Neural Renormalization Group Flow for Percolation

• URL: http://arxiv.org/abs/2608.26764v1
• Date: Thu, 27 Aug 2026 07:56:45 GMT
• Title: Neural Renormalization Group Flow for Percolation
• Abstract summary: We develop a supervised, scale-shared neural architecture for two-dimensional site percolation.<n>We observe that it is key that the learned latent representation exhibits critical fluctuations and scale-dependent flows consistent with the renormalization-group structure of percolation.
• Score: 2.6754482304270018
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Machine learning offers a possible route to data-driven real-space renormalization when the relevant observables are nonlocal and difficult to prescribe explicitly. We explore this idea for two-dimensional site percolation developping a supervised, scale-shared neural architecture. The model recursively applies the same learned coarse-graining rule across scales, producing a latent field from which the crossing probability is predicted, while a corresponding fine-graining decoder reconstructs the largest-cluster mask. Trained only on small lattices, the model extrapolates to substantially larger systems, recovers the spanning cluster with high fidelity, and produces observables obeying the expected finite-size scaling near the critical point. We observe that to get such performance it is key that the learned latent representation exhibits critical fluctuations and scale-dependent flows consistent with the renormalization-group structure of percolation.

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