However, there are three challenges.

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This paper explores sparsification methods as a form of regularization in Graph Neural Networks (GNNs) to address high memory usage and computational costs in large-scale graph applications. Using techniques from Network Science and Machine Learning, including Erdős-Rényi for model sparsification, we enhance the efficiency of GNNs for real-world applications. We demonstrate our approach on N-1 contingency assessment in electrical grids, a critical task for ensuring grid reliability. We apply our methods to three datasets of varying sizes, exploring Graph Convolutional Networks (GCN) and Graph Isomorphism Networks (GIN) with different degrees of sparsification and rewiring. Comparison across sparsification levels shows the potential of combining insights from both research fields to improve GNN performance and scalability. Our experiments highlight the importance of tuning sparsity parameters: while sparsity can improve generalization, excessive sparsity may hinder learning of complex patterns. Our adaptive rewiring approach, particularly when combined with early stopping, proves promising by allowing the model to adapt its connectivity structure during training. This research contributes to understanding how sparsity can be effectively leveraged in GNNs for critical applications like power grid reliability analysis.

Pi 1, which is clearly not possible. The possibility form 1 prior-data conflicts is witnessed in the followingexample. Assume a conflict at the upper boundPi. Then kiN > Pi Pi, which is a prior-data agreementwithPi bydefinition. Next, we consider the case for a prior-data conflict, that is, the bounds from Equation 5. We consider a larger version of the chain problem Araya-López et al. [2011] with30-states.

Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical instabilities along class-separating directions, but practical methods to detect and exploit these windows in trained models are still limited. We show that tracking the class-conditional entropy of a latent semantic variable given the noisy state provides a reliable signature of these transition regimes. By restricting the entropy to semantic partitions, the entropy can furthermore resolve semantic decisions at different levels of abstraction. We analyze this behavior in high-dimensional Gaussian mixture models and show that the entropy rate concentrates on the same logarithmic time scale as the speciation symmetry-breaking instability previously identified in variance-preserving diffusion. We validate our method on EDM2-XS and Stable Diffusion 1.5, where class-conditional entropy consistently isolates the noise regimes critical for semantic structure formation. Finally, we use our framework to quantify how guidance redistributes semantic information over time. Together, these results connect information-theoretic and statistical physics perspectives on diffusion and provide a principled basis for time-localized control.