Learning Coarse-Graining Transformations in the 2D Ising Model: A Physics-Informed Approach to Neural Network Interpretability

Understanding how neural networks learn to abstract and simplify information is a fundamental challenge in AI interpretability. We demonstrate that simple physics models can provide a rigorous testbed for evaluating learned representations. Using the 2D Ising model as a case study, we train a convolutional neu ral network to perform coarse-graining—a fundamental operation in statistical physics that reduces degrees of freedom while preserving essential macroscopic proper ties. Our CNN achieves near-perfect performance (MSE = 0.020, spatial correlation = 0.9997) with only 9,569 parameters, outperforming a fully-connected MLP by 648× despite using 32× fewer parameters. This work es tablishes physics-based coarse-graining as a benchmark for evaluating inherent biases in neural network archi tectures, revealing how spatial inductive biases enable efficient learning of physical abstractions.