4.8 Article

Space of Functions Computed by Deep-Layered Machines

Journal

PHYSICAL REVIEW LETTERS
Volume 125, Issue 16, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.125.168301

Keywords

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Funding

  1. Leverhulme Trust [RPG-2018-092]
  2. European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant [835913]
  3. EPSRC program grant TRANSNET [EP/R035342/1]
  4. EPSRC [EP/R035342/1] Funding Source: UKRI
  5. Marie Curie Actions (MSCA) [835913] Funding Source: Marie Curie Actions (MSCA)

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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.

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