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Graph Neural Networks (GNNs) have demonstrated remarkable performance in various graph-based machine learning tasks, yet evaluating the importance of neighbors of testing nodes remains largely unexplored due to the challenge of assessing data importance without test labels. To address this gap, we propose Shapley-Guided Utility Learning (SGUL), a novel framework for graph inference data valuation. SGUL innovatively combines transferable data-specific and model-specific features to approximate test accuracy without relying on ground truth labels. By incorporating Shapley values as a preprocessing step and using feature Shapley values as input, our method enables direct optimization of Shapley value prediction while reducing computational demands. SGUL overcomes key limitations of existing methods, including poor generalization to unseen test-time structures and indirect optimization. Experiments on diverse graph datasets demonstrate that SGUL consistently outperforms existing baselines in both inductive and transductive settings. SGUL offers an effective, efficient, and interpretable approach for quantifying the value of test-time neighbors. 

Abstract We show that any symplectically aspherical/Calabi–Yau filling of Y := ∂(V × D) has vanishing symplectic cohomology for any Liouville domain V . In particular, we make no topological requirement on the filling and c₁(V ) can be nonzero. Moreover, we show that for any symplectically aspherical/Calabi–Yau filling W of Y , the interior W˚ is diffeomorphic to the interior of V × D if π₁(Y ) is abelian and dim V ≥ 4. And W is diffeomorphic to V × D if moreover the Whitehead group of π₁(Y ) is trivial. 

We construct counterexamples to classical calculus facts such as the inverse and implicit function theorems in scale calculus—a generalization of multivariable calculus to infinite-dimensional vector spaces, in which the reparameterization maps relevant to symplectic geometry are smooth. Scale calculus is a corner stone of polyfold theory, which was introduced by Hofer, Wysocki, and Zehnder as a broadly applicable tool for regularizing moduli spaces of pseudoholomorphic curves. We show how the novel nonlinear scale-Fredholm notion in polyfold theory overcomes the lack of implicit function theorems, by formally establishing an often implicitly used fact: The differentials of basic germs—the local models for scale-Fredholm maps—vary continuously in the space of bounded operators when the base point changes. We moreover demonstrate that this continuity holds only in specific coordinates, by constructing an example of a scale-diffeomorphism and scale-Fredholm map with discontinuous differentials. This justifies the high technical complexity in the foundations of polyfold theory.