Models trained on small inputs can generalize to larger ones if they're continuous with respect to appropriate sampling operations—the paper provides explicit rates and identifies which sampling strategies (replacement, binning, species sampling) work for different problem types.
This paper develops a unified framework for understanding how machine learning models generalize from small to large inputs of variable sizes (like point clouds or graphs). Using random sampling maps, the authors characterize when models can reliably extrapolate to unseen input sizes and how to compress large inputs while preserving model predictions.