Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical Study of Momentum-Based Acceleration Methods in Paradigmatic
  High-Dimensional Non-Convex Problems   The optimization step in many machine learning problems rarely relies on
vanilla gradient descent but it is common practice to use momentum-based
accelerated methods. Despite these algorithms being widely applied to arbitrary
loss functions, their behaviour in generically non-convex, high dimensional
landscapes is poorly understood. In this work, we use dynamical mean field
theory techniques to describe analytically the average dynamics of these
methods in a prototypical non-convex model: the (spiked) matrix-tensor model.
We derive a closed set of equations that describe the behaviour of heavy-ball
momentum and Nesterov acceleration in the infinite dimensional limit. By
numerical integration of these equations, we observe that these methods speed
up the dynamics but do not improve the algorithmic threshold with respect to
gradient descent in the spiked model.

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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg