THE EFFICACY OF L1 REGULARIZATION IN NEURAL NETWORKS

1 Jan 2021  ·  Gen Li, Yuantao Gu, Jie Ding ·

A crucial problem in neural networks is to select the most appropriate number of hidden neurons and obtain tight statistical risk bounds. In this work, we present a new perspective towards the bias-variance tradeoff in neural networks. As an alternative to selecting the number of neurons, we theoretically show that $L_1$ regularization can control the generalization error and sparsify the input dimension. In particular, with an appropriate $L_1$ regularization on the output layer, the network can produce a statistical risk that is near minimax optimal. Moreover, an appropriate $L_1$ regularization on the input layer leads to a risk bound that does not involve the input data dimension. Our analysis is based on a new amalgamation of dimension-based and norm-based complexity analysis to bound the generalization error. A consequent observation from our results is that an excessively large number of neurons do not necessarily inflate generalization errors under a suitable regularization.

PDF Abstract
No code implementations yet. Submit your code now

Tasks


Datasets


  Add Datasets introduced or used in this paper

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods


No methods listed for this paper. Add relevant methods here