Concentration Result for Multilayer Feedforward Neural Networks
A recent theorem in mathematics introduces a concentration result for multilayer feedforward artificial neural networks. For any specified number of layers ρ and any positive integer n, the network comprises n neurons in the input layer and one output neuron. The key finding indicates that if the weight distributions between layers can be closely represented by a fixed continuous curve, independent of n, and if the input neuron values follow an independent and identically distributed pattern with a continuous probability density function, then there exists a number ψ such that for any ε > 0, the likelihood of the output neuron's value falling within [ψ - ε, ψ + ε] approaches 1 as n increases indefinitely. This research, available on arXiv (ID 2608.15335), enhances the theoretical insights into neural network behavior as input size grows. The paper is listed under Computer Science and Artificial Intelligence and includes HTML, references, citations, and BibTeX formatting. Additionally, arXiv emphasizes its dedication to transparency and community engagement through arXivLabs, which fosters innovative projects.
Key facts
- The theorem applies to multilayer feedforward neural networks with ρ layers and n input neurons.
- The network has a single output neuron in the last layer.
- Weight distributions from each layer to the next are approximated by a fixed continuous curve for large n.
- Input neuron values are independently and identically distributed with a continuous probability density function.
- There exists a number ψ such that the output neuron's value concentrates around ψ with high probability as n grows.
- The result holds for any ε > 0, with probability tending to 1 as n tends to infinity.
- The paper is available on arXiv with ID 2608.15335.
- The paper is categorized under Computer Science and Artificial Intelligence.
Entities
Institutions
- arXiv