$m$-Bell and $m$-Stirling numbers: Iterated binomial transforms, hyper-Bessel functions, and moments of the Conway--Maxwell--Poisson distribution

What the math gives to ML

The paper supplies structured, non-learned triangular transforms whose coefficients obey simple recurrences and whose repeated binomial transform has an explicit closed form. This can be transferred into sequence models as an invertible global-mixing layer or as a fixed basis change over the token/feature axis, providing long-range interaction without quadratic attention parameters. The main transferable asset is algebraic structure: the transform is deterministic, composable, and admits a cheap recurrence or convolution implementation, although numerical normalization is essential because coefficients grow rapidly.