# A concentration result for multilayer feedforward neural networks

arXiv: https://arxiv.org/abs/2608.15335 · HTML: https://mlsanity.com/paper/2608.15335/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 15 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [An asymptotic analysis of probabilistic logic programming, with implications for expressing projective families of distributions](https://mlsanity.com/paper/2102.08777/) (2021)
- [Zero-One Laws of Graph Neural Networks](https://mlsanity.com/paper/2301.13060/) (2023)
- [Asymptotic elimination of partially continuous aggregation functions in directed graphical models](https://mlsanity.com/paper/2106.10122/) (2021)
- [Probabilities of the Third Type: Statistical Relational Learning and Reasoning with Relative Frequencies](https://mlsanity.com/paper/2202.10367/) (2022)
- [On the relative asymptotic expressivity of inference frameworks](https://mlsanity.com/paper/2204.09457/) (2022)
- [Random expansions of trees with bounded height](https://mlsanity.com/paper/2410.11775/) (2024)
- [Domain size asymptotics for Markov logic networks](https://mlsanity.com/paper/2509.04192/) (2025)
- [Random coloured digraphs defined by a Markov logic network](https://mlsanity.com/paper/2606.23715/) (2026)
- [A convergence law for continuous logic and continuous structures with finite domains](https://mlsanity.com/paper/2504.08923/) (2025)

## Abstract (arXiv)

We consider for an arbitrary fixed ρ and for each positive integer n a multilayer feedforward artificial neural network with ρ layers, n neurons in the first layer (the input layer) and only one neuron, the output neuron, in the last layer. Very roughly formulated, the main result is that if the distribution of weights of connections from a layer to the next are, for all large n, approximated well by a fixed continuous (but otherwise arbitrary) curve which does not depend on n, and if the values of the n input neurons are independently and identically distributed with a continuous probability density function, then there is a number psi such that for all varepsilon > 0 the probability that the value of the output neuron is in [psi - varepsilon, psi + varepsilon] tends to 1 as n tends to infinity.