Federated Graph Learning (FGL) offers a promising framework for collaboratively training Graph Neural Networks (GNNs) while preserving data privacy. In resourceconstrained environments, One-shot Federated Learning (OFL) emerges as an effective solution by limiting communication to a single round. Current OFL approaches employing generative models have attracted considerable attention; however, they face unresolved challenges: these methods are primarily designed for traditional image data and fail to capture the fine-grained structural information of local graph data. Consequently, they struggle to integrate the intricate correlations necessary and transfer subtle structural insights from each client to the global model. To address these issues, we introduce OASIS, an innovative one-shot FGL framework. In OASIS, we propose a Synergy Graph Synthesizer designed to generate informative synthetic graphs and introduce a Topological Codebook to construct a structural latent space. Moreover, we propose the WassersteinEnhanced Semantic Affinity Distillation (WESAD) to incorporate rich inter-class relationships and the Wasserstein-Driven Structural Relation Distillation (WDSRD) to facilitate the effective transfer of structural knowledge from the Topological Codebook. Extensive experiments on real-world tasks demonstrate the superior performance and generalization capability of OASIS, with an average improvement of 15.81% over the baseline.

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities. We take inspiration from neuroscience, specifically the hippocampal-entorhinal system known to be important for generalisation. We propose that to generalise structural knowledge, the representations of the structure of the world, i.e. how entities in the world relate to each other, need to be separated from representations of the entities themselves. We show, under these principles, artificial neural networks embedded with hierarchy and fast Hebbian memory, can learn the statistics of memories and generalise structural knowledge. Spatial neuronal representations mirroring those found in the brain emerge, suggesting spatial cognition is an instance of more general organising principles. We further unify many entorhinal cell types as basis functions for constructing transition graphs, and show these representations effectively utilise memories. We experimentally support model assumptions, showing a preserved relationship between entorhinal grid and hippocampal place cells across environments.

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities.

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities. We take inspiration from neuroscience, specifically the hippocampal-entorhinal system known to be important for generalisation. We propose that to generalise structural knowledge, the representations of the structure of the world, i.e. how entities in the world relate to each other, need to be separated from representations of the entities themselves. We show, under these principles, artificial neural networks embedded with hierarchy and fast Hebbian memory, can learn the statistics of memories and generalise structural knowledge. Spatial neuronal representations mirroring those found in the brain emerge, suggesting spatial cognition is an instance of more general organising principles. We further unify many entorhinal cell types as basis functions for constructing transition graphs, and show these representations effectively utilise memories. We experimentally support model assumptions, showing a preserved relationship between entorhinal grid and hippocampal place cells across environments.

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities.

We thank all reviewers for their valuable and constructive comments. Below, we address the detailed comments. It is shown that PR can be extended to "selectively" incorporate uncertain We'll make this clearer in the final version. The odd columns are real data and even ones are the reconstruction results. It was a fault to miss the 8-th column (i.e., the reconstruction We'll fix these issues for better presentation.

In this work we introduce GreenLightningAI (GLAI), a new architectural block designed as an alternative to conventional Multilayer Perceptrons (MLPs). The central idea is to separate two types of knowledge that are usually entangled during training: (i) structural knowledge, encoded by the stable activation patterns induced by Rectified Linear Unit (ReLU) activations; and (ii) quantitative knowledge, carried by the numerical weights and biases. By fixing the structure once stabilized, GLAI reformulates the MLP as a combination of paths, where only the quantitative component is optimized. This refor-mulation retains the universal approximation capabilities of MLPs, yet achieves a more efficient training process, reducing training time by 40% on average across the cases examined in this study. Crucially, GLAI is not just another classifier, but a generic block that can replace MLPs wherever they are used, from supervised heads with frozen backbones to projection layers in self-supervised learning or few-shot classifiers. Across diverse experimental setups, GLAI consistently matches or exceeds the accuracy of MLPs with an equivalent number of parameters, while converging faster. Overall, GLAI establishes a new design principle that opens a direction for future integration into large-scale architectures such as Transformers, where MLP blocks dominate the computational footprint.