Scale Partitioning by Incremental Nested Entropy: A Measure-Oriented Theory of Multiscale Structure

What the math gives to ML

The paper offers a deterministic multiscale detector based on Shannon entropy computed over every ordered prefix of a measure-valued sequence. Its transferable asset is the conversion of a heterogeneous prefix into an effective component count, 2^{E_n}, and an entropy-increment profile that can expose scale boundaries without specifying the number of groups or a cutoff percentile. A practical neural-network transfer is to apply this construction to ordered singular values, gradient magnitudes, attention scores, or feature energies, then create adaptive spectral groups and assign separate optimization or regularization schedules. The main falsifiable prediction is that genuinely separated spectral bands produce stable extrema or sign changes in the nested-entropy increments, whereas a single-scale spectrum produces a smooth profile with no persistent boundary.