Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural
  Networks   Lipschitz constants of neural networks allow for guarantees of robustness in
image classification, safety in controller design, and generalizability beyond
the training data. As calculating Lipschitz constants is NP-hard, techniques
for estimating Lipschitz constants must navigate the trade-off between
scalability and accuracy. In this work, we significantly push the scalability
frontier of a semidefinite programming technique known as LipSDP while
achieving zero accuracy loss. We first show that LipSDP has chordal sparsity,
which allows us to derive a chordally sparse formulation that we call
Chordal-LipSDP. The key benefit is that the main computational bottleneck of
LipSDP, a large semidefinite constraint, is now decomposed into an equivalent
collection of smaller ones: allowing Chordal-LipSDP to outperform LipSDP
particularly as the network depth grows. Moreover, our formulation uses a
tunable sparsity parameter that enables one to gain tighter estimates without
incurring a significant computational cost. We illustrate the scalability of
our approach through extensive numerical experiments.

34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin