Graph machine learning architectures are typically tailored to specific tasks on specific datasets, which hinders their broader applicability. This has led to a new quest in graph machine learning: how to build graph foundation models capable of generalizing across arbitrary graphs and features? In this work, we present a recipe for designing graph foundation models for node-level tasks from first principles. The key ingredient underpinning our study is a systematic investigation of the symmetries that a graph foundation model must respect. In a nutshell, we argue that label permutation-equivariance alongside feature permutation-invariance are necessary in addition to the common node permutation-equivariance on each local neighborhood of the graph. To this end, we first characterize the space of linear transformations that are equivariant to permutations of nodes and labels, and invariant to permutations of features. We then prove that the resulting network is a universal approximator on multisets that respect the aforementioned symmetries. Our recipe uses such layers on the multiset of features induced by the local neighborhood of the graph to obtain a class of graph foundation models for node property prediction. We validate our approach through extensive experiments on 29 real-world node classification datasets, demonstrating both strong zero-shot empirical performance and consistent improvement as the number of training graphs increases.

Image dehazing has been a popular topic of research for a long time. Previous deep learning-based image dehazing methods have failed to achieve satisfactory dehazing effects on both synthetic datasets and real-world datasets, exhibiting poor generalization. Moreover, single-stage networks often result in many regions with artifacts and color distortion in output images. To address these issues, this paper proposes a two-stage image dehazing network called TSNet, mainly consisting of the multi-scale fusion module (MSFM) and the adaptive learning module (ALM). Specifically, MSFM and ALM enhance the generalization of TSNet. The MSFM can obtain large receptive fields at multiple scales and integrate features at different frequencies to reduce the differences between inputs and learning objectives. The ALM can actively learn of regions of interest in images and restore texture details more effectively. Additionally, TSNet is designed as a two-stage network, where the first-stage network performs image dehazing, and the second-stage network is employed to improve issues such as artifacts and color distortion present in the results of the first-stage network. We also change the learning objective from ground truth images to opposite fog maps, which improves the learning efficiency of TSNet. Extensive experiments demonstrate that TSNet exhibits superior dehazing performance on both synthetic and real-world datasets compared to previous state-of-the-art methods.

We present a method for balancing between the Local and Global Structures (LGS) in graph embedding, via a tunable parameter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few methods attempt to do both, and it is not always possible to capture well both local and global information in two dimensions, which is where most graph drawing live. The choice of using a local or a global embedding for visualization depends not only on the task but also on the structure of the underlying data, which may not be known in advance. For a given graph, LGS aims to find a good balance between the local and global structure to preserve. We evaluate the performance of LGS with synthetic and real-world datasets and our results indicate that it is competitive with the state-of-the-art methods, using established quality metrics such as stress and neighborhood preservation. We introduce a novel quality metric, cluster distance preservation, to assess intermediate structure capture. All source-code, datasets, experiments and analysis are available online.

In future 6G Mobile Edge Computing (MEC), autopilot systems require the capability of processing multimodal data with strong interdependencies. However, traditional heuristic algorithms are inadequate for real-time scheduling due to their requirement for multiple iterations to derive the optimal scheme. We propose a novel TSNet-SAC based on Transformer, that utilizes heuristic algorithms solely to guide the training of TSNet. Additionally, a Sliding Augment Component (SAC) is introduced to enhance the robustness and resolve algorithm defects. Furthermore, the Extender component is designed to handle multi-scale training data and provide network scalability, enabling TSNet to adapt to different access scenarios. Simulation demonstrates that TSNet-SAC outperforms existing networks in accuracy and robustness, achieving superior scheduling-making latency compared to heuristic algorithms.