Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Relation Between the Sharpest Directions of DNN Loss and the SGD
  Step Length   Stochastic Gradient Descent (SGD) based training of neural networks with a
large learning rate or a small batch-size typically ends in well-generalizing,
flat regions of the weight space, as indicated by small eigenvalues of the
Hessian of the training loss. However, the curvature along the SGD trajectory
is poorly understood. An empirical investigation shows that initially SGD
visits increasingly sharp regions, reaching a maximum sharpness determined by
both the learning rate and the batch-size of SGD. When studying the SGD
dynamics in relation to the sharpest directions in this initial phase, we find
that the SGD step is large compared to the curvature and commonly fails to
minimize the loss along the sharpest directions. Furthermore, using a reduced
learning rate along these directions can improve training speed while leading
to both sharper and better generalizing solutions compared to vanilla SGD. In
summary, our analysis of the dynamics of SGD in the subspace of the sharpest
directions shows that they influence the regions that SGD steers to (where
larger learning rate or smaller batch size result in wider regions visited),
the overall training speed, and the generalization ability of the final model.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn