Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Principle of Least Action for the Training of Neural Networks   Neural networks have been achieving high generalization performance on many
tasks despite being highly over-parameterized. Since classical statistical
learning theory struggles to explain this behavior, much effort has recently
been focused on uncovering the mechanisms behind it, in the hope of developing
a more adequate theoretical framework and having a better control over the
trained models. In this work, we adopt an alternate perspective, viewing the
neural network as a dynamical system displacing input particles over time. We
conduct a series of experiments and, by analyzing the network's behavior
through its displacements, we show the presence of a low kinetic energy
displacement bias in the transport map of the network, and link this bias with
generalization performance. From this observation, we reformulate the learning
problem as follows: finding neural networks which solve the task while
transporting the data as efficiently as possible. This offers a novel
formulation of the learning problem which allows us to provide regularity
results for the solution network, based on Optimal Transport theory. From a
practical viewpoint, this allows us to propose a new learning algorithm, which
automatically adapts to the complexity of the given task, and leads to networks
with a high generalization ability even in low data regimes.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph