Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Uniform Boundedness Properties of SGD and its Momentum Variants   A theoretical, and potentially also practical, problem with stochastic
gradient descent is that trajectories may escape to infinity. In this note, we
investigate uniform boundedness properties of iterates and function values
along the trajectories of the stochastic gradient descent algorithm and its
important momentum variant. Under smoothness and $R$-dissipativity of the loss
function, we show that broad families of step-sizes, including the widely used
step-decay and cosine with (or without) restart step-sizes, result in uniformly
bounded iterates and function values. Several important applications that
satisfy these assumptions, including phase retrieval problems, Gaussian mixture
models and some neural network classifiers, are discussed in detail.

25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn