Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sample Compression, Support Vectors, and Generalization in Deep Learning   Even though Deep Neural Networks (DNNs) are widely celebrated for their
practical performance, they possess many intriguing properties related to depth
that are difficult to explain both theoretically and intuitively. Understanding
how weights in deep networks coordinate together across layers to form useful
learners has proven challenging, in part because the repeated composition of
nonlinearities has proved intractable. This paper presents a reparameterization
of DNNs as a linear function of a feature map that is locally independent of
the weights. This feature map transforms depth-dependencies into simple tensor
products and maps each input to a discrete subset of the feature space. Then,
using a max-margin assumption, the paper develops a sample compression
representation of the neural network in terms of the discrete activation state
of neurons induced by s ``support vectors". The paper shows that the number of
support vectors s relates with learning guarantees for neural networks through
sample compression bounds, yielding a sample complexity of O(ns/epsilon) for
networks with n neurons. Finally, the number of support vectors s is found to
monotonically increase with width and label noise but decrease with depth.

23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc