# Space of Functions Computed by Deep-Layered Machines

arXiv: https://arxiv.org/abs/2004.08930 · HTML: https://mlsanity.com/paper/2004.08930/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2020.

## Built on by (most cited first, 2 of 2)

- [Unified field theoretical approach to deep and recurrent neuronal networks](https://mlsanity.com/paper/2112.05589/) (2021)
- [Dynamics of Meta-learning Representation in the Teacher-student Scenario](https://mlsanity.com/paper/2408.12545/) (2024)

## Abstract (arXiv)

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.