Mittag-Leffler-Type Forecast-Error Growth as a Diagnostic Indicator of Fractional Dynamics

What the math gives to ML

The paper provides a data-driven mechanism for distinguishing fractional-memory error propagation from ordinary exponential divergence using multi-horizon forecast errors. Its transferable asset is the quantitative fit of forecast-error curves to Mittag-Leffler versus exponential laws, together with the local logarithmic slope and kNN contraction test. A neural-network implementation can use this diagnostic to detect when a sequence task requires long power-law memory, select or activate a fractional-kernel SSM/RNN module, and assign horizon-dependent training weights. The fitted order must be treated as an effective error-geometry parameter rather than as a proof of the underlying system's fractional order.