aiqbench analysis
This paper establishes a theoretical concentration result showing that the output of large multilayer feedforward neural networks converges to a deterministic limit under specific weight and input distribution assumptions. The finding provides rigorous mathematical insight into how network behavior stabilizes as width increases, which is relevant for understanding fundamental properties in machine learning theory rather than immediate product applications or policy shifts.
A concentration result for multilayer feedforward neural networks
arXiv:2608.15335v1 Announce Type: new Abstract: We consider for an arbitrary fixed $\rho$ and for each positive integer $n$ a multilayer feedforward artificial neural network with $\rho$ 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.
Abstract:We consider for an arbitrary fixed $\rho$ and for each positive integer $n$ a multilayer feedforward artificial neural network with $\rho$ 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.
Artificial Intelligence (cs.AI); Logic (math.LO); Probability (math.PR)
arXiv:2608.15335 [cs.AI]
(or arXiv:2608.15335v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2608.15335 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 240 words
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