Graph kernels have emerged as a fundamental and widely adopted technique in graph machine learning. However, most existing graph kernel methods rely on fixed graph similarity estimation that cannot be directly optimized for task-specific objectives, leading to sub-optimal performance. To address this limitation, we propose a kernel-based learning framework called Hierarchical Shortest-Path Graph Kernel Network (HSP-GKN), which seamlessly integrates graph similarity estimation with downstream tasks within a unified optimization framework. Specifically, we design a hierarchical shortest-path graph kernel that efficiently preserves both the semantic and structural information of a given graph by transforming it into hierarchical features used for subsequent neural network learning. Building upon this kernel, we develop a novel end-to-end learning framework that matches hierarchical graph features with learnable hidden graph features to produce a similarity vector. This similarity vector subsequently serves as the graph embedding for endto-end training, enabling the neural network to learn task-specific representations. Extensive experimental results demonstrate the effectiveness and superiority of the designed kernel and its corresponding learning framework compared to current competitors.

Graph kernels have emerged as a fundamental and widely adopted technique in graph machine learning. However, most existing graph kernel methods rely on fixed graph similarity estimation that cannot be directly optimized for task-specific objectives, leading to sub-optimal performance. To address this limitation, we propose a kernel-based learning framework called Hierarchical Shortest-Path Graph Kernel Network HSP-GKN, which seamlessly integrates graph similarity estimation with downstream tasks within a unified optimization framework. Specifically, we design a hierarchical shortest-path graph kernel that efficiently preserves both the semantic and structural information of a given graph by transforming it into hierarchical features used for subsequent neural network learning. Building upon this kernel, we develop a novel end-to-end learning framework that matches hierarchical graph features with learnable $hidden$ graph features to produce a similarity vector. This similarity vector subsequently serves as the graph embedding for end-to-end training, enabling the neural network to learn task-specific representations. Extensive experimental results demonstrate the effectiveness and superiority of the designed kernel and its corresponding learning framework compared to current competitors.

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As such, the twobaselines were trained and evaluated on asubset ofthe full REAL library.

Hence, when a message passing kernel satisfies the naturality condition for local isomorphisms of the edge neighbourhood (Eq.

We5 use aneural network with random weights on a graph and compute agraph embedding by mean-pooling. Indeed, we mean that the parameters are shared, but the resulting kernels differ by a basis28 transformation. We think that the use of gauges are a necessity to precisely describe the feature spaces and41 equivariantmaps.

Functional brain graphs are often characterized with separate graph-theoretic or spectral descriptors, overlooking how these properties covary and partially overlap across brains and conditions. We anticipate that dense, weighted functional connectivity graphs occupy a low-dimensional latent geometry along which both topological and spectral structures display graded variations. Here, we estimated this unified graph representation and enabled generation of dense functional brain graphs through a graph transformer autoencoder with latent diffusion, with spectral geometry providing an inductive bias to guide learning. This geometry-aware latent representation, although unsupervised, meaningfully separated working-memory states and decoded visual stimuli, with performance further enhanced by incorporating neural dynamics. From the diffusion modeled distribution, we were able to sample biologically plausible and structurally grounded synthetic dense graphs.

Following the milestones in large language models (LLMs) and multimodal models, we have seen a surge in applying LLMs to biochemical tasks. Leveraging graph features and molecular text representations, LLMs can tackle various tasks, such as predicting chemical reaction outcomes and describing molecular properties. However, most current work overlooks the multi-level nature of graph features. The impact of different feature levels on LLMs and the importance of each level remain unexplored, and it is possible that different chemistry tasks require different feature levels. In this work, we first investigate the effect of feature granularity by fusing GNN-generated feature tokens, discovering that even reducing all tokens to a single token does not significantly impact performance. We then explore the effect of various feature levels on performance, finding that both the quality of LLM-generated molecules and performance on different tasks benefit from different feature levels. We conclude with two key insights: (1) current molecular Multimodal LLMs(MLLMs) lack a comprehensive understanding of graph features, and (2) static processing is not sufficient for hierarchical graph feature. Our code will be publicly available soon.

In many industrial applications, it is common that the graph embeddings generated from training GNNs are used in an ensemble model where the embeddings are combined with other tabular features (e.g., original node or edge features) in a downstream ML task. The tabular features may even arise naturally if, e.g., one tries to build a graph such that some of the node or edge features are stored in a tabular format. Here we address the problem of explaining the output of such ensemble models for which the input features consist of learned neural graph embeddings combined with additional tabular features. We propose MBExplainer, a model-agnostic explanation approach for downstream models with augmented graph embeddings. MBExplainer returns a human-legible triple as an explanation for an instance prediction of the whole pipeline consisting of three components: a subgraph with the highest importance, the topmost important nodal features, and the topmost important augmented downstream features. A game-theoretic formulation is used to take the contributions of each component and their interactions into account by assigning three Shapley values corresponding to their own specific games. Finding the explanation requires an efficient search through the corresponding local search spaces corresponding to each component. MBExplainer applies a novel multilevel search algorithm that enables simultaneous pruning of local search spaces in a computationally tractable way. In particular, three interweaved Monte Carlo Tree Search are utilized to iteratively prune the local search spaces. MBExplainer also includes a global search algorithm that uses contextual bandits to efficiently allocate pruning budget among the local search spaces. We show the effectiveness of MBExplainer by presenting a set of comprehensive numerical examples on multiple public graph datasets for both node and graph classification tasks.