A differentiable Sandpile Stabilization Layer (SSL) and congestion-aware objectives designed to redistribute excess load and manage stabilization costs are proposed and Experiments on long-range benchmarks show that targeting sandpile-identified bottlenecks mitigates representation collapse and improves over standard baselines.
Yang Shi, Li-Xian Chen, Jingchao Wang et al.· Proceedings of the 32nd ACM...· 0 citations
Non-Euclidean spaces inherently enable high-fidelity embeddings for hierarchical and cyclical data due to their geometric properties. Existing approaches unify hyperbolic and spherical embeddings within the framework of constant curvature spaces. However, current methods for Lipschitz regularization remain limited to non-positive curvature geometries, such as hyperbolic and Euclidean spaces, and cannot be naturally extended to the general constant curvature setting. In this paper, we present a rigorous Lipschitz analysis for constant curvature graph convolutional networks ( \(\kappa\) -GCNs) and enhance their robustness through Lipschitz regularization. We derive upper bounds for the Lipschitz constants across constant curvature spaces, thereby standardizing the Lipschitz limits of the \(\kappa\) -stereographic model. Furthermore, we incorporate these bounds into a regularization framework for \(\kappa\) -GCNs to improve stability and robustness. Experimental results demonstrate that the proposed regularization method often strengthens the robustness of \(\kappa\) -GCNs across various curvature regimes, particularly under Gaussian feature noise.
Yang Shi, Jingchao Wang, Liangsi Lu et al.· ACM Transactions on Knowledg...· 0 citations
Message-passing graph neural networks (MP-GNNs) are widely used for learning on relational data. However, their performance drops on tasks requiring long-range interactions due to over-squashing, where exponential information compression overwhelms fixed-width embeddings. While existing analyses often attribute this to geometric bottlenecks under linear diffusion assumptions, thresholded nonlinearities in GNNs motivate a load-release view akin to Abelian sandpiles. Using the discrete sandpile model as a structural proxy, we show that graph bottlenecks force large stabilization cost, effectively creating zones of high transport congestion. We characterize stabilization-invariant equivalence classes induced by the reduced Laplacian and derive cut-based lower bounds linking bottlenecks to unavoidable stabilization effort. The resulting theory is discrete, whereas our implementation is a continuous vector-valued surrogate. The theory identifies the relevant design factors, namely capacity and cut size. Guided by these insights, we propose a differentiable Sandpile Stabilization Layer (SSL) and congestion-aware objectives designed to redistribute excess load and manage stabilization costs. Experiments on long-range benchmarks, together with congestion and collision diagnostics, show that targeting sandpile-identified bottlenecks mitigates representation collapse and improves over standard baselines. Project Page: https://sandpile-gnn.github.io/
Yang Shi, Lixian Chen, Jingchao Wang et al.· Proceedings of the 32nd ACM...· 0 citations
This approach combines local editing and background preservation without external or user-provided spatial masks and without model fine-tuning, and achieves the strongest reported preservation metrics, including 27.44~dB PSNR and 0.055 LPIPS.
Yang Shi, Liangsi Lu, Minzhe Guo et al.· 0 citations
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