to jointly identify the message passing mechanism and fine-tune the GNN hyper-parameters on top of the elucidated message passing operators.

This paper studies the problem of class-incremental learning (CIL), a core setting within continual learning where a model learns a sequence of tasks, each containing a distinct set of classes. Traditional CIL methods, which do not leverage pre-trained models (PTMs), suffer from catastrophic forgetting (CF) due to the need to incrementally learn both feature representations and the classifier. The integration of PTMs into CIL has recently led to efficient approaches that treat the PTM as a fixed feature extractor combined with analytic classifiers, achieving state-of-the-art performance. However, they still face a major limitation: the inability to continually adapt feature representations to best suit the CIL tasks, leading to suboptimal performance. To address this, we propose AnaCP (Analytic Contrastive Projection), a novel method that preserves the efficiency of analytic classifiers while enabling incremental feature adaptation without gradient-based training, thereby eliminating the CF caused by gradient updates. Our experiments show that AnaCP not only outperforms existing baselines but also achieves the accuracy level of joint training, which is regarded as the upper bound of CIL.

Graphs are ubiquitous in various domains, such as social networks and biological systems. Despite the great successes of graph neural networks (GNNs) in modeling and analyzing complex graph data, the inductive bias of locality assumption, which involves exchanging information only within neighboring connected nodes, restricts GNNs in capturing long-range dependencies and global patterns in graphs. Inspired by the classic Brachistochrone problem, we seek how to devise a new inductive bias for cutting-edge graph application and present a general framework through the lens of variational analysis. The backbone of our framework is a two-way mapping between the discrete GNN model and continuous diffusion functional, which allows us to design application-specific objective function in the continuous domain and engineer discrete deep model with mathematical guarantees. First, we address over-smoothing in current GNNs.