Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning deep linear neural networks: Riemannian gradient flows and
  convergence to global minimizers   We study the convergence of gradient flows related to learning deep linear
neural networks (where the activation function is the identity map) from data.
In this case, the composition of the network layers amounts to simply
multiplying the weight matrices of all layers together, resulting in an
overparameterized problem. The gradient flow with respect to these factors can
be re-interpreted as a Riemannian gradient flow on the manifold of rank-$r$
matrices endowed with a suitable Riemannian metric. We show that the flow
always converges to a critical point of the underlying functional. Moreover, we
establish that, for almost all initializations, the flow converges to a global
minimum on the manifold of rank $k$ matrices for some $k\leq r$.

5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics