Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A proof of convergence of multi-class logistic regression network   This paper revisits the special type of a neural network known under two
names. In the statistics and machine learning community it is known as a
multi-class logistic regression neural network. In the neural network
community, it is simply the soft-max layer. The importance is underscored by
its role in deep learning: as the last layer, whose autput is actually the
classification of the input patterns, such as images. Our exposition focuses on
mathematically rigorous derivation of the key equation expressing the gradient.
The fringe benefit of our approach is a fully vectorized expression, which is a
basis of an efficient implementation. The second result of this paper is the
positivity of the second derivative of the cross-entropy loss function as
function of the weights. This result proves that optimization methods based on
convexity may be used to train this network. As a corollary, we demonstrate
that no $L^2$-regularizer is needed to guarantee convergence of gradient
descent.

9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph