Finite-Sample Limits of Entropy-Based Structure Identification in Discretized Nonlinear Systems

What the math gives to ML

The paper provides a transferable mechanism for deciding when discretized, entropy-based structure discovery is statistically reliable: a resolution-stochasticity ratio creates a hard identifiability boundary that cannot be removed by simply collecting more samples. It also separates explanatory variable selection from predictive selection, showing that an entropy-selected mask can incur excess prediction risk when inputs are numerous or the entropy signal is weak. A useful neural-network transfer is a dual-mask selector that estimates this reliability ratio before committing to interpretable sparse inputs, and falls back to prediction-oriented selection when discretization noise dominates. The key falsifiable signature is a sharp collapse of entropy-mask recovery as stochasticity exceeds discretization resolution, together with increasing prediction regret as the number of selected categorical combinations grows.