Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Efficacy of $L_1$ Regularization in Two-Layer Neural Networks   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.

26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con