On the Role of Noise in the Sample Complexity of Learning Recurrent Neural Networks: Exponential Gaps for Long Sequences
Alireza Fathollah Pour, Hassan Ashtiani
Abstract
We consider the class of noisy multi-layered sigmoid recurrent neural networks with $w$ (unbounded) weights for classification of sequences of length $T$, where independent noise distributed according to $\mathcal{N}(0,\sigma^2)$ is added to the output of each neuron in the network. Our main result shows that the sample complexity of PAC learning this class can be bounded by $O (w\log(T/\sigma))$. For the non-noisy version of the same class (i.e., $\sigma=0$), we prove a lower bound of $\Omega (wT)$ for the sample complexity. Our results indicate an exponential gap in the dependence of sample complexity on $T$ for noisy versus non-noisy networks. Moreover, given the mild logarithmic dependence of the upper bound on $1/\sigma$, this gap still holds even for numerically negligible values of $\sigma$.
BibTeX
@inproceedings{
pour2023on,
title={On the Role of Noise in the Sample Complexity of Learning Recurrent Neural Networks: Exponential Gaps for Long Sequences},
author={Alireza Fathollah Pour and Hassan Ashtiani},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=rpuEARqB54}
}