78 citations · 298 across the 26 of their papers we have counts for
26 papers
Exact distribution of the output of a deep-layered machine
Thomas Fink, Thomas M. A. Fink
Deep learning builds complex global functions through the repeated composition of local functions. But the resulting distribution over global functions is unknown. We derive this d…
Deep-layered machines have a built-in Occam's razor
Thomas M. A. Fink
Input-output maps are prevalent throughout science and technology. They are empirically observed to be biased towards simple outputs, but we don't understand why. To address this p…
Number of ordered factorizations and recursive divisors
T. M. A. Fink
The number of ordered factorizations and the number of recursive divisors are two related arithmetic functions that are recursively defined. But it is hard to construct explicit re…
Properties of the recursive divisor function and the number of ordered factorizations
T. M. A. Fink
We recently introduced the recursive divisor function , a recursive analogue of the usual divisor function. Here we calculate its Dirichlet series, which is ${ζ(s-x)}/(2 -…
Number of attractors in the critical Kauffman model is exponential
T. M. A. Fink, F. C. Sheldon
The Kauffman model is the archetypal model of genetic computation. It highlights the importance of criticality, at which many biological systems seem poised. In a series of advance…
Exact dynamics of the critical Kauffman model with connectivity one
T. M. A. Fink
The critical Kauffman model with connectivity one is the simplest class of critical Boolean networks. Nevertheless, it exhibits intricate behavior at the boundary of order and chao…