Space of Functions Computed by Deep-Layered Machines

Alexander Mozeika, Bo Li, David Saad

Research output: Contribution to journalArticlepeer-review


We study the space of functions computed by random-layered machines, including deep neural networks and Boolean circuits. Investigating the distribution of Boolean functions computed on the recurrent and layer-dependent architectures, we find that it is the same in both models. Depending on the initial conditions and computing elements used, we characterize the space of functions computed at the large depth limit and show that the macroscopic entropy of Boolean functions is either monotonically increasing or decreasing with the growing depth.
Original languageEnglish
Article number168301
Number of pages6
JournalPhysical Review Letters
Issue number16
Publication statusPublished - 12 Oct 2020

Bibliographical note

© 2020 American Physical Society. Space of Functions Computed by Deep-Layered Machines. Alexander Mozeika, Bo Li, and David Saad. Phys. Rev. Lett. 125, 168301 – Published 12 October 2020

Funding: B. L. and D. S. acknowledge support from the
Leverhulme Trust (RPG-2018-092), European Union’s
Horizon 2020 research and innovation program under the
Marie Skłodowska-Curie Grant Agreement No. 835913.
D. S. acknowledges support from the EPSRC program
grant TRANSNET (EP/R035342/1).


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