Classification fields are infinite recursive hierarchical cluster structures generated by a local refinement rule, and a ReLU network predictor learned from finite prefixes can approximate the generator and extend it to deeper levels with exponential convergence in the completed cell metric.
Fractals and self similarity.Indiana University Mathematics Journal, 30 (5):713–747
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Classification Fields: Arbitrarily Fine Recursive Hierarchical Clustering From Few Examples
Classification fields are infinite recursive hierarchical cluster structures generated by a local refinement rule, and a ReLU network predictor learned from finite prefixes can approximate the generator and extend it to deeper levels with exponential convergence in the completed cell metric.